HP (Hewlett Packard) HP 12C Financial Calculator 12C User Manual

hp  
12c platinum financial calculator  
user's guide  
H
HP part number F2232-90001  
Edition 4  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 1 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Introduction  
About This Handbook  
This hp 12c platinum user's guide is intended to help you get the most out of your  
investment in your hp 12c platinum Programmable Financial Calculator. Although  
the excitement of acquiring this powerful financial tool may prompt you to set this  
handbook aside and immediately begin “pressing buttons,” in the long run you’ll  
profit by reading through this handbook and working through the examples it  
contains.  
Following this introduction is a brief section called Making Financial Calculations  
Easy—which shows you that your hp 12c platinum does just that! The remainder of  
this handbook is organized basically into three parts:  
z
Part I (sections 1 through 7) describes how to use the various financial,  
mathematics, statistics, and other functions (except for programming)  
provided in the calculator:  
z
Section 1 is about Getting Started. It tells you how to use the keyboard,  
how to do simple arithmetic calculations and chain calculations, and  
how to use the storage registers (“memories”).  
z
z
Section 2 tells you how to use the percentage and calendar functions.  
Section 3 tells you how to use the simple interest, compound interest, and  
amortization functions.  
z
z
z
Section 4 tells you how to do discounted cash flow analysis, bond, and  
depreciation calculations.  
Section 5 tells you about miscellaneous operating features such as  
Continuous Memory, the display, and special function keys.  
Sections 6 and 7 tell you how to use the statistics, mathematics, and  
number-alteration functions.  
z
z
Part II (sections 8 through 11) describes how to use the powerful  
programming capabilities of the hp 12c platinum.  
Part III (sections 12 through 16) gives you step-by-step solutions to  
specialized problems in real estate, lending, savings, investment analysis,  
and bonds. Some of these solutions can be done manually, while others  
involve running a program. Since the programmed solutions are both  
self-contained and step-by-step, you can easily employ them even if you don’t  
care to learn how to create your own programs. But if you do start to create  
your own programs, look over the programs used in the solutions: they  
contain examples of good programming techniques and practices.  
3
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4
Introduction  
z
z
The various appendices describe additional details of calculator operation as  
well as warranty and service information.  
The Function Key Index and Programming Key Index at the back of the  
handbook can be used as a handy page reference to the comprehensive  
information inside the manual.  
Financial Calculations in the United Kingdom  
The calculations for most financial problems in the United Kingdom are identical to  
the calculations for those problems in the United States — which are described in  
this handbook. Certain problems, however, require different calculation methods in  
the United Kingdom than in the United States. Refer to Appendix G for more  
information.  
For More Solutions to Financial Problems  
In addition to the specialized solutions found in Sections 12 through 16 of this  
handbook, many more are available in the optional hp 12c platinum Solutions  
Handbook. Included are solutions to problems in lending, forecasting, pricing,  
statistics, savings, investment analysis, personal finance, securities, Canadian  
mortgages, learning curves in manufacturing, options pricing, and queuing theory.  
The solutions handbook is available online at the hp 12c platinum website.  
HP would like to thank the following for their contribution:  
Gene Wright, Lipscomb University, Nashville, TN, USA  
and  
Tony Hutchins, Wellington, NZ  
Jordi Hidalgo, Barcelona, Spain  
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Contents  
Introduction.................................................................... 3  
About This Handbook.....................................................................3  
Financial Calculations in the United Kingdom.....................................4  
For More Solutions to Financial Problems...........................................4  
Part I: Problem Solving ......................................... 15  
Section 1: Getting Started ................................................. 16  
Power On and Off........................................................................16  
Low-Power Indication..............................................................16  
Adjusting the Display Contrast.................................................16  
The Keyboard ..............................................................................16  
Keying in Numbers................................................................17  
Digit Separators ....................................................................17  
Negative Numbers ................................................................17  
Keying in Large Numbers .......................................................18  
Backspacing .........................................................................18  
The CLEAR Keys ....................................................................19  
Undo Operation....................................................................20  
The RPN and ALG Keys..........................................................20  
Simple Arithmetic Calculations in RPN Mode...................................21  
Simple Arithmetic Calculations in ALG Mode ...................................22  
Chain Calculations in RPN Mode...................................................23  
Chain Calculations in ALG Mode...................................................26  
Parentheses Calculations ...............................................................26  
Storage Registers..........................................................................27  
Storing and Recalling Numbers...............................................27  
Clearing Storage Registers......................................................29  
Storage Register Arithmetic .....................................................29  
Section 2: Percentage and Calendar Functions .................... 31  
Percentage Functions.....................................................................31  
Percentages in RPN Mode ......................................................31  
Percentages in ALG Mode ......................................................32  
Net Amount in RPN Mode......................................................33  
Net Amount in ALG Mode......................................................33  
Percent Difference..................................................................34  
Percent of Total in RPN Mode..................................................35  
5
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Contents  
Percent of Total in ALG Mode ................................................. 36  
Calendar Functions...................................................................... 37  
Date Format ......................................................................... 37  
Future or Past Dates............................................................... 38  
Number of Days Between Dates ............................................. 40  
Section 3: Basic Financial Functions ....................................41  
The Financial Registers ................................................................. 41  
Storing Numbers into the Financial Registers ............................ 41  
Displaying Numbers in the Financial Registers .......................... 41  
Clearing the Financial Registers .............................................. 42  
Simple Interest Calculations........................................................... 42  
Financial Calculations and the Cash Flow Diagram.......................... 44  
The Cash Flow Sign Convention.............................................. 46  
The Payment Mode ............................................................... 46  
Generalized Cash Flow Diagrams........................................... 47  
Compound Interest Calculations..................................................... 49  
Specifying the Number of Compounding Periods and the Periodic  
Interest Rate ......................................................................... 49  
Calculating the Number of Payments or Compounding Periods ... 49  
Calculating the Periodic and Annual Interest Rates..................... 55  
Calculating the Present Value ................................................. 56  
Calculating the Payment Amount............................................. 58  
Calculating the Future Value................................................... 60  
Odd-Period Calculations ........................................................ 63  
Amortization............................................................................... 69  
Section 4: Additional Financial Functions.............................72  
Discounted Cash Flow Analysis: NPV and IRR ................................. 72  
Calculating Net Present Value (NPV) ....................................... 73  
Calculating Internal Rate of Return (IRR) ................................... 78  
Reviewing Cash Flow Entries................................................... 79  
Changing Cash Flow Entries................................................... 80  
Bond Calculations ....................................................................... 82  
Bond Price ........................................................................... 82  
Bond Yield........................................................................... 83  
Depreciation Calculations............................................................. 84  
Section 5: Additional Operating Features ............................86  
Continuous Memory..................................................................... 86  
The Display................................................................................. 87  
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Contents  
7
Status Indicators ....................................................................87  
Number Display Formats ........................................................87  
Scientific Notation Display Format ...........................................88  
Special Displays....................................................................90  
Key in RPN Mode..........................................................90  
Key in RPN Mode .........................................................91  
Arithmetic Calculations With Constants ....................................91  
Recovering From Errors in Digit Entry........................................92  
The  
The  
Section 6: Statistics Functions ............................................ 93  
Accumulating Statistics..................................................................93  
Correcting Accumulated Statistics ...................................................94  
Mean .........................................................................................94  
Standard Deviation.......................................................................96  
Linear Estimation ..........................................................................97  
Weighted Mean...........................................................................99  
Section 7: Mathematics and Number-Alteration Functions.. 100  
One-Number Functions ...............................................................100  
The Power Function in RPN Mode.................................................102  
The Power Function in ALG Mode.................................................102  
Part II: Programming........................................... 103  
Section 8: Programming Basics ........................................ 104  
?
Why Use Programs ...................................................................104  
Creating a Program....................................................................104  
Running a Program.....................................................................106  
Program Memory .......................................................................108  
Identifying Instructions in Program Lines..................................108  
Displaying Program Lines......................................................109  
The  
000 Instruction and Program Line 000 ......................112  
Expanding Program Memory ................................................112  
Setting the Calculator to a Particular Program Line ...................114  
Executing a Program One Line at a Time.......................................114  
Interrupting Program Execution.....................................................117  
Pausing During Program Execution.........................................117  
Stopping Program Execution .................................................122  
Section 9: Branching and Looping.....................................125  
Simple Branching.......................................................................125  
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8
Contents  
Looping.................................................................................... 126  
Conditional Branching ............................................................... 129  
Section 10: Program Editing...............................................139  
Changing the Instruction in a Program Line ................................... 139  
Adding Instructions at the End of a Program.................................. 140  
Adding Instructions within a Program ........................................... 142  
Adding Instructions by Replacement ...................................... 142  
Adding Instructions by Branching.......................................... 144  
Section 11: Multiple Programs............................................149  
Storing Another Program ............................................................ 149  
Running Another Program........................................................... 153  
Part III: Solutions.................................................. 155  
Section 12: Real Estate and Lending....................................156  
Annual Percentage Rate Calculations With Fees............................. 156  
Price of a Mortgage Traded at a Discount or Premium.................... 159  
Yield of a Mortgage Traded at a Discount or Premium ................... 161  
The Rent or Buy Decision ............................................................ 163  
Deferred Annuities..................................................................... 169  
Section 13: Investment Analysis..........................................171  
Partial-Year Depreciation............................................................. 171  
Straight-Line Depreciation..................................................... 171  
Declining-Balance Depreciation .............................................176  
Sum-of-the-Years-Digits Depreciation ...................................... 180  
Full- and Partial-Year Depreciation with Crossover .......................... 184  
Excess Depreciation................................................................... 191  
Modified Internal Rate of Return................................................... 192  
Black-Scholes Formula for Valuing European Options...................... 194  
Section 14: Leasing ...........................................................202  
Advance Payments..................................................................... 202  
Solving for Payment............................................................. 202  
Solving for Yield ................................................................. 206  
Advance Payments With Residual ................................................ 209  
Solving for Payment............................................................. 209  
Solving for Yield ................................................................. 212  
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Contents  
9
Section 15: Savings .......................................................... 213  
Nominal Rate Converted to Effective Rate......................................213  
Effective Rate Converted to Nominal Rate......................................215  
Continuous Rate Converted to Effective Rate...................................216  
Section 16: Bonds............................................................. 217  
30/360 Day Basis Bonds ...........................................................217  
Annual Coupon Bonds................................................................222  
Appendices ................................................................ 227  
Appendix A: RPN and the Stack................................... 228  
Getting Numbers Into the Stack: The  
Key..............................229  
Termination of Digit Entry .....................................................230  
Stack Lift.............................................................................230  
Rearranging Numbers in the Stack ...............................................230  
The  
The  
Key.....................................................................230  
Key.......................................................................230  
One-Number Functions and the Stack...........................................231  
Two-Number Functions and the Stack............................................231  
Mathematics Functions .........................................................231  
Percentage Functions............................................................232  
Calendar and Financial Functions.................................................233  
The LAST X Register and the  
Key .........................................234  
Chain Calculations in RPN Mode.................................................234  
Arithmetic Calculations with Constants ..........................................235  
Appendix B: Algebraic Mode (ALG).............................. 237  
Simple Arithmetic Calculations in ALG Mode .................................237  
Keying in Negative Numbers (  
Chain Calculations in ALG Mode.................................................238  
The Key in ALG Mode .......................................................239  
) .............................................238  
The History Stack in ALG Mode....................................................239  
Parentheses Calculations .............................................................240  
Percentage Functions...................................................................241  
Percent Difference................................................................241  
Percent of Total....................................................................242  
The Power Function.....................................................................242  
Appendix C: More About L...................................... 243  
Appendix D: Error Conditions ...................................... 245  
Error 0: Mathematics..................................................................245  
Error 1: Storage Register Overflow ...............................................246  
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10 Contents  
Error 2: Statistics........................................................................ 246  
Error 3: IRR............................................................................... 246  
Error 4: Memory ....................................................................... 246  
Error 5: Compound Interest..........................................................247  
Error 6: Storage Registers ............................................................248  
Error 7: IRR ................................................................................248  
Error 8: Calendar.......................................................................249  
Error 9: Service ..........................................................................249  
Pr Error .....................................................................................249  
Appendix E: Formulas Used......................................... 250  
Percentage................................................................................ 250  
Interest ..................................................................................... 250  
Simple Interest.................................................................... 250  
Compound Interest.............................................................. 251  
Amortization............................................................................. 251  
Discounted Cash Flow Analysis ....................................................252  
Net Present Value ................................................................252  
Internal Rate of Return...........................................................252  
Calendar...................................................................................252  
Actual Day Basis..................................................................252  
30/360 Day Basis...............................................................252  
Bonds .......................................................................................253  
Black-Scholes Formula for Valuing European Options .................... 254  
Depreciation............................................................................. 254  
Straight-Line Depreciation......................................................255  
Sum-of-the-Years-Digits Depreciation .......................................255  
Declining-Balance Depreciation .............................................255  
Modified Internal Rate of Return................................................... 256  
Advance Payments..................................................................... 256  
Interest Rate Conversions ............................................................ 256  
Finite Compounding............................................................ 256  
Continuous Compounding.................................................... 256  
Statistics....................................................................................257  
Mean.................................................................................257  
Weighted Mean ..................................................................257  
Linear Estimation..................................................................257  
Standard Deviation ..............................................................257  
Factorial .............................................................................257  
The Rent or Buy Decision ............................................................ 258  
Appendix F: Battery, Warranty, and Service Information 259  
Battery ......................................................................................259  
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Contents 11  
Low-Power Indication ..................................................................259  
Installing a New Battery.......................................................260  
Verifying Proper Operation (Self-Tests)...........................................261  
Warranty ..................................................................................263  
Service .....................................................................................264  
Regulatory Information................................................................265  
Temperature Specifications ..........................................................266  
Noise Declaration ......................................................................266  
Disposal of Waste Equipment by Users in Private Household in the  
European Union.........................................................................266  
Appendix G: United Kingdom Calculations.....................267  
Mortgages ................................................................................267  
Annual Percentage Rate (APR) Calculations....................................268  
Bond Calculations ......................................................................268  
Function Key Index.......................................................269  
Programming Key Index ...............................................272  
Subject Index ..............................................................274  
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Making Financial  
Calculations Easy  
Before you begin to read through this handbook, let’s take a look at how easy  
financial calculations can be with your hp 12c platinum. While working through  
the examples below, don’t be concerned about learning how to use the calculator;  
we’ll cover that thoroughly beginning with Section 1.  
Example 1: Suppose you want to ensure that you can finance your daughter’s  
college education 14 years from today. You expect that the cost will be about  
$6,000 a year ($500 a month) for 4 years. Assume she will withdraw $500 at the  
beginning of each month from a savings account. How much would you have to  
deposit into the account when she enters college if the account pays 6% annual  
?
interest compounded monthly  
This is an example of a compound interest calculation. All such problems involve at  
least three of the following quantities:  
z
z
z
z
z
n: the number of compounding periods.  
i: the interest rate per compounding period.  
PV: the present value of a compounded amount.  
PMT: the periodic payment amount.  
FV: the future value of a compounded amount.  
In this particular example:  
z
z
z
n is 4 years × 12 periods per year = 48 periods.  
i is 6% per year ÷ 12 periods per year = 0.5% per period.  
PV is the quantity to be calculated — the present value when the financial  
transaction begins.  
z
z
PMT is $500.  
FV is zero, since by the time your daughter graduates she (hopefully!) will  
not need any more money.  
To begin, turn the calculator on by pressing the ; key. Then, press the keys  
shown in the Keystrokes column below.  
*
If you are not familiar with the use of an hp calculator keyboard, refer to the description on  
pages 16 and 17.  
*
12  
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Making Financial Calculations Easy  
13  
Note: A battery symbol (  
) shown in the upper-left corner of the display  
when the calculator is on signifies that the available battery power is nearly  
exhausted. To install new batteries, refer to Appendix F.  
The calendar functions and nearly all of the financial functions take some  
time to produce an answer. (This is typically just a few seconds, but the¼,  
!, L, and S functions could require a half-minute or more.) During  
these calculations, the word running flashes in the display to let you know  
that the calculator is running.  
Keystrokes  
Display  
fCLEARHf2  
0.00  
Clears previous data inside the  
calculator and sets display to show  
two decimal places.  
48.00  
0.50  
4gA  
Calculates and stores the number  
of compounding periods.  
6gC  
Calculates and stores the periodic  
interest rate.  
500.00  
500P  
g×  
$
Stores periodic payment amount.  
Sets payment mode to Begin.  
500.00  
-21,396.61  
Amount required to be deposited.  
*
Example 2: We now need to determine how to accumulate the required deposit  
by the time your daughter enters college 14 years from now. Let’s say that she has  
a paid-up $5,000 insurance policy that pays 5.35%, compounded annually. How  
?
much would it be worth by the time she enters college  
In this example, we need to calculate FV, the future value.  
Keystrokes  
Display  
fCLEARG  
-21,396.61 Clears previous financial data  
inside the calculator.  
14.00  
14n  
Stores the number of compounding  
periods.  
5.35  
5.35¼  
Stores the periodic interest rate.  
-5,000.00  
5000Þ$  
Stores the present value of the  
policy.  
Don’t be concerned now about the minus sign in the display. That and other details will be  
explained in Section 3.  
*
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14 Making Financial Calculations Easy  
Keystrokes  
Display  
M
10,371.79  
Value of policy in 14 years.  
Example 3: The preceding example showed that the insurance policy will  
provide about half the required amount. An additional amount must be set aside to  
provide the balance (21,396.61 – 10,371.79 = 11,024.82). Suppose you make  
monthly payments, beginning at the end of next month, into an account that pays  
6% annually, compounded monthly. What payment amount would be required in  
?
order to accumulate $11,024.82 in the 14 years remaining  
Keystrokes  
Display  
fCLEARG  
10,371.79  
Clears previous financial data  
inside the calculator.  
168.00  
0.50  
14gA  
Calculates and stores the number  
of compounding periods.  
6gC  
Calculates and stores the periodic  
interest rate.  
11,024.82  
11,024.82  
–42.03  
11024.82M  
g  
Stores the future value required.  
Sets payment mode to End.  
Monthly payment required.  
P
Example 4: Suppose you cannot find a bank that currently offers an account  
with 6% annual interest compounded monthly, but you can afford to make $45  
monthly payments. What is the minimum interest rate that will enable you to  
?
accumulate the required amount  
In this problem, we do not need to clear the previous financial data inside the  
calculator, since most of it is unchanged from the preceding example.  
Keystrokes  
Display  
–45.00  
0.43  
45ÞP  
¼
Stores payment amount.  
Periodic interest rate.  
Annual interest rate.  
:gC  
5.13  
This is only a small sampling of the many financial calculations that can now be  
done easily with your hp 12c platinum. To begin learning about this powerful  
financial tool, just turn the page.  
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Part I  
Problem Solving  
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Section 1  
Getting Started  
Power On and Off  
To begin using your hp 12c platinum, press the ; key . Pressing ; again  
*
turns the calculator off. If not manually turned off, the calculator will turn off  
automatically 12 minutes after it was last used.  
Low-Power Indication  
A battery symbol (  
) shown in the upper-left corner of the display when the  
calculator is on signifies that the available battery power is nearly exhausted. To  
replace the batteries, refer to Appendix F.  
Adjusting the Display Contrast  
The display’s readability depends on lighting, your viewing angle, and the display  
contrast setting. You can adjust the display contrast, by holding down the f key  
and pressing + or -.  
The Keyboard  
Many keys on the hp 12c platinum perform two or even three functions. The  
primary function of a key is indicated by the characters printed in white on the  
upper face of the key. The alternate function(s) of a key are indicated by the  
characters printed in gold above the key and the characters printed in blue on the  
lower face of the key. These alternate functions are specified by pressing the  
appropriate prefix key before the function key:  
z
To specify the alternate function printed in gold  
above a key, press the gold prefix key (f), then  
press the function key.  
z
z
To specify the primary function printed on the upper  
face of a key, press the key alone.  
To specify the alternate function printed in blue on the  
lower face of a key, press the blue prefix key (g),  
then press the function key.  
Note that the ; key is lower than the other keys to help prevent its being pressed  
*
inadvertently.  
16  
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Section 1: Getting Started  
17  
Throughout this handbook, references to the functions shown on the keyboard in gold  
under the bracket labeled CLEAR” appear throughout this handbook preceded by  
the word “CLEAR” (for example, “The CLEAR function …” or “Pressing  
CLEAR …”).  
H
f
H
If you press the f or g prefix key mistakenly, you can cancel it by pressing  
fCLEARX. This can also be pressed to cancel the ?, :, and i keys.  
(These keys are “prefix” keys in the sense that other keys must be pressed after  
them in order to execute the corresponding function.) Since the X key is also  
used to display the mantissa (all 10 digits) of a displayed number, the mantissa of  
the number in the display will appear for a moment after the X key is released.  
Pressing the f or g prefix key turns on the corresponding status indicator — f  
or g — in the display. Each indicator turns off when you press a function key  
(executing an alternate function of that key), another prefix key, or fCLEARX.  
Keying in Numbers  
To key a number into the calculator, press the digit keys in sequence, just as if you  
were writing the number on paper. A decimal point must be keyed in (using the  
decimal point key) if it is part of the number unless it appears to the right of the last  
digit.  
Digit Separators  
As a number is keyed in, each group of three digits to the left of the decimal point  
is automatically separated in the display. When the calculator is first turned on  
after coming from the factory — or after Continuous Memory is reset — the  
decimal point in displayed numbers is a dot, and the separator between each  
group of three digits is a comma. If you wish, you can set the calculator to display  
a comma for the decimal point and a dot for the three-digit separator. To do so,  
turn the calculator off, then press and hold down the . key while you press ;.  
Doing so again sets the calculator to use the original digit separators in the  
display.  
Negative Numbers  
To make a displayed number negative — either one that has just been keyed in or  
one that has resulted from a calculation — simply press Þ (change sign) —.  
When the display shows a negative number — that is, the number is preceded by  
a minus sign — pressing Þ removes the minus sign from the display, making the  
number positive.  
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18 Section 1: Getting Started  
Keying in Large Numbers  
Since the display cannot show more than 10 digits of a number, numbers greater  
than 9,999,999,999 cannot be entered into the display by keying in all the digits  
in the number. However, such numbers can be easily entered into the display if the  
number is expressed in a mathematical shorthand called “scientific notation.” To  
convert a number into scientific notation, move the decimal point until there is only  
one digit (a nonzero digit) to its left. The resulting number is called the “mantissa”  
of the original number, and the number of decimal places you moved the decimal  
point is called the “exponent” of the original number. If you moved the decimal  
point to the left, the exponent is positive; if you moved the decimal point to the  
right (this would occur for numbers less than one), the exponent is negative. To key  
the number into the display, simply key in the mantissa, press Æ (enter exponent),  
then key in the exponent. If the exponent is negative, press Þ after pressing  
Æ.  
For example, to key in $1,781,400,000,000, we move the decimal point 12  
places to the left, giving a mantissa of 1.7814 and an exponent of 12:  
Keystrokes  
Display  
1.7814 12  
1.7814Æ12  
1,781,400,000,000 entered  
in scientific notation.  
Numbers entered in scientific notation can be used in calculations just like any  
other number.  
Backspacing  
While you are entering a number, pressing deletes the last character you  
entered. After performing a calculation, pressing deletes the current  
number.  
Keystrokes  
Display  
(RPN mode)  
12345gÚgÚ  
.63\  
123.63  
Correcting removes the 4 and  
5. clears the most recent  
digit entered.  
128.63  
0.00  
5+  
gÚ  
Clears the calculator line.  
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Section 1: Getting Started  
19  
Keystrokes  
(ALG mode)  
Display  
12345gÚgÚ  
.63+  
123.63  
Correcting removes the 4 and  
5. clears the most recent  
digit entered.  
128.63  
0.00  
}
\ key.  
5}  
is also labeled the  
gÚ  
Clears the calculator line.  
The CLEAR Keys  
Clearing a register or the display replaces the number in it with zero. Clearing  
program memory replaces the instructions there with gi000. There are  
several clearing operations on the hp 12c platinum, as shown in the table below:  
Key(s)  
Clears:  
O
Display and X-register.  
fCLEAR²  
Statistics registers (R1 through R6), stack registers, and  
display.  
fCLEARÎ Program memory (only when pressed in Program mode).  
fCLEARG Financial registers.  
fCLEARH Data storage registers, financial registers, stack and LAST X  
registers, and display.  
Note: In ALG mode, it is a good idea to begin calculations by pressing  
OO. This will ensure that there are no pending arithmetic calculations  
that might interfere with the solution of a new problem. The reason this key is  
pressed twice is that pressing it the first time clears the display and X-register  
only, allowing you to correct an erroneous entry by keying in a correct  
number. The second press of O will clear any pending operations as well.  
Pressing the } key is another way to ensure that there are no pending  
operations before beginning a new calculation, since the } key will  
evaluate any pending expressions.  
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20 Section 1: Getting Started  
Undo Operation  
Every time you press O, , fCLEARH, fCLEAR² or  
fCLEARG key to clear data, the  
status indicator appears in the display.  
This means you can press to undo the last operation (i.e., to recover the  
data.)  
Note: the Undo function is only available immediately after data has been  
cleared. When the Undo indicator is turned off no operation can be undone.  
The RPN and ALG Keys  
The calculator can be set to perform arithmetic operations in either RPN (Reverse  
Polish Notation) or ALG (Algebraic) mode.  
In Reverse Polish Notation (RPN) mode, the intermediate results of calculations are  
stored automatically, hence you do not have to use parentheses.  
In algebraic (ALG) mode, you perform addition, subtraction, multiplication, and  
division in the traditional way, using parentheses if needed.  
To select RPN mode: Press f] to set the calculator to RPN mode. When  
the calculator is in RPN mode, the RPN status indicator is lit.  
To select ALG mode: Press f[ to set the calculator to ALG mode. When  
the calculator is in ALG mode, the ALG status indicator is lit.  
Example  
Suppose you want to calculate 1 + 2 = 3.  
In RPN mode, you enter the first number, press the \ key, enter the second  
number, and finally press the arithmetic operator key: +.  
In ALG mode, you enter the first number, press +, enter the second number, and  
finally press the equals key: }. Don’t forget to press OO before doing the  
calculation.  
RPN mode  
ALG mode  
1 \ 2 +  
1 + 2 }  
You can choose either ALG (Algebraic) or RPN (Reverse Polish  
Notation) mode for your calculations. Throughout the manual, most  
examples are shown in both modes. The Keystrokes column will  
indicate RPN mode or ALG mode where the keystrokes differ. When  
the keystrokes are the same, the column is simply titled  
“Keystrokes”.  
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Section 1: Getting Started  
21  
Simple Arithmetic Calculations in RPN Mode  
In RPN mode, any simple arithmetic calculation involves two numbers and an  
operation — addition, subtraction, multiplication, or division. To do such a  
calculation on your hp 12c platinum, you first tell the calculator the two numbers,  
then tell the calculator the operation to be performed. The answer is calculated  
when the operation key (+,-,§, or z) is pressed.  
The two numbers should be keyed into the calculator in the order they would  
appear if the calculation were written down on paper left-to-right. After keying in  
the first number, press the \ key to tell the calculator that you have completed  
entering the number. Pressing \ separates the second number to be entered  
from the first number already entered.  
In summary, to perform an arithmetic operation:  
1. Key in the first number.  
2. Press \ to separate the second number from the first.  
3. Key in the second number.  
4. Press +,-,§, or z to perform the desired operation.  
For example to calculate 13 ÷ 2, proceed as follows:  
Keystrokes  
Display  
(RPN mode)  
13.  
13  
Keys the first number into the  
calculator.  
\
13.00  
2.  
\
Pressing  
separates the second  
number from the first.  
2
Keys the second number into the  
calculator.  
z
6.50  
Pressing the operation key calculates  
the answer.  
Notice that after you pressed \, two zeroes appeared following the decimal  
point. This is nothing magical: the calculator’s display is currently set to show two  
decimal places of every number that has been entered or calculated. Before you  
pressed \, the calculator had no way of knowing that you had completed  
entering the number, and so displayed only the digits you had keyed in. Pressing  
\ tells the calculator that you have completed entering the number: it terminates  
digit entry. You need not press \ after keying in the second number because  
the +,-,§ and z keys also terminate digit entry. (In fact, all keys terminate  
digit entry except for digit entry keys — digit keys, ., Þ, and Æ — and  
prefix keys — f, g, ?, :, and (.)  
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22 Section 1: Getting Started  
Simple Arithmetic Calculations in ALG Mode  
In ALG mode, any simple arithmetic calculation involves two numbers and an  
operation — addition, subtraction, multiplication, or division. To do such a  
calculation on your hp 12c platinum, you tell the calculator the first number, then  
the operation to be performed, and then tell the calculator the second number. The  
answer is calculated when the equals key (}) is pressed.  
For example, to calculate 21.1 + 23.8, do the following:  
Keystrokes  
Display  
(ALG mode)  
OO  
0.00  
Clears any pending operations.  
21.10  
21.1+  
Keys in the first number and  
prepares to add the second.  
23.8  
23.8  
Keys the second number.  
}
44.90  
}
completes the calculation.  
Once a calculation has been completed:  
z
pressing another digit key starts a new calculation, or  
pressing an operator key continues the calculation.  
z
Keystrokes  
(ALG mode)  
Display  
OO  
0.00  
Clears any pending operations.  
77.35  
–13.54  
96.75  
77.35-  
90.89}  
}
completes the calculation.  
New calculation:  
Calculates 96.75 ÷ 3.5  
65gr§12}  
65 ×12  
z3.5}  
27.64  
You can also do long calculations without pressing } after each intermediate  
calculation: just press it at the end. The operators perform from left to right, in the  
order you enter them. Note that if you have just pressed }, there is no need to  
press OO before starting a new calculation – the } key will have completed  
any pending operations.  
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Section 1: Getting Started  
23  
Chain Calculations in RPN Mode  
Whenever the answer has just been calculated and is therefore in the display, you  
can perform another operation with this number by simply keying in the second  
number and then pressing the operation key: you need not press \ to separate  
the second number from the first. This is because when a number is keyed in after  
a function key (such as +,-,§, z, etc.) is pressed, the result of that prior  
calculation is stored inside the calculator — just as when the \ key is pressed.  
The only time you must press the \ key to separate two numbers is when you  
are keying them both in, one immediately following the other.  
The hp 12c platinum is designed so that each time you press a function key in RPN  
mode, the calculator performs the operation then — not later — so that you see the  
results of all intermediate calculations, as well as the “bottom line.”  
Example: Suppose you’ve written three checks without updating your checkbook,  
and you’ve just deposited your paycheck for $1,053 into your checking account. If  
your latest balance was $58.33 and the checks were written for $22.95, $13.70,  
?
and $10.14, what is the new balance  
Solution: When written down on paper, this problem would read  
58.33 – 22.95 – 13.70 – 10.14 + 1053  
Keystrokes  
Display  
(RPN mode)  
58.33  
58.33  
58.33  
Keys the first number.  
\
Pressing  
\
separates the second  
number from the first.  
22.95  
35.38  
22.95  
Keys in the second number.  
-
Pressing  
-
subtracts the second  
number from the first. The calculator  
displays the result of this calculation,  
which is the balance after subtracting  
the first check.  
13.7  
13.7  
Keys in the next number. Since a  
calculation has just been performed,  
do not press \; the next number  
entered (13.7) is automatically  
separated from the one previously in  
the display (35.38).  
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24 Section 1: Getting Started  
Keystrokes  
(RPN mode)  
Display  
-
21.68  
-
Pressing  
subtracts the number just  
entered from the number previously in  
the display. The calculator displays  
the result of this calculation, which is  
the balance after subtracting the  
second check.  
11.54  
10.14-  
Keys in the next number and  
subtracts it from the previous  
balance. The new balance appears  
in the display. (It’s getting rather  
low!)  
1,064.54  
1053+  
Keys in the next number — the  
paycheck deposited — and adds it to  
the previous balance. The new,  
current balance appears in the  
display.  
The preceding example demonstrates how the hp 12c platinum calculates just as  
you would using pencil and paper (except a lot faster!):  
Let’s see this happening in a different type of calculation — one that involves  
multiplying groups of two numbers and then adding the results. (This is the type of  
calculation that would be required to total up an invoice consisting of several items  
with different quantities and different prices.)  
For example, consider the calculation of (3 × 4) + (5 × 6). If you were doing this  
on paper, you would do the multiplication in the first parentheses, then the  
multiplication in the second parentheses, and finally add the results of the two  
multiplications:  
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Section 1: Getting Started  
25  
Your hp 12c platinum calculates the answer in just the same way in RPN mode:  
Keystrokes  
Display  
(RPN mode)  
12.00  
30.00  
42.00  
3\4§  
5\6§  
+
Step 1: Multiply the numbers in the  
first parentheses.  
Step 2: Multiply the numbers in the  
second parentheses.  
Step 3: Add the results of the two  
multiplications.  
Notice that before doing step 2, you did not need to store or write down the result  
of step 1: it was stored inside the calculator automatically. And after you keyed in  
the 5 and the 6 in step 2, the calculator was holding two numbers (12 and 5)  
inside for you, in addition to the 6 in the display. (The hp 12c platinum can hold a  
total of three numbers inside, in addition to the number in the display.) After step 2,  
the calculator was still holding the 12 inside for you, in addition to the 30 in the  
display. You can see that the calculator holds the number for you, just as you  
would have them written on paper, and then calculates with them at the proper  
time, just as you would yourself. But with the hp 12c platinum, you don’t need to  
*
write down the results of an intermediate calculation, and you don’t even need to  
manually store it and recall it later.  
By the way, notice that in step 2 you needed to press \ again. This is simply  
because you were again keying in two numbers immediately following each other,  
without performing a calculation in between.  
To check your understanding of how to calculate with your hp 12c platinum, try  
the following problems yourself. Although these problems are relatively simple,  
more complicated problems can be solved using the same basic steps. If you have  
difficulty obtaining the answers shown, review the last few pages.  
(3 + 4)× (5 + 6) = 77.00  
(27 14)  
(14 + 38)  
= 0.25  
5
= 0.13  
3 +16 + 21  
Although you don’t need to know just how these numbers are stored and brought back at just  
*
the right time, if you’re interested you can read all about it in Appendix A. By gaining a more  
complete understanding of the calculator’s operation, you’ll use it more efficiently and  
confidently, yielding a better return on the investment in your hp 12c platinum.  
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26 Section 1: Getting Started  
Chain Calculations in ALG Mode  
To do a chain calculation, you don’t need to press } after each operation, but  
only at the very end.  
750x12  
360  
For instance, to calculate  
you can enter either:  
z
z
750 § 12 } z 360 } or  
750 § 12 z 360 }  
In the second case, the z key acts like the } key by displaying the result of 750  
× 12.  
456 75 68  
×
Here’s a longer chain calculation:  
18.5  
1.9  
This calculation can be written as: 456 – 75 ÷ 18.5 × 68 ÷ 1.9. Watch what  
happens in the display as you key it in:  
Keystrokes  
Display  
(ALG mode)  
OO  
456-75z  
18.5§  
68z  
0.00  
Clears any pending operations.  
Subtracts 75 from 456.  
Divides 381 by 18.5.  
Multiplies by 68.  
381.00  
20.59  
1,400.43  
737.07  
1.9}  
Divides by 1.9 and displays the  
result.  
Parentheses Calculations  
In ALG mode, parentheses can be used in calculations to change the order in  
which operations are evaluated. When there are pending open parentheses, the ( )  
status indicator will be shown in the display. As open parentheses are closed, the  
expression contained within the parentheses is evaluated, from left to right. The  
final result of a calculation will be displayed when you press the ³ key, and then  
any pending parentheses will be closed. You can’t use more than 13 pending  
(opened) parentheses at the same time.  
For example, suppose you want to calculate:  
8
(5 1)  
Keying 8 ÷ 5 – 1 will calculate 8 ÷ 5 first and then the result (1.6) will have 1  
subtracted from it (resulting in 0.6), which is not what is intended.  
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Section 1: Getting Started  
27  
8
(5 1)  
If you want to calculate  
, use the following keystrokes:  
Keystrokes  
(ALG mode)  
Display  
OO  
0.00  
5.00  
4.00  
2.00  
Clears any pending operations.  
No calculation is done.  
Calculates 5 1.  
8
8zgØ5-  
1gÙ  
³
Calculates  
.
(5 1)  
Storage Registers  
Numbers (data) in the hp 12c platinum are stored in memories called “storage  
registers” or simply “registers.” (The singular term “ memory” is sometimes used in  
this handbook to refer to the entire collection of storage registers.) Four special  
registers are used for storing numbers during calculations (these “stack registers”  
are described in Appendix A), and another (called the “LAST X” register) is used  
for storing the number last in the display before an operation is performed in RPN  
mode. In addition to these registers into which numbers are stored automatically,  
up to 20 “data storage” registers are available for manual storage of numbers.  
These data storage registers are designated R0 through R9 and R.0 through R.9. Still  
other storage registers — referred to as the “financial registers” — are reserved for  
numbers used in financial calculations.  
Storing and Recalling Numbers  
To store the number from the display into a data storage register:  
1. Press ? (store).  
2. Key in the register number: 0 through 9 for registers R0 through R9, or .0  
through .9 for registers R.0 through R.9.  
Similarly, to recall a number from a storage register into the display, press :  
(recall), then key in the register number. This copies the number from the storage  
register into the display; the number remains unaltered in the storage register.  
Furthermore, when this is done, the number previously in the display is  
automatically held inside the calculator for a subsequent calculation, just as the  
number in the display is held when you key in another number.  
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28 Section 1: Getting Started  
Example: Before you leave to call on a customer interested in your personal  
computer, you store the cost of the computer ($1,250) and also the cost of a  
printer ($500) in data storage registers. Later, the customer decides to buy six  
computers and one printer. You recall the cost of the computer, multiply by the  
quantity ordered, and then recall and add the cost of the printer to get the total  
invoice.  
Keystrokes  
Display  
1,250.00  
500.00  
1250?0  
500?2  
;
Stores the cost of the computer in R0.  
Stores the cost of the printer in R2.  
Turns the calculator off.  
Later that same day …  
Keystrokes  
(RPN mode)  
Display  
;
500.00  
Turns the calculator back on.  
:0  
1,250.00  
Recalls the cost of the computer to  
the display.  
7,500.00  
500.00  
6§  
:2  
+
Multiplies the quantity ordered to get  
the cost of the computers.  
Recalls the cost of the printer to the  
display.  
8,000.00  
Total invoice.  
Keystrokes  
(ALG mode)  
Display  
;
500.00  
Turns the calculator back on.  
:0  
1,250.00  
Recalls the cost of the computer to  
the display.  
§6  
6.  
Multiplies by the quantity ordered to  
get the cost of the computers.  
+:2  
³
500.00  
8,000.00  
Recalls the cost of the printer to the  
display.  
Total invoice.  
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Section 1: Getting Started  
29  
Clearing Storage Registers  
To clear a single storage register — that is, to replace the number in it with  
zero — merely store zero into it. You need not clear a storage register before  
storing data into it; the storing operation automatically clears the register before  
the data is stored.  
To clear all storage registers at once — including the financial registers, the stack  
registers, and the LAST X register — press fCLEARH. This also clears the  
*
display.  
All storage registers are also cleared when Continuous Memory is reset (as  
described on page 86).  
Storage Register Arithmetic  
Suppose you wanted to perform an arithmetic operation with the number in the  
display and the number in a storage register, then store the result back into the  
same register without altering the number in the display. The hp 12c platinum  
enables you to do all this in a single operation:  
1. Press ?.  
2. Press +, -, §, or z to specify the desired operation.  
3. Key in the register number.  
When storage register arithmetic is performed, the new number in the register is  
determined according to the following rule:  
Storage register arithmetic is possible with only registers R0 through R4  
.
Example: In the example on page 23, we updated the balance in your  
checkbook. Let’s suppose that because data is stored indefinitely in your  
calculator’s Continuous Memory, you keep track of your checking account balance  
in the calculator. You could use storage register arithmetic to quickly update the  
balance after depositing or writing checks.  
Keystrokes  
Display  
58.33  
58.33?0  
Stores the current balance in register  
R0.  
fCLEARH is not programmable.  
*
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30 Section 1: Getting Started  
Keystrokes  
Display  
22.95  
22.95?-0  
Subtracts the first check from the  
balance in R0. Note that the display  
continues to show the amount  
subtracted; the answer is placed only  
in R0.  
13.70  
13.7?-0  
10.14?-0  
1053?+0  
:0  
Subtracts the second check.  
Subtracts the third check.  
Adds the deposit.  
10.14  
1,053.00  
1,064.54  
Recalls the number in R0 to check the  
new balance.  
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Section 2  
Percentage and Calendar  
Functions  
Percentage Functions  
The hp 12c platinum includes three keys for solving percentage problems: b, à,  
and Z. You don’t need to convert percentages to their decimal equivalents; this  
is done automatically when you press any of these keys. Thus, 4% need not be  
changed to 0.04; you key it in the way you see and say it: 4b.  
Percentages in RPN Mode  
In RPN mode, to find the amount corresponding to a percentage of a number:  
1. Key in the base number.  
2. Press \.  
3. Key in the percentage.  
4. Press b.  
For example, to find 14% of $300:  
Keystrokes  
Display  
(RPN mode)  
300.  
300  
Keys in the base number.  
\
300.00  
\
Pressing  
separates the next  
number entered from the first number,  
just as when an ordinary arithmetic  
calculation is performed.  
14.  
14  
Keys in the percentage.  
Calculates the amount.  
b
42.00  
If the base number is already in the display as a result of a previous calculation,  
you should not press \ before keying in the percentage — just as in a chain  
arithmetic calculation.  
31  
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32 Section 2: Percentage and Calendar Functions  
Percentages in ALG Mode  
In ALG mode, to find the amount corresponding to a percentage of a number:  
1. Key in the base number.  
2. Press §.  
3. Key in the percentage.  
4. Press b.  
5. Press }.  
For example, to find 14% of $300:  
Keystrokes  
Display  
(ALG mode)  
OO  
0.00  
Clears any pending operations.  
Keys in the base number.  
300.  
300  
§
300.00  
Tells the calculator to multiply the 300  
by the percentage entered next.  
14.  
14  
b
}
Keys in the percentage.  
0.14  
42.00  
Divides the percentage by 100.  
Calculates the amount.  
In most cases, b divides a number by 100. The one exception is when a plus or  
minus sign precedes the number. For instance, 25 b results in 0.25. To find 25%  
of 200, press: 200 § 25 b}. (Result is 50.)  
Note: This is the last time the initial OO will be shown in these  
examples. Don’t forget to clear the calculator in ALG mode before beginning  
a new calculation.  
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Section 2: Percentage and Calendar Functions  
33  
Net Amount in RPN Mode  
A net amount — that is, the base amount plus or minus the percentage amount —  
can be calculated easily with your hp 12c platinum, since the calculator holds the  
base amount inside after you calculate a percentage amount. To calculate a net  
amount, simply calculate the percentage amount, then press = or -.  
Example: You’re buying a new car that lists for $23,250. The dealer offers you  
a discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging  
you, then find the total cost to you, including tax.  
Keystrokes  
(RPN mode)  
Display  
23,250.00  
23250\  
Keys in the base amount and  
separates it from the percentage.  
1,860.00  
21,390.00  
1,283.40  
22,673.40  
8b  
Amount of discount.  
-
Base amount less discount.  
Amount of tax (on $21,390).  
6b  
=
Total cost: base amount less discount  
plus tax.  
Net Amount in ALG Mode  
In ALG mode, you can calculate a net amount all in one calculation:  
For example, to decrease 200 by 25%, just enter 200-25b}. (Result is 150.)  
Example: You borrow $1,250 from a relative, and agree to repay the loan in a  
?
year with 7% simple interest. How much money will you owe  
Keystrokes  
(ALG mode)  
Display  
87.50  
1250+7b  
Interest on the loan is $87.50.  
}
1,337.50  
You owe this amount at the end of  
one year.  
Example: You’re buying a new car that lists for $23,250. The dealer offers you  
a discount of 8%, and the sales tax is 6%. Find the amount the dealer is charging  
you, then find the total cost to you, including tax.  
Keystrokes  
(ALG mode)  
Display  
23,250.00  
23250-  
Keys in the base amount and  
prepares to subtract the discount  
percentage.  
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34 Section 2: Percentage and Calendar Functions  
Keystrokes  
Display  
(ALG mode)  
1,860.00  
21,390.00  
1,283.40  
22,673.40  
8b  
Amount of discount.  
=
Base amount less discount.  
Amount of tax (on $21,390).  
6b  
}
Total cost: base amount less discount  
plus tax.  
Percent Difference  
In RPN or ALG mode, to find the percent difference between two numbers:  
1. Key in the base number.  
2. Press \ to separate the other number from the base number.  
3. Key in the other number.  
4. Press à.  
If the other number is greater than the base number, the percent difference will be  
positive. If the other number is less than the base number, the percent difference  
will be negative. Therefore, a positive answer indicates an increase, while a  
negative answer indicates a decrease.  
If you are calculating a percent difference over time, the base number is typically  
the amount occurring first.  
Example: Yesterday your stock fell from $58.50 to $53.25 per share. What is  
?
the percent change (Note that the \ key is the same as the } key in ALG  
mode.)  
Keystrokes  
Display  
58.50  
58.5\  
Keys in the base number and  
separates it from the other number.  
53.25  
–8.97  
53.25  
Keys in the other number.  
Nearly a 9% decrease.  
à
The à key can be used for calculations of the percent difference between a  
wholesale cost and a retail cost. If the base number entered is the wholesale cost,  
the percent difference is called the markup; if the base number entered is the retail  
cost, the percent difference is called the margin. Examples of markup and margin  
calculations are included in the hp 12c platinum Solutions Handbook.  
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Section 2: Percentage and Calendar Functions  
35  
Percent of Total in RPN Mode  
In RPN mode, to calculate what percentage one number is of another:  
1. Calculate the total amount by adding the individual amounts, just as in a  
chain arithmetic calculation.  
2. Key in the number whose percentage equivalent you wish to find.  
3. Press Z.  
Example: Last month, your company posted sales of $3.92 million in the U.S.,  
$2.36 million in Europe, and $1.67 million in the rest of the world. What  
?
percentage of the total sales occurred in Europe  
Keystrokes  
Display  
(RPN mode)  
3.92  
3.92\  
Keys in the first number and  
separates it from the second.  
6.28  
7.95  
2.36+  
Adds the second number.  
1.67+  
Adds the third number to get the  
total.  
2.36  
2.36  
Keys in 2.36 to find what percentage  
it is of the number in the display.  
Z
29.69  
Europe had nearly 30% of the total  
sales.  
In RPN mode, the hp 12c platinum holds the total amount inside after a percent of  
total is calculated. Therefore, to calculate what percentage another amount is of  
the total:  
1. Clear the display by pressing O.  
2. Key in that amount.  
3. Press Z again.  
For example, to calculate what percent of the total sales in the preceding example  
occurred in the U.S. and what percent occurred in the rest of the world:  
Keystrokes  
Display  
(RPN mode)  
O3.92Z  
49.31  
21.01  
The U.S. had about 49% of the total  
sales.  
O1.67 Z  
The rest of the world had about 21%  
of the total sales.  
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36 Section 2: Percentage and Calendar Functions  
To find what percentage a number is of a total, when you already know the total  
number:  
1. Key in the total number.  
2. Press \ to separate the other number from the total number.  
3. Key in the number whose percentage equivalent you wish to find.  
4. Press Z.  
For example, if you already knew in the preceding example that the total sales  
were $7.95 million and you wanted to find what percentage of that total occurred  
in Europe:  
Keystrokes  
Display  
(RPN mode)  
7.95  
2.36  
29.69  
7.95\  
2.36  
Keys in the total amount and  
separates it from the next number.  
Keys in 2.36 to find what % it is of  
the number in the display.  
Z
Europe had nearly 30% of the total  
sales.  
Percent of Total in ALG Mode  
In ALG mode, to calculate what percentage one number is of another:  
1. Calculate the total amount by adding the individual amounts, just as in a  
chain arithmetic calculation.  
2. Key in the number whose percentage equivalent you wish to find.  
3. Press Z.  
Example: Last month, your company posted sales of $3.92 million in the U.S.,  
$2.36 million in Europe, and $1.67 million in the rest of the world. What  
?
percentage of the total sales occurred in Europe  
Keystrokes  
Display  
(ALG mode)  
3.92  
3.92+  
Keys in the first number and  
separates it from the second.  
6.28  
7.95  
2.36+  
Adds the second number.  
1.67}  
Adds the third number to get the  
total.  
2.36  
2.36  
Keys in 2.36 to find what % it is of  
the number in the display.  
Z
29.69  
Europe had nearly 30% of the total  
sales.  
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Section 2: Percentage and Calendar Functions  
37  
To find what percentage a number is of a total, when you already know the total  
number:  
1. Key in the total number.  
2. Press } to separate the other number from the total number.  
3. Key in the number whose percentage equivalent you wish to find.  
4. Press Z.  
For example, if you already knew in the preceding example that the total sales  
were $7.95 million and you wanted to find what percentage of that total occurred  
in Europe:  
Keystrokes  
Display  
(ALG mode)  
7.95  
2.36  
29.69  
7.95}  
2.36  
Keys in the total amount and  
separates it from the next number.  
Keys in 2.36 to find what percentage  
it is of the number in the display.  
Z
Europe had nearly 30% of the total  
sales.  
Calendar Functions  
The calendar functions provided by the hp 12c platinum — gD and  
— can handle dates from October 15, 1582 through November 25,  
4046. These calendar functions work the same in both RPN and ALG modes.  
Date Format  
For each of the calendar functions — and also for bond calculations (fE and  
fS)  
the calculator uses one of two date formats. The date format is used to  
interpret dates when they are keyed into the calculator as well as for displaying  
dates.  
Month-Day-Year. To set the date format to month-day-year, press . To  
key in a date with this format in effect:  
1. Key in the one or two digits of the month.  
2. Press the decimal point key (.).  
3. Key in the two digits of the day.  
4. Key in the four digits of the year.  
Dates are displayed in the same format.  
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38 Section 2: Percentage and Calendar Functions  
For example, to key in April 7, 2004:  
Keystrokes  
Display  
4.072004  
4.072004  
Day-Month-Year. To set the date format to day-month-year, press . To  
key in a date with this format in effect:  
1. Key in the one or two digits of the day.  
2. Press the decimal point key (.).  
3. Key in the two digits of the month.  
4. Key in the four digits of the year.  
For example, to key in 7 April, 2004:  
Keystrokes  
Display  
7.042004  
7.042004  
When the date format is set to day-month-year, the D.MY status indicator in the  
display is lit. If D.MY is not lit, the date format is set to month-day-year.  
The date format remains set to what you last specified until you change it; it is not  
reset each time the calculator is turned on. However, if Continuous Memory is reset,  
the date format is set to month-day-year.  
Future or Past Dates  
To determine the date and day that is a given number of days from a given date:  
1. Key in the given date and press \.  
2. Key in the number of days.  
3. If the other date is in the past, press Þ.  
4. Press gD.  
The answer calculated by the gD function is displayed in a special format. The  
numbers of the month, day, and year (or day, month, and year) are separated by  
digit separators, and the digit at the right of the displayed answer indicates the  
day of the week: 1 for Monday through 7 for Sunday.  
*
The day of the week indicated by the D function may differ from that recorded in history  
*
for dates when the Julian calendar was in use. The Julian calendar was standard in England  
and its colonies until September 14, 1752, when they switched to the Gregorian calendar.  
Other countries adopted the Gregorian calendar at various times.  
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Section 2: Percentage and Calendar Functions  
39  
Example: If you purchased a 120-day option on a piece of land on 14 May  
?
2004, what would be the expiration date Assume that you normally express  
dates in the day-month-year format.  
Keystrokes  
Display  
gÔ  
7.04  
Sets date format to  
day-month-year. (Display shown  
assumes date remains from  
preceding example. The full date  
is not now displayed because the  
display format is set to show only  
two decimal places, as described  
in Section 5.)  
14.05  
14.052004\  
Keys in the date and separates it  
from the number of days to be  
entered.  
11,09,2004 6  
120gD  
The expiration date is 11  
September 2004, a Saturday.  
When gD is executed as an instruction in a running program, the calculator  
pauses for about 1 second to display the result, then resumes program execution.  
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40 Section 2: Percentage and Calendar Functions  
Number of Days Between Dates  
To calculate the number of days between two given dates:  
1. Key in the earlier date and press \.  
2. Key in the later date and press .  
The answer shown in the display is the actual number of days between the two  
dates, including leap days (the extra days occurring in leap years), if any. In  
addition, the hp 12c platinum also calculates the number of days between the two  
dates on the basis of a 30-day month. This answer is held inside the calculator; to  
display it, press ~. Pressing ~ again will return the original answer to the  
display.  
Example: Simple interest calculations can be done using either the actual number  
of days or the number of days counted on the basis of a 30-day month. What  
would be the number of days counted each way, to be used in calculating the  
?
simple interest accruing from June 3, 2004 to October 14, 2005 Assume that  
you normally express dates in the month-day-year format.  
Keystrokes  
Display  
gÕ  
11.09  
Sets date format to month-day-year.  
(Display shown assumes date  
remains from preceding example.)  
6.03  
6.032004\  
10.142005gÒ  
~
Keys in the earlier date and  
separates it from the later date.  
498.00  
491.00  
Keys in the later date. Display shows  
actual number of days.  
Number of days counted on the  
basis of a 30-day month.  
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Section 3  
Basic Financial Functions  
The Financial Registers  
In addition to the data storage registers discussed on page 27, the hp 12c  
platinum has five special registers in which numbers are stored for financial  
calculations. These registers are designated n, i, PV, PMT, and FV. The first five  
keys on the top row of the calculator are used to store a number from the display  
into the corresponding register, to calculate the corresponding financial value and  
store the result into the corresponding register, or to display the number stored in  
the corresponding register.  
*
Storing Numbers into the Financial Registers  
To store a number into a financial register, key the number into the display, then  
press the corresponding key (n, ¼, $, P, or M).  
Displaying Numbers in the Financial Registers  
To display a number stored in a financial register, press : followed by the  
corresponding key.  
Which operation is performed when one of these keys is pressed depends upon the last  
*
preceding operation performed: If a number was just stored into a financial register (using  
n, ¼, $, P, M, gA, or gC), pressing one of these five keys calculates the  
corresponding value and stores it into the corresponding register; otherwise pressing one of  
these five keys merely stores the number from the display into the corresponding register.  
It’s good practice to press the corresponding key twice after :, since often you may want  
to calculate a financial value right after displaying another financial value. As indicated in  
the preceding footnote, if you wanted to display FV and then calculate PV, for example, you  
should press :MM$. If you didn’t press M the second time, pressing $ would  
store FV in the PV register rather than calculating PV, and to calculate PV you would have to  
press $ again.  
41  
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42 Section 3: Basic Financial Functions  
Clearing the Financial Registers  
Every financial function uses numbers stored in several of the financial registers.  
Before beginning a new financial calculation, it is good practice to clear all of the  
financial registers by pressing fCLEARG. Frequently, however, you may want  
to repeat a calculation after changing a number in only one of the financial  
registers. To do so, do not press fCLEARG; instead, simply store the new  
number in the register. The numbers in the other financial registers remain  
unchanged.  
The financial registers are also cleared when you press fCLEARH and when  
Continuous Memory is reset (as described on page 86).  
Simple Interest Calculations  
The hp 12c platinum simultaneously calculates simple interest on both a 360-day  
basis and a 365-day basis. You can display either one, as described below.  
Furthermore, with the accrued interest in the display, you can calculate the total  
amount (principal plus accrued interest) by pressing + in RPN mode or  
+~} in ALG mode.  
1. Key in or calculate the number of days, then press n.  
2. Key in the annual interest rate, then press ¼.  
3. Key in the principal amount, then press Þ$.  
*
4. Press to calculate and display the interest accrued on a 360-day  
basis.  
5. If you want to display the interest accrued on a 365-day basis, press  
d~.  
6. In RPN mode, press + or in ALG mode, press +~} to calculate the  
total of the principal and the accrued interest shown in the display.  
The quantities n, i, and PV can be entered in any order.  
Pressing the $ key stores the principal amount in the PV register, which then contains the  
*
present value of the amount on which interest will accrue. The Þ key is pressed first to  
change the sign of the principal amount before storing it in the PV register. This is required by  
the cash flow sign convention (see page 46), which is applicable primarily to compound  
interest calculations.  
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Section 3: Basic Financial Functions  
43  
Example 1: Your good friend needs a loan to start his latest enterprise and has  
requested that you lend him $450 for 60 days. You lend him the money at 7%  
simple interest, to be calculated on a 360-day basis. What is the amount of  
?
accrued interest he will owe you in 60 days, and what is the total amount owed  
Keystrokes  
(RPN mode)  
Display  
60.00  
7.00  
60n  
Stores the number of days.  
Stores the annual interest rate.  
Stores the principal.  
7¼  
–450.00  
5.25  
450Þ$  
fÏ  
+
Accrued interest, 360-day basis.  
455.25  
Total amount: principal plus accrued  
interest.  
In ALG mode, perform the steps in the RPN listing above, except replace the last  
step with the step below.  
Keystrokes  
(ALG mode)  
Display  
+~}  
455.25  
Total amount: principal plus accrued  
interest.  
Example 2: Your friend agrees to the 7% interest on the loan from the preceding  
example, but asks that you compute it on a 365-day basis rather than a 360-day  
basis. What is the amount of accrued interest he will owe you in 60 days, and  
?
what is the total amount owed  
Keystrokes  
(RPN mode)  
Display  
60.00  
7.00  
–450.00  
60n  
7¼  
450Þ$  
If you have not altered the numbers in  
the n, i, and PV registers since the  
preceding example, you may skip  
these keystrokes.  
fÏd~  
+
5.18  
Accrued interest, 365-day basis.  
455.18  
Total amount: principal plus accrued  
interest.  
In ALG mode, perform the steps in the RPN listing above, except replace the last  
step with the step below.  
Keystrokes  
Display  
(ALG mode)  
+~}  
455.18  
Total amount: principal plus accrued  
interest.  
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44 Section 3: Basic Financial Functions  
Financial Calculations and the Cash Flow Diagram  
The concepts and examples presented in this section are representative of a wide  
range of financial calculations. If your specific problem does not appear to be  
illustrated in the pages that follow, don’t assume that the calculator is not capable  
of solving it. Every financial calculation involves certain basic elements; but the  
terminology used to refer to these elements typically differs among the various  
segments of the business and financial communities. All you need to do is identify  
the basic elements in your problem, and then structure the problem so that it will  
be readily apparent what quantities you need to tell the calculator and what  
quantity you want to solve for.  
An invaluable aid for using your calculator in a financial calculation is the cash  
flow diagram. This is simply a pictorial representation of the timing and direction  
of financial transactions, labeled in terms that correspond to keys on the calculator.  
The diagram begins with a horizontal line, called a time line. It represents the  
duration of a financial problem, and is divided into compounding periods. For  
example, a financial problem that transpires over 6 months with monthly  
compounding would be diagrammed like this:  
The exchange of money in a problem is depicted by vertical arrows. Money you  
receive is represented by an arrow pointing up from the point in the time line when  
the transaction occurs; money you pay out is represented by an arrow pointing  
down.  
Suppose you deposited (paid out) $1,000 into an account that pays 6% annual  
interest and is compounded monthly, and you subsequently deposited an  
additional $50 at the end of each month for the next 2 years. The cash flow  
diagram describing the problem would look like this:  
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Section 3: Basic Financial Functions  
45  
The arrow pointing up at the right of the diagram indicates that money is received  
at the end of the transaction. Every completed cash flow diagram must include at  
least one cash flow in each direction. Note that cash flows corresponding to the  
accrual of interest are not represented by arrows in the cash flow diagram.  
The quantities in the problem that correspond to the first five keys on the top row of  
the keyboard are now readily apparent from the cash flow diagram.  
z
n is the number of compounding periods. This quantity can be expressed in  
years, months, days, or any other time unit, as long as the interest rate is  
expressed in terms of the same basic compounding period. In the problem  
illustrated in the cash flow diagram above, n = 2 × 12.  
The form in which n is entered determines whether or not the calculator  
performs financial calculations in Odd-Period mode (as described on pages  
63 through 67). If n is a noninteger (that is, there is at least one nonzero  
digit to the right of the decimal point), calculations of i, PV, PMT, and FV are  
performed in Odd-Period mode.  
z
i is the interest rate per compounding period. The interest rate shown in the  
cash flow diagram and entered into the calculator is determined by dividing  
the annual interest rate by the number of compounding periods. In the  
problem illustrated above, i = 6% ÷ 12.  
z
z
PV — the present value — is the initial cash flow or the present value of a  
series of future cash flows. In the problem illustrated above, PV is the $1,000  
initial deposit.  
PMT is the period payment. In the problem illustrated above PMT is the $50  
deposited each month. When all payments are equal, they are referred to as  
annuities. (Problems involving equal payments are described in this section  
under Compound Interest Calculations; problems involving unequal  
payments can be handled as described in under Discounted Cash Flow  
Analysis: NPV and IRR. Procedures for calculating the balance in a savings  
account after a series of irregular and/or unequal deposits are included in  
the hp 12c platinum Solutions Handbook.)  
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46 Section 3: Basic Financial Functions  
z
FV — the future value — is the final cash flow or the compounded value of a  
series of prior cash flows. In the particular problem illustrated above, FV is  
unknown (but can be calculated).  
Solving the problem is now basically a matter of keying in the quantities identified  
in the cash flow diagram using the corresponding keys, and then calculating the  
unknown quantity by pressing the corresponding key. In the particular problem  
illustrated in the cash flow diagram above, FV is the unknown quantity; but in other  
problems, as we shall see later, n, i, PV, or PMT could be the unknown quantity.  
Likewise, in the particular problem illustrated above there are four known  
quantities that must be entered into the calculator before solving for the unknown  
quantity; but in other problems only three quantities may be known — which must  
always include n or i.  
The Cash Flow Sign Convention  
When entering the PV, PMT, and FV cash flows, the quantities must be keyed into  
the calculator with the proper sign, + (plus) or – (minus), in accordance with …  
The Cash Flow Sign Convention: Money received (arrow pointing up)  
is entered or displayed as a positive value (+). Money paid out (arrow  
pointing down) is entered or displayed as a negative value (–).  
The Payment Mode  
One more bit of information must be specified before you can solve a problem  
involving periodic payments. Such payments can be made either at the beginning  
of a compounding period (payments in advance, or annuities due) or at the end of  
the period (payments in arrears, or ordinary annuities). Calculations involving  
payments in advance yield different results than calculations involving payments in  
arrears. Illustrated below are portions of cash flow diagrams showing payments in  
advance (Begin) and payments in arrears (End). In the problem illustrated in the  
cash flow diagram above, payments are made in arrears.  
Regardless of whether payments are made in advance or in arrears, the number of  
payments must be the same as the number of compounding periods.  
To specify the payment mode:  
z
z
Press if payments are made at the beginning of the compounding  
periods.  
Press if payments are made at the end of the compounding periods.  
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Section 3: Basic Financial Functions  
47  
The BEGIN status indicator is lit when the payment mode is set to Begin. If BEGIN  
is not lit, the payment mode is set to End.  
The payment mode remains set to what you last specified until you change it; it is  
not reset each time the calculator is turned on. However, if Continuous Memory is  
reset, the payment mode will be set to End.  
Generalized Cash Flow Diagrams  
Examples of various kinds of financial calculations, together with the applicable  
cash flow diagrams, appear under Compound Interest Calculations later in this  
section. If your particular problem does not match any of those shown, you can  
solve it nevertheless by first drawing a cash flow diagram, then keying the  
quantities identified in the diagram into the corresponding registers. Remember  
always to observe the sign convention when keying in PV, PMT, and FV.  
The terminology used for describing financial problems varies among the different  
segments of the business and financial communities. Nevertheless, most problems  
involving compound interest can be solved by drawing a cash flow diagram in  
one of the following basic forms. Listed below each form are some of the problems  
to which that diagram applies.  
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48 Section 3: Basic Financial Functions  
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Section 3: Basic Financial Functions  
49  
Compound Interest Calculations  
Specifying the Number of Compounding Periods and the Periodic  
Interest Rate  
Interest rates are usually quoted at the annual rate (also called the nominal rate):  
that is, the interest rate per year. However, in compound interest problems, the  
interest rate entered into i must always be expressed in terms of the basic  
compounding period, which may be years, months, days, or any other time unit.  
For example, if a problem involves 6% annual interest compounded quarterly for 5  
years, n — the number of quarters — would be 5 × 4 = 20 and i — the interest  
rate per quarter — would be 6% ÷ 4 = 1.5%. If the interest were instead  
compounded monthly, n would be 5 × 12 = 60 and i would be 6% ÷ 12 = 0.5%.  
If you use the calculator to multiply the number of years by the number of  
compounding periods per year, pressing n then stores the result into n. The same  
is true for i. Values of n and i are calculated and stored like this in Example 2 on  
page 59.  
If interest is compounded monthly, you can use a shortcut provided on the  
calculator to calculate and store n and i:  
z
To calculate and store n, key the number of years into the display, then press  
gA.  
z
To calculate and store i, key the annual rate into the display, then press  
gC.  
Note that these keys not only multiply or divide the displayed number by 12; they  
also automatically store the result in the corresponding register, so you need not  
press the n or ¼ key next. The gA and gC keys are used in Example 1  
on page 59.  
Calculating the Number of Payments or Compounding Periods  
1. Press fCLEARG to clear the financial registers.  
2. Enter the periodic interest rate, using ¼ or gC.  
3. Enter at least two of the following values:  
z
z
z
Present value, using $.  
Payment amount, using P.  
Future value, using M.  
Note: Remember to observe  
the cash flow sign  
convention.  
4. If a PMT was entered, press or to set the payment mode.  
5. Press n to calculate the number of payments or periods.  
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50 Section 3: Basic Financial Functions  
If the answer calculated is not an integer (that is, there would be nonzero digits to  
the right of the decimal point), the calculator rounds the answer up to the next  
higher integer before storing it in the n register and displaying it. For example, if  
*
n were calculated as 318.15, 319.00 would be the displayed answer.  
n is rounded up by the calculator to show the total number of payments needed:  
n–1 equal, full payments, and one final, smaller payment. The calculator does not  
automatically adjust the values in the other financial registers to reflect n equal  
payments; rather, it allows you to choose which, if any, of the values to adjust.  
Therefore, if you want to know the value of the final payment (with which you can  
calculate a balloon payment) or desire to know the payment value for n equal  
payments, you will need to press one of the other financial keys, as shown in the  
following two examples.  
Example 1: You’re planning to build a log cabin on your vacation property.  
Your rich uncle offers you a $35,000 loan at 10.5% interest. If you make $325  
payments at the end of each month, how many payments will be required to pay  
?
off the loan, and how many years will this take  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
10.5gC  
0.88  
Calculates and stores i.  
35,000.00  
35000$  
Stores PV.  
–325.00  
–325.00  
325ÞP  
Stores PMT (with minus sign for cash  
paid out).  
g  
Sets the payment mode to End.  
The calculator will round n down to the next lower integer if the fractional portion of n is less  
than 0.005.  
*
After calculating n, pressing ¼,$,P, or M will recalculate the value in the  
corresponding financial register.  
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Section 3: Basic Financial Functions  
51  
Keystrokes  
(RPN mode)  
Display  
n
328.00  
27.33  
Number of payments required.  
Twenty-seven years and four months.  
12z  
In ALG mode, perform the RPN steps but replace the last step with the step below.  
Keystrokes  
Display  
(ALG mode)  
z12}  
27.33  
Twenty-seven years and four months.  
Because the calculator rounds the calculated value of n up to the next higher  
integer, in the preceding example it is likely that — while 328 payments will be  
required to pay off the loan — only 327 full payments of $325 will be required,  
the next and final payment being less than $325. You can calculate the final,  
fractional, 328th payment as follows:  
Keystrokes  
Display  
(RPN mode)  
328.00  
181.89  
328n  
Stores total number of payments.  
*
M
Calculates FV — which equals the  
overpayment if 328 full payments  
were made.  
:P  
+
–325.00  
–143.11  
Recalls payment amount.  
Final, fractional payment.  
Keystrokes  
(ALG mode)  
Display  
328.00  
181.89  
328n  
Stores total number of payments.*  
M
Calculates FV — which equals the  
overpayment if 328 full payments  
were made.  
You could skip this step, since 328 is already stored in the n register. If you do so, however,  
*
you will need to press M twice in the next step (for the reason discussed in the first footnote  
on page 41; you would not have to press M twice if you had not pressed 12z in RPN  
mode or z12} in ALG mode after w in the example above.) We choose to show this  
and the following example in a parallel format so that the procedure is easy to remember: the  
number you key is the number of the final payment — either the fractional payment or the  
balloon payment — whose amount is to be calculated.  
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52 Section 3: Basic Financial Functions  
Keystrokes  
Display  
(ALG mode)  
+:P  
}
–325.00  
–143.11  
Recalls payment amount.  
Final, fractional payment.  
Alternatively, you could make the fractional payment together with the 327th  
payment. (Doing so will result in a somewhat smaller total of all payments, since  
you will not have to pay interest during the 328th payment period.) You can  
calculate this final, larger, 327th payment (essentially a balloon payment) as  
follows:  
Keystrokes  
Display  
(RPN mode)  
327.00  
327n  
Stores number of full payments.  
M
–141.87  
Calculates FV — which is the  
balance remaining after 327 full  
payments.  
:P  
+
–325.00  
–466.87  
Recalls payment amount.  
Final, balloon payment.  
Keystrokes  
(ALG mode)  
Display  
327.00  
327n  
Stores number of full payments.  
M
–141.87  
Calculates FV — which is the  
balance remaining after 327 full  
payments.  
+:P  
}
–325.00  
–466.87  
Recalls payment amount.  
Final, balloon payment.  
Instead of having a fractional (or balloon) payment at the end of the loan, you  
might wish to make 327 or 328 equal payments. Refer to “Calculating the  
Payment Amount” on page 58 for a complete description of this procedure.  
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Section 3: Basic Financial Functions  
53  
Example 2: You’re opening a savings account today (the middle of the month)  
with a $775 deposit. The account pays 6.25% interest compounded semimonthly.  
If you make semimonthly deposits of $50 beginning next month, how long will it  
?
take for your account to reach $4,000  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
6.25\24z¼  
0.26  
Calculates and stores i.  
–775.00  
775Þ$  
Stores PV (with minus sign for cash  
paid out).  
–50.00  
50ÞP  
Stores PMT (with minus sign for cash  
paid out).  
4,000.00  
4,000.00  
58.00  
4000M  
g  
n
Stores FV.  
Sets the payment mode to End.  
Number of semimonthly deposits.  
Number of months.  
29.00  
2z  
Keystrokes  
(ALG mode)  
Display  
fCLEARG  
6.25z24¼  
0.26  
Calculates and stores i.  
–775.00  
775Þ$  
50ÞP  
4000M  
Stores PV (with minus sign for cash  
paid out).  
–50.00  
Stores PMT (with minus sign for cash  
paid out).  
4,000.00  
Stores FV.  
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54 Section 3: Basic Financial Functions  
Keystrokes  
Display  
(ALG mode)  
g  
n
4,000.00  
58.00  
Sets the payment mode to End.  
Number of semimonthly deposits.  
Number of months.  
z2}  
29.00  
As in Example 1, it is likely that only 57 full deposits will be required, the next and  
final deposit being less than $50. You can calculate this final, fractional, 58th  
deposit as in Example 1, except that for this example you must subtract the original  
FV. (In Example 1, the original FV was zero.) The procedure is as follows:  
Keystrokes  
Display  
(RPN mode)  
Calculates FV – which equals the  
MM  
4,027.27  
balance in the account if 58 full  
deposits were made.  
*
Recalls amount of deposits.  
:P  
+
–50.00  
Calculates the balance in the account  
if 57 full deposits were made and  
interest accrued during the 58th  
3,977.27  
month.  
Calculates final, fractional, 58th  
deposit required to reach $4,000.  
–22.73  
4000-  
Keystrokes  
(ALG mode)  
Display  
Calculates FV – which equals the  
MM  
4,027.27  
balance in the account if 58 full  
deposits were made.  
*
Recalls amount of deposits.  
+:P  
-
–50.00  
Calculates the balance in the account  
if 57 full deposits were made and  
interest accrued during the 58th  
3,977.27  
month.  
In this example, M must be pressed twice, since the preceding key pressed was z in RPN  
mode and } in ALG mode. If we had stored the number of deposits in n (as we did  
following Example 1), we would have to press M only once here, since the preceding key  
pressed would have been w (as it was following Example 1). Remember that it is not  
necessary to store the number of payments in n before calculating the amount of the final,  
fractional payment. (Refer to the preceding footnote.)  
You might think that we could calculate the balance in the account after 57 full deposits were  
made simply by storing that number in n and then calculating FV, as we did using the second  
method following Example 1. However, this balance would not include the interest accrued  
during the 58th month.  
*
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Section 3: Basic Financial Functions  
55  
Keystrokes  
(ALG mode)  
Display  
–22.73  
Calculates final, fractional, 58th  
deposit required to reach $4,000.  
4000}  
Calculating the Periodic and Annual Interest Rates  
1. Press fCLEARG to clear the financial registers.  
2. Enter the number of payments or periods, using n or gA.  
3. Enter at least two of the following values:  
z
z
z
Present value, using $.  
Payment amount, using P.  
Future value, using M.  
Note: Remember to observe the  
cash flow sign convention.  
4. If a PMT was entered, press or to set the payment mode.  
5. Press ¼ to calculate the periodic interest rate.  
6. To calculate the annual interest rate in RPN mode, key in the number of  
periods per year, then press §. To calculate the annual interest rate in ALG  
mode, press §, key in the number of periods per year, then press }.  
Example: What annual interest rate must be obtained to accumulate $10,000 in  
?
8 years on an investment of $6,000 with quarterly compounding  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
8\4§w  
32.00  
Calculates and stores n.  
–6,000.00  
6000Þ$  
Stores PV (with minus sign for cash  
paid out).  
10,000.00  
10000M  
Stores FV.  
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56 Section 3: Basic Financial Functions  
Keystrokes  
Display  
(RPN mode)  
¼
1.61  
6.44  
Periodic (quarterly) interest rate.  
Annual interest rate.  
4§  
Keystrokes  
(ALG mode)  
Display  
fCLEARG  
8§4w  
32.00  
Calculates and stores n.  
–6,000.00  
6000Þ$  
Stores PV (with minus sign for cash  
paid out).  
10,000.00  
1.61  
10000M  
Stores FV.  
¼
Periodic (quarterly) interest rate.  
Annual interest rate.  
§4}  
6.44  
Calculating the Present Value  
1. Press fCLEARG to clear the financial registers.  
2. Enter the number of payments or periods, using n or gA.  
3. Enter the periodic interest rate, using ¼ or gC.  
4. Enter either or both of the following:  
z
z
Payment amount, using P.  
Note: Remember to observe  
the cash flow sign convention.  
Future value, using M.  
5. If a PMT was entered, press or to set the payment mode.  
6. Press $ to calculate the present value.  
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Section 3: Basic Financial Functions  
57  
Example 1: You’re financing a new car purchase with a loan from an institution  
that requires 5.9% interest compounded monthly over the 4-year term of the loan.  
If you can make payments of $450 at the end of each month and your down  
?
payment will be $1,500, what is the maximum price you can pay for the car  
(Assume the purchase date is one month prior to the date of the first payment.)  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
4gA  
48.00  
0.49  
Calculates and stores n.  
5.9gC  
450ÞP  
Calculates and stores i.  
–450.00  
Stores PMT (with minus sign for cash  
paid out).  
g  
$
–450.00  
Sets payment mode to End.  
Maximum amount of loan.  
Maximum purchase price.  
19,198.60  
20,698.60  
1500+  
In ALG mode, press the keys listed for RPN mode but replace the last step above  
with the step below.  
Keystrokes  
Display  
(ALG mode)  
+1500}  
20,698.60 Maximum purchase price.  
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58 Section 3: Basic Financial Functions  
Example 2: A development company would like to purchase a group of  
condominiums with an annual net cash flow of $17,500. The expected holding  
period is 5 years, and the estimated selling price at that time is $540,000.  
Calculate the maximum amount the company can pay for the condominiums in  
order to realize at least a 12% annual yield.  
Keystrokes  
Display  
fCLEARG  
5n  
5.00  
Stores n.  
12.00  
12¼  
Stores i.  
17,500.00  
17500P  
Stores PMT. Unlike in the previous  
problem, here PMT is positive  
since it represents cash received.  
540,000.00  
540,000.00  
–369,494.09  
540000M  
g  
$
Stores FV.  
Sets payment mode to End.  
The maximum purchase price to  
provide a 12% annual yield. PV  
is displayed with a minus sign  
since it represents cash paid out.  
Calculating the Payment Amount  
1. Press fCLEARG to clear the financial registers.  
2. Enter the number of payments or periods, using n or gA.  
3. Enter the periodic interest rate, using ¼ or gC.  
4. Enter either or both of the following:  
z
z
Present value, using $.  
Note: Remember to observe the  
cash flow sign convention.  
Future value, using M.  
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Section 3: Basic Financial Functions  
59  
5. Press or to set the payment mode.  
6. Press P to calculate the payment amount.  
Example 1: Calculate the payment amount on a 29-year, $243,400 mortgage  
at 5.25% annual interest, compounded monthly.  
Keystrokes  
Display  
fCLEARG  
29gA  
348.00  
Calculates and stores n.  
Calculates and stores i.  
Stores PV.  
0.44  
5.25gC  
243400$  
g  
243,400.00  
243,400.00  
–1,363.29  
Sets payment mode to End.  
P
Monthly payment (with minus sign  
for cash paid out).  
Example 2: Looking forward to retirement, you wish to accumulate $60,000  
after 15 years by making deposits in an account that pays 9.75% interest  
compounded semiannually. You open the account with a deposit of $3,200 and  
intend to make semiannual deposits, beginning six months later, from your  
profit-sharing bonus paychecks. Calculate how much these deposits should be.  
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60 Section 3: Basic Financial Functions  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
30.00  
15\2µw  
9.75\2z¼  
3200Þ$  
Calculates and stores n.  
4.88  
Calculates and stores i.  
–3,200.00  
Stores PV (with minus sign for cash  
paid out).  
60,000.00  
60,000.00  
–717.44  
60000M  
g  
P
Stores FV.  
Sets payment mode to End.  
Semiannual payment (with minus  
sign for cash paid out).  
Keystrokes  
(ALG mode)  
Display  
fCLEARG  
15µ2w  
30.00  
Calculates and stores n.  
4.88  
9.75z2¼  
Calculates and stores i.  
–3,200.00  
3200Þ$  
Stores PV (with minus sign for cash  
paid out).  
60,000.00  
60,000.00  
–717.44  
60000M  
g  
P
Stores FV.  
Sets payment mode to End.  
Semiannual payment (with minus  
sign for cash paid out).  
Calculating the Future Value  
1. Press fCLEARG to clear the financial registers.  
2. Enter the number of payments or periods, using n or gA.  
3. Enter the periodic interest rate, using ¼ or gC.  
4. Enter either or both of the following:  
z
z
Present value, using $.  
Note: Remember to observe the  
cash flow sign convention.  
Payment amount, using P.  
5. If a PMT was entered, press or to set the payment mode.  
6. Press M to calculate the future value.  
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Section 3: Basic Financial Functions  
61  
Example 1: In Example 1 on page 59, we calculated that the payment amount  
on a 29-year, $243,400 mortgage at 5.25% annual interest compounded monthly  
is $1,363.29. If the seller requests a balloon payment at the end of 5 years, what  
?
would be the amount of the balloon  
Keystrokes  
Display  
fCLEARG  
5gA  
60.00  
Calculates and stores n.  
Calculates and stores i.  
Stores PV.  
0.44  
5.25gC  
243,400.00  
–1,363.29  
243400$  
1363.29ÞP  
Stores PMT (with minus sign for  
cash paid out).  
g  
M
–1,363.29  
Sets payment mode to End.  
Amount of balloon payment.  
–222,975.98  
Example 2: If you deposit $50 a month (at the beginning of each month) into a  
new account that pays 6.25% annual interest compounded monthly, how much  
?
will you have in the account after 2 years  
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62 Section 3: Basic Financial Functions  
Keystrokes  
Display  
fCLEARG  
2gA  
24.00  
0.52  
Calculates and stores n.  
6.25gC  
Calculates and stores i.  
–50.00  
50ÞP  
Stores PMT (with minus sign for cash  
paid out).  
g×  
M
–50.00  
Sets payment mode to Begin.  
Balance after 2 years.  
1,281.34  
Example 3: Property values in an unattractive area are depreciating at the rate  
of 2% per year. Assuming this trend continues, calculate the value in 6 years of  
property presently appraised at $32,000.  
Keystrokes  
Display  
fCLEARG  
6n  
6.00  
Stores n.  
–2.00  
2Þ¼  
Stores i (with minus sign for a  
“negative interest rate”).  
–32,000.00  
28,346.96  
32000Þ $  
M
Stores PV (with minus sign for cash  
paid out).  
Property value after 6 years.  
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Section 3: Basic Financial Functions  
63  
Odd-Period Calculations  
The cash flow diagrams and examples presented so far have dealt with financial  
transactions in which interest begins to accrue at the beginning of the first regular  
payment period. However, interest often begins to accrue prior to the beginning of  
the first regular payment period. The period from the date interest begins accruing  
to the date of the first payment, being not equal to the regular payment periods is  
sometimes referred to as an “odd first period”. For simplicity, in using the hp 12c  
platinum we will always regard the first period as equal to the remaining periods,  
and we will refer to the period between the date interest begins accruing and the  
beginning of the first payment period as simply the “odd period” or the “odd  
days”. (Note that the odd period is always assumed by the calculator to occur  
before the first full payment period.) The following two cash flow diagrams  
represent transactions including an odd period for payments in advance (Begin)  
and for payments in arrears (End).  
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64 Section 3: Basic Financial Functions  
You can calculate i, PV, PMT, and FV for transactions involving an odd period  
simply by entering a noninteger n. (A noninteger is a number with at least one  
nonzero digit to the right of the decimal point.) This places the calculator in  
Odd-Period mode. The integer part of n (the part to the left of the decimal point)  
*
specifies the number of full payment periods, and the fractional part (the part to the  
right of the decimal) specifies the length of the odd period as a fraction of a full  
period. The odd period, therefore, cannot be greater than one full period.  
The fractional part of n can be determined using either the actual number of odd  
days or the number of odd days counted on the basis of a 30-day month. The  
function can be used to calculate the number of odd days either way. The  
fractional part of n is a fraction of a payment period, so the number of odd days  
must be divided by the number of days in a period. If interest is compounded  
monthly, for this number you can use either 30, 365/12, or (if the odd period falls  
entirely within a single month) the actual number of days in that month. Usually, a  
monthly period is taken to be 30 days long.  
At your option, the calculations of i, PV, PMT, and FV can be performed with either  
simple interest or compound interest accruing during the odd period. If the C status  
indicator in the display is not lit, simple interest is used. To specify compound  
interest, turn the C indicator on by pressing . Pressing again  
turns the C indicator off, and calculations will then be performed using simple  
interest for the odd period.  
Calculations of i, PMT, and FV are performed using the present value at the end of the odd  
*
period. This is equal to the number in the PV register plus the interest accrued during the odd  
period. When calculating PV in Odd-Period mode, the calculator returns a value equal to the  
present value at the beginning of the odd period and stores it in the PV register.  
After calculating i, PV, PMT, or FV in Odd-Period mode, you should not try to calculate n. If  
you do, the calculator will switch out of Odd-Period mode and compute n without taking the  
odd period into account. The values in the other financial registers will correspond to the new  
n, but the original assumptions for the problem will be changed.  
The two methods of counting odd days will yield slightly different answers. If you are  
calculating i to determine the annual percentage rate (APR) for an odd-period transaction, the  
lower APR will result if the calculation uses the greater number of odd days determined using  
the two methods.  
is not programmable.  
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Section 3: Basic Financial Functions  
65  
Example 1: A 36-month loan for $4,500 accrues interest at a 5% annual  
percentage rate (APR), with the payments made at the end of each month. If  
interest begins accruing on this loan on February 15, 2004 (so that the first period  
begins on March 1, 2004), calculate the monthly payment, with the odd days  
counted on the basis of a 30-day month and compound interest used for the odd  
period.  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
gÕ  
Clears financial registers.  
Sets date format to month-day-year.  
Sets payment mode to End.  
g  
?Æ  
Turns on the C indicator in the  
display, so that compound interest  
will be used for the odd period.  
2.15  
2.152004\  
Keys in the date interest begins  
accruing and separates it from the  
next date entered.  
3.012004  
3.012004  
Keys in the date of the beginning of  
the first period.  
gÒ  
~
15.00  
16.00  
Actual number of odd days.  
Number of odd days counted on the  
basis of a 30-day month.  
0.53  
30z  
Divides by the length of a monthly  
period to get the fractional part of n.  
36.53  
36+n  
Adds the fractional part of n to the  
number of complete payment  
periods, then stores the result in n.  
0.42  
5gC  
4500$  
P
Calculates and stores i.  
Stores PV.  
4,500.00  
–135.17  
Monthly payment.  
Keystrokes  
(ALG mode)  
Display  
?Æ  
Turns on the C indicator in the  
display, so that compound interest  
will be used for the odd period.  
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66 Section 3: Basic Financial Functions  
Keystrokes  
Display  
(ALG mode)  
2.15  
2.152004}  
Keys in the date interest begins  
accruing and separates it from the  
next date entered.  
3.012004  
3.012004  
Keys in the date of the beginning of  
the first period.  
gÒ  
~
15.00  
16.00  
Actual number of odd days.  
Number of odd days counted on the  
basis of a 30-day month.  
z30+  
0.53  
Divides by the length of a monthly  
period to get the fractional part of n.  
36.53  
36n  
Adds the fractional part of n to the  
number of complete payment  
periods, then stores the result in n.  
0.42  
5gC  
4500$  
P
Calculates and stores i.  
Stores PV.  
4,500.00  
–135.17  
Monthly payment.  
Example 2: A 42-month loan of $3,950 for a used car began accruing interest  
on July 19, 2004, so that the first period began on August 1, 2004. Payments of  
$120 are made at the end of each month. Calculate the annual percentage rate  
(APR), using the actual number of odd days and simple interest for the odd period.  
Keystrokes  
Display  
(RPN mode)  
fCLEARG  
Clears financial registers.  
?Æ  
Turns off the C indicator in the  
display, so that simple interest will be  
used for the odd period.  
7.19  
7.192004\  
Keys in the date interest begins  
accruing and separates it from the  
next date entered.  
8.012004  
8.012004  
Keys in the date of the beginning of  
the first period.  
gÒ  
13.00  
0.43  
Actual number of odd days.  
30z  
Divides by the length of a monthly  
period to get the fractional part of n.  
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Section 3: Basic Financial Functions  
67  
Keystrokes  
(RPN mode)  
Display  
42.43  
42+n  
Adds the fractional part of n to the  
number of complete payment  
periods, then stores the result in n.  
3,950.00  
–120.00  
3950$  
Stores PV.  
120ÞP  
Stores PMT (with minus sign for cash  
paid out).  
¼
1.16  
Periodic (monthly) interest rate.  
Annual percentage rate (APR).  
13.95  
12§  
Keystrokes  
(ALG mode)  
Display  
fCLEARG  
Clears financial registers.  
?Æ  
Turns off the C indicator in the  
display, so that simple interest will be  
used for the odd period.  
7.19  
7.192004}  
Keys in the date interest begins  
accruing and separates it from the  
next date entered.  
8.012004  
8.012004  
Keys in the date of the beginning of  
the first period.  
gÒ  
13.00  
0.43  
Actual number of odd days.  
z30+  
Divides by the length of a monthly  
period to get the fractional part of n.  
42.43  
42n  
Adds the fractional part of n to the  
number of complete payment  
periods, then stores the result in n.  
3,950.00  
–120.00  
3950$  
Stores PV.  
120ÞP  
Stores PMT (with minus sign for cash  
paid out).  
¼
1.16  
Periodic (monthly) interest rate.  
Annual percentage rate (APR).  
§12}  
13.95  
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68 Section 3: Basic Financial Functions  
Before leaving this Odd-Period mode example, you may now press to  
turn the C annunciator off, if needed. Note that when the calculator is not in  
Odd-Period mode, the status of the C annunciator actually has no effect on  
calculator operation. You will find another use of Odd-Period mode and  
in Section 16 of this manual, where the C must be set before the two  
Bond programs will work correctly.  
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Section 3: Basic Financial Functions  
69  
Amortization  
The hp 12c platinum enables you to calculate the amounts applied toward  
principal and toward interest from a single loan payment or from several payments,  
and also tells you the remaining balance of the loan after the payments are  
made.  
*
To obtain an amortization schedule:  
1. Press fCLEARG to clear the financial registers.  
2. Enter the periodic interest rate, using ¼ or gC.  
3. Enter the amount of the loan (the principal), using $.  
4. Key in the periodic payment, then press ÞP (the sign of PMT must be  
negative, in accordance with the cash flow sign convention).  
5. Press or (for most direct reduction loans) to set the payment  
mode.  
6. Key in the number of payments to be amortized.  
7. Press f! to display the amount from those payments applied toward  
interest.  
8. Press ~ to display the amount from those payments applied toward the  
principal.  
9. To display the number of payments just amortized, press dd.  
10.To display the remaining balance of the loan, press :$.  
11.To display the total number of payments amortized, press :n.  
Example: For a house you’re about to buy, you can obtain a 25-year mortgage  
for $250,000 at 5.25% annual interest. This requires payments of $1,498.12 (at  
the end of each month). Find the amounts that would be applied to interest and to  
the principal from the first year’s payments.  
Keystrokes  
Display  
fCLEARG  
5.25gC  
0.44  
Enters i.  
250,000.00  
250000$  
Enters PV.  
All amounts calculated when f! is pressed are automatically rounded to the number of  
*
decimal places specified by the display format. (The display format is described in Section 5.)  
This rounding affects the number inside the calculator as well as how the number appears in  
the display. The amounts calculated on your hp 12c platinum may differ from those on the  
statements of lending institutions by a few cents, since different rounding techniques are  
sometimes used. To calculate answers rounded to a different number of decimal places, press  
f followed by the number of decimal places desired before you press f!.  
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70 Section 3: Basic Financial Functions  
Keystrokes  
Display  
–1,498.12  
1498.12ÞP  
Enters PMT (with minus sign for cash  
paid out).  
g  
–1,498.12  
Sets payment mode to End.  
–13,006.53  
12f!  
Portion of first year’s payments (12  
months) applied to interest.  
~
–4,970.91  
Portion of first year’s payments  
applied to principal.  
:$  
:n  
245,029.09  
12.00  
Balance remaining after 1 year.  
Total number of payments amortized.  
The number of payments keyed in just before f! is pressed is taken to be the  
payments following any that have already been amortized. Thus, if you now press  
12f!, your hp 12c platinum will calculate the amounts applied to interest and  
to the principal from the second year’s payments (that is, the second 12 months):  
Keystrokes  
Display  
–12,739.18  
12f!  
Portion of second year’s payments  
applied to interest.  
~
–5,238.26  
Portion of second year’s payments  
applied to principal.  
dd  
12.00  
Number of payments just amortized.  
Balance remaining after 2 years.  
Total number of payments amortized.  
:$  
:n  
239,790.83  
24.00  
Pressing :$ or :n displays the number in the PV or n register. When you  
did so after each of the last two calculations, you may have noticed that PV and n  
had been changed from their original values. The calculator does this so that you  
can easily check the remaining balance and the total number of payments  
amortized. But because of this, if you want to generate a new amortization  
schedule from the beginning, you must reset PV to its original value and reset n to  
0.  
For example, suppose you now wanted to generate an amortization schedule for  
each of the first two months:  
Keystrokes  
Display  
250,000.00  
0.00  
250000$  
Resets PV to original value.  
0n  
Resets n to zero.  
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Section 3: Basic Financial Functions  
71  
Keystrokes  
Display  
–1,093.75  
–404.37  
–1,091.98  
–406.14  
2.00  
1f!  
Portion of first payment applied to  
interest.  
~
Portion of first payment applied to  
principal.  
1f!  
~
Portion of second payment applied to  
interest.  
Portion of second payment applied to  
principal.  
:n  
Total number of payments amortized.  
If you want to generate an amortization schedule but do not already know the  
monthly payment:  
1. Calculate PMT as described on page 58.  
2. Press 0n to reset n to zero.  
3. Proceed with the amortization procedure listed on page 69 beginning with  
step 6.  
Example: Suppose you obtained a 30-year mortgage instead of a 25-year  
mortgage for the same principal ($250,000) and at the same interest rate (5.25%)  
as in the preceding example. Calculate the monthly payment, then calculate the  
amounts applied to interest and to the principal from the first month’s payment.  
Since the interest rate is not being changed, do not press fCLEARG; to  
calculate PMT, just enter the new value for n, reset PV, then press P.  
Keystrokes  
Display  
360.00  
30gA  
250000$  
P
Enters n.  
250,000.00  
–1,380.51  
0.00  
Enters PV.  
Monthly payment.  
Resets n to zero.  
0n  
–1,093.75  
1f!  
Portion of first payment applied to  
interest.  
~
–286.76  
Portion of first payment applied to  
principal.  
:$  
249,713.24  
Remaining balance.  
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Section 4  
Additional Financial  
Functions  
Discounted Cash Flow Analysis: NPV and IRR  
The hp 12c platinum provides functions for the two most widely-used methods of  
discounted cash flow analysis: fl (net present value) and fL (internal  
rate of return). These functions enable you to analyze financial problems involving  
cash flows (money paid out or received) occurring at regular intervals. As in  
compound interest calculations, the interval between cash flows can be any time  
period; however, the amounts of these cash flows need not be equal.  
To understand how to use fl and fL, let’s consider the cash flow  
diagram for an investment that requires an initial cash outlay (CF0) and generates  
a cash flow (CF1) at the end of the first year, and so on up to the final cash flow  
(CF6) at the end of the sixth year. In the following diagram, the initial investment is  
denoted by CF0, and is depicted as an arrow pointing down from the time line  
since it is cash paid out. Cash flows CF1 and CF4 also point down from the time  
line, because they represent projected cash flow losses.  
NPV is calculated by adding the initial investment (represented as a negative cash  
flow) to the present value of the anticipated future cash flows. The interest rate, i,  
will be referred to in this discussion of NPV and IRR as the rate of return. The  
*
value of NPV indicates the result of the investment:  
Other terms are sometimes used to refer to the rate of return. These include: required rate of  
*
return, minimally acceptable rate of return, and cost of capital.  
72  
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Section 4: Additional Financial Functions  
73  
z
z
z
If NPV is positive, the financial value of the investor’s assets would be  
increased: the investment is financially attractive.  
If NPV is zero, the financial value of the investor’s assets would not change:  
the investor is indifferent toward the investment.  
If NPV is negative, the financial value of the investor’s assets would be  
decreased: the investment is not financially attractive.  
A comparison of the NPV’s of alternative investment possibilities indicates which of  
them is most desirable: the greater the NPV, the greater the increase in the  
financial value of the investor’s assets.  
IRR is the rate of return at which the discounted future cash flows equal the initial  
cash outlay: IRR is the discount rate at which NPV is zero. The value of IRR relative  
to the present value discount rate also indicates the result of the investment:  
z
z
z
If IRR is greater than the desired rate of return, the investment is financially  
attractive.  
If IRR is equal to the desired rate of return, the investor is indifferent toward  
the investment.  
If IRR is less than the desired rate of return, the investment is not financially  
attractive.  
Calculating Net Present Value (NPV)  
Calculating NPV for Ungrouped Cash Flows. If there are no equal  
consecutive cash flows, use the procedure described (and then summarized) below.  
With this procedure, NPV (and IRR) problems involving up to 80 cash flows (in  
addition to the initial investment CF0) can be solved. If two or more consecutive  
cash flows are equal — for example, if the cash flows in periods three and four  
are both $8,500 — you can solve problems involving more than 80 cash flows, or  
you can minimize the number of storage registers required for problems involving  
less than 80 cash flows, by using the procedure described next (under Calculating  
NPV for Grouped Cash Flows, page 75).  
The amount of the initial investment (CF0) is entered into the calculator using the  
gJ keys.  
Each cash flow (CF1, CF2, etc.) is designated CFj, where j takes on values from 1  
up to the number of the final cash flow. The amount of a cash flow is entered using  
the gK keys. Each time gK is pressed, the amount in the display is stored  
in the next available storage register, and the number in the n register is increased  
by 1. This register therefore counts how many cash flow amounts (in addition to  
the initial investment CF0) have been entered.  
Note: When entering cash flow amounts — including the initial investment  
CF0 — remember to observe the cash flow sign convention by pressing Þ  
after keying in a negative cash flow.  
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74 Section 4: Additional Financial Functions  
In summary, to enter the cash flow amounts:  
1. Press fCLEARH to clear the financial and storage registers.  
2. Key in the amount of the initial investment, press Þ if that cash flow is  
negative, then press gJ.  
3. Key in the amount of the next cash flow, press Þ if the cash flow is  
negative, then press gK. If the cash flow amount is zero in the next  
period, press 0 gK.  
4. Repeat step 3 for each cash flow until all have been entered.  
With the amounts of the cash flows stored in the calculator’s registers, you can  
calculate NPV as follows:  
1. Enter the interest rate, using ¼ or gC.  
2. Press fl.  
The calculated value of NPV appears in the display and also is automatically  
stored in the PV register.  
Example: An investor has an opportunity to buy a duplex for $80,000 and  
would like a return of at least 13%. He expects to keep the duplex 5 years and  
then sell it for $130,000; and he anticipates the cash flows shown in the diagram  
below. Calculate NPV to determine whether the investment would result in a return  
or a loss.  
Note that although a cash flow amount ($4,500) occurs twice, these cash flows  
are not consecutive. Therefore, these cash flows must be entered using the method  
described above.  
Keystrokes  
Display  
fCLEARH  
0.00  
Clears financial and storage  
registers.  
–80,000.00  
80000ÞgJ  
Stores CF0 (with minus sign for a  
negative cash flow).  
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Section 4: Additional Financial Functions  
75  
Keystrokes  
Display  
–500.00  
500ÞgK  
Stores CF1 (with minus sign for a  
negative cash flow).  
4,500.00  
5,500.00  
4,500.00  
130,000.00  
5.00  
4500gK  
5500gK  
4500gK  
130000gK  
:n  
Stores CF2.  
Stores CF3.  
Stores CF4.  
Stores CF5.  
Checks number of cash flow amounts  
entered (in addition to CF0 ).  
13.00  
13¼  
Stores i.  
fl  
212.18  
NPV.  
Since NPV is positive, the investment would increase the financial value of the  
investor’s assets.  
Calculating NPV for Grouped Cash Flows. A maximum of 80 cash flow  
amounts (in addition to the initial investment CF0) can be stored in the hp 12c  
platinum. However, problems involving more than 80 cash flows can be handled  
*
if among the cash flows there are equal consecutive cash flows. For such problems,  
you merely enter along with the amounts of the cash flows the number of times —  
up to 99 — each amount occurs consecutively. This number is designated Nj,  
corresponding to cash flow amount CFj, and is entered using the ga keys. Each  
Nj is stored in a special register inside the calculator.  
This method can, of course, be used for problems involving fewer than 80 cash  
flows — and it will require fewer storage registers than the method described  
above under Calculating NPV for Ungrouped Cash Flows. Equal consecutive cash  
flows can be entered using that method — provided there are enough storage  
registers available to accommodate the total number of individual cash flows. The  
facility of grouping equal consecutive cash flows is provided to minimize the  
number of storage registers required.  
Note: When entering cash flow amounts — including the initial investment  
CF0 — remember to observe the cash flow sign convention by pressing Þ  
after keying in the amount for a negative cash flow.  
If you have stored a program in the calculator, the number of registers available for storing  
*
cash flow amounts may be less than 81.  
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76 Section 4: Additional Financial Functions  
In summary, to enter the amounts of the cash flows and the number of times they  
occur consecutively:  
1. Press fCLEARH to clear the financial and storage registers.  
2. Key in the amount of the initial investment, press Þ if that cash flow is  
negative, then press gJ.  
3. If the initial investment consists of more than one cash flow of the amount  
entered in step 2, key in the number of those cash flows, then press ga. If  
ga is not pressed, the calculator assumes that N0 is 1.  
4. Key in the amount of the next cash flow, press Þ if that cash flow is  
negative, then press gK. If the cash flow amount is zero in the next  
period, press 0gK.  
5. If the amount entered in step 4 occurs more than once consecutively, key in  
the number of times that cash flow amount occurs consecutively, then press  
ga. If ga is not pressed, the calculator assumes that Nj is 1 for the CFj  
just entered.  
6. Repeat steps 4 and 5 for each CFj and Nj until all cash flows have been  
entered.  
With the amounts of the cash flows and the number of times they occur  
consecutively stored in the calculator, NPV can be calculated by entering the  
interest rate and pressing fl, just as described earlier.  
Example: An investor has an opportunity to purchase a piece of property for  
$79,000; and he would like a 13.5% return. He expects to be able to sell it after  
10 years for $100,000 and anticipates the yearly cash flows shown in the table  
below:  
Year  
Cash Flow  
Year  
Cash Flow  
1
2
3
4
5
$14,000  
$11,000  
$10,000  
$10,000  
$10,000  
6
7
8
9
10  
$9,100  
$9,000  
$9,000  
$4,500  
$100,000  
Since two cash flow amounts ($10,000 and $9,000) are repeated consecutively,  
we can minimize the number of storage registers required by using the method just  
described.  
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Section 4: Additional Financial Functions  
77  
Keystrokes  
Display  
fCLEARH  
0.00  
Clears financial and storage  
registers.  
–79,000.00  
79000ÞgJ  
Initial investment (with minus sign  
for a negative cash flow).  
14,000.00  
11,000.00  
10,000.00  
3.00  
14000gK  
11000gK  
10000gK  
3ga  
First cash flow amount.  
Next cash flow amount.  
Next cash flow amount.  
Number of times this cash flow  
amount occurs consecutively.  
9,100.00  
9,000.00  
2.00  
9100gK  
9000gK  
2ga  
Next cash flow amount.  
Next cash flow amount.  
Number of times this cash flow  
amount occurs consecutively.  
4,500.00  
100,000.00  
7.00  
4500gK  
100000gK  
:n  
Next cash flow amount.  
Final cash flow amount.  
Seven different cash flow amounts  
have been entered.  
13.50  
13.5¼  
Stores i.  
fl  
907.77  
NPV.  
Since NPV is positive, the investment would increase the financial value of the  
investor’s assets by $907.77.  
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78 Section 4: Additional Financial Functions  
Calculating Internal Rate of Return (IRR)  
1. Enter the cash flows using either of the methods described above under  
Calculating Net Present Value.  
2. Press fL.  
The calculated value of IRR appears in the display and also is automatically stored  
in the i register.  
Note: Remember that the fL function may take a significant amount of  
time to produce an answer, during which the calculator displays running.  
Example: The NPV calculated in the preceding example was positive, indicating  
that the actual rate of return (that is, the IRR) was greater than the 13.5 used in the  
calculation. Find the IRR.  
Assuming the cash flows are still stored in the calculator, we need only press  
fL:  
Keystrokes  
Display  
fL  
13.72  
IRR is 13.72%.  
Note that the value calculated by fL is the periodic rate of return. If the cash  
flow periods are other than years (for example, months or quarters), you can  
calculate the nominal annual rate of return by multiplying the periodic IRR by the  
number of periods per year.  
As noted above, the calculator may take several seconds or even minutes to  
produce an answer for IRR. This is because the mathematical calculations for  
finding IRR are extremely complex, involving a series of iterations — that is, a  
series of successive calculations. In each iteration, the calculator uses an estimate  
of IRR as the interest rate in a computation of NPV. The iterations are repeated  
until the computed NPV reaches about zero.  
*
The complex mathematical characteristics of the IRR computation have an  
additional ramification: Depending on the magnitudes and signs of the cash flows,  
the computation of IRR may have a single answer, multiple answers, a negative  
answer or no answer.  
For additional information regarding fL, refer to Appendix C. For an  
alternative method of calculating IRR, refer to Section 13.  
In practice, because the complex mathematical calculations inside the calculator are done  
*
with numbers rounded to 10 digits, NPV may never reach exactly zero. Nevertheless, the  
interest rate that results in a very small NPV is very close to the actual IRR.  
In the case of multiple answers for IRR, the decision criteria listed on page 72 should be  
modified accordingly.  
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Section 4: Additional Financial Functions  
79  
Reviewing Cash Flow Entries  
z
To display a single cash flow amount, press :, then key in the number of  
the register containing the cash flow amount to be displayed. Alternatively,  
store the number of that cash flow amount (that is, the value of j for the CFj  
desired) in the n register, then press :gK.  
z
z
z
To review all the cash flow amounts, press :g K repeatedly. This  
displays the cash flow amounts in reverse order — that is, beginning with the  
final cash flow and proceeding to CF0.  
To display the number of times a cash flow amount occurs consecutively —  
that is, to display the Nj for a CFj store the number of that cash flow  
amount (that is, the value of j) in the n register, then press :ga.  
To review all the cash flow amounts together with the number of times each  
cash flow amount occurs consecutively (that is, to review each CFj and Nj  
pair), press :ga:gK repeatedly. This displays Nj followed by  
CFj beginning with the final cash flow amount and proceeding to N0 and  
CF0.  
Note: Neither fL nor fl changes the number in the n register.  
However, each time :gK is pressed, the number in the n register is  
decreased by 1. If this is done, or if you manually change the number in the  
n register in order to display a single Nj and/or CFj, be sure to reset the  
number in the n register to the total number of cash flow amounts originally  
entered (not including the amount of the initial investment CF0). If this is not  
done, NPV and IRR calculations will give incorrect results; also, a review of  
cash flow entries would begin with Nn and CFn, where n is the number  
currently in the n register.  
For example, to display the fifth cash flow amount and the number of times that  
amount occurs consecutively:  
Keystrokes  
Display  
:5  
9,000.00  
5.00  
CF5  
5n  
Stores the value of j in the n  
register.  
:ga  
2.00  
7.00  
N5  
7n  
Resets the number in the n register  
to its original value.  
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80 Section 4: Additional Financial Functions  
To display all the cash flow amounts and the number of times they occur  
consecutively:  
Keystrokes  
Display  
:ga  
:gK  
:ga  
:gK  
:ga  
:gK  
1.00  
N7  
100,000.00  
1.00  
CF7  
N6  
4,500.00  
2.00  
CF6  
N5  
9,000.00  
CF5  
.
.
.
.
.
.
.
.
.
:ga  
:gK  
:ga  
:gK  
7n  
1.00  
N1  
14,000.00  
1.00  
CF1  
N0  
–79,000.00  
7.00  
CF0  
Resets the number in the n register  
to its original value.  
Changing Cash Flow Entries  
z
To change a cash flow amount:  
1. Key the amount into the display.  
2. Press ?.  
3. Key in the number of the register containing the cash flow amount to be  
changed.  
z
To change the number of times a cash flow amount occurs consecutively —  
that is, to change the Nj for a CFj:  
1. Store the number of that cash flow amount (that is, j) in the n register.  
2. Key the number of times the cash flow amount occurs consecutively into  
the display.  
3. Press ga.  
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Section 4: Additional Financial Functions  
81  
Note: If you change the number in the n register in order to change an Nj,  
be sure to reset the number in the n register to the total number of cash flow  
amounts originally entered (not including the amount of the initial investment  
CF0). If this is not done, NPV and IRR calculations will give incorrect results.  
Example 1: With the cash flows now stored in the calculator, change CF2 from  
$11,000 to $9,000, then calculate the new NPV for a 13.5% return.  
Keystrokes  
Display  
9,000.00  
13.50  
9000?2  
13.5¼  
Stores the new CF2 in R2.  
Stores i.  
*
fl  
–644.75  
The new NPV.  
Since this NPV is negative, the investment would decrease the financial value of  
the investor’s assets.  
Example 2: Change N5 from 2 to 4, then calculate the new NPV.  
Keystrokes  
Display  
5.00  
4.00  
5n  
Stores j in the n register.  
4ga  
Stores the new N5.  
7.00  
7n  
Resets the number in the n register  
to its original value.  
fl  
–1,857.21  
The new NPV.  
This step is necessary in this example because we have calculated IRR since the first time we  
*
calculated NPV. The IRR calculation replaced the 13.5 we keyed into i before calculating  
NPV with the result for IRR – 13.72.  
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82 Section 4: Additional Financial Functions  
Bond Calculations  
The hp 12c platinum enables you to solve for bond price (and the interest accrued  
since the last interest date) and the yield to maturity. The fE and fS  
*
calculations are done assuming a semiannual coupon payment and using an  
actual/actual basis (such as for U.S. Treasury bonds and U.S. Treasury notes). In  
accordance with market convention, prices are based on a redemption (par) value  
of 100.  
To calculate bond price and yield for a 30/360 bond (that is, using the basis of a  
30-day month and a 360-day year —such as for municipal bonds, corporate  
bonds, and to calculate bond price for bonds with an annual coupon payment),  
refer to Section 16: Bonds.  
Bond Price  
1. Enter the desired yield to maturity (as a percentage), using ¼.  
2. Enter the annual coupon rate (as a percentage), using P.  
3. Key in the settlement (purchase) date (as described on page 37), then press  
\.  
4. Key in the maturity (redemption) date.  
5. Press fE.  
The price is shown in the display and also is stored in the PV register. The interest  
accrued since the last interest date is held inside the calculator: to display the  
interest, press ~; to add the interest to the price, press + in RPN mode and  
+~} in ALG mode.  
Example: What price should you pay on April 28, 2004 for a 6.75% U.S.  
Treasury bond that matures on June 4, 2018, if you want a yield of 4.75%.  
Assume that you normally express dates in the month-day-year format.  
Keystrokes  
Display  
(RPN mode)  
4.75  
4.75¼  
6.75P  
gÕ  
Enters yield to maturity.  
6.75  
Enters coupon rate.  
6.75  
Sets date format to month-day-year.  
Enters settlement (purchase) date.  
Enters maturity (redemption) date.  
Bond price (as a percent of par).  
Total price, including accrued interest.  
4.28  
4.282004\  
6.042018  
fE  
6.042018  
120.38  
123.07  
+
All bond calculations are performed in accordance with. the Securities Industry Association’s  
*
recommendations as contained in Jan Mayle, TIPS Inc., Standard Securities Calculation  
Methods, Volume 1, Third Edition, Securities Industry Association Inc., New York, 1993.  
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Section 4: Additional Financial Functions  
83  
In ALG mode, perform the steps listed for RPN mode above but replace the last  
step with the step below.  
Keystrokes  
Display  
(ALG mode)  
+~}  
123.07  
Total price, including accrued  
interest.  
Bond Yield  
1. Enter the quoted price (as a percent of par), using $.  
2. Enter the annual coupon rate (as a percentage), using P.  
3. Key in the settlement (purchase) date, then press \.  
4. Key in the maturity (redemption) date.  
5. Press fS.  
The yield to maturity is shown in the display and also is stored in the i register.  
Note: Remember that the fS function may take a significant amount of  
time to produce an answer, during which the calculator displays running.  
Example: The market is quoting 122.125% for the bond described in the  
?
preceding example. What yield will that provide  
Keystrokes  
Display  
122.13  
6.75  
122.125$  
6.75P  
Enters quoted price.  
Enters coupon rate.  
4.28  
4.282004\  
6.042018  
fS  
Enters settlement (purchase) date.  
Enters maturity (redemption) date.  
Bond yield.  
6.042018  
4.60  
After solving a bond problem, the FV register contains the redemption value plus  
the annual coupon rate percentage divided by two, and the n register contains the  
days from settlement date to the next coupon date divided by the number of days  
in the coupon period in which settlement occurs.  
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84 Section 4: Additional Financial Functions  
Depreciation Calculations  
The hp 12c platinum enables you to calculate depreciation and the remaining  
depreciable value (book value minus salvage value) using the straight-line,  
sum-of-the-years-digits, and declining-balance methods. To do so with any of these  
methods:  
1. Enter the original cost of the asset, using $.  
2. Enter the salvage value of the asset, using M. If the salvage value is zero,  
press 0M.  
3. Enter the expected useful life of the asset (in years), using n.  
4. If the declining-balance method is being used, enter the declining-balance  
factor (as a percentage), using ¼. For example, 1.25 times the straight-line  
rate — 125 percent declining-balance — would be entered as 125¼.  
5. Key in the number of the year for which depreciation is to be calculated.  
6. Press:  
z
z
z
fV for depreciation using the straight-line method.  
for depreciation using the sum-of-the-years digits method.  
f# for depreciation using the declining-balance method.  
fV, , and f# each place the amount of depreciation in the display.  
To display the remaining depreciable value (the book value less the salvage value)  
after the depreciation has been calculated, press ~.  
Example: A metalworking machine, purchased for $10,000, is depreciated over  
5 years. Its salvage value is estimated at $500. Find the depreciation and  
remaining depreciable value for the first 3 years of the machine’s life using the  
declining-balance method at double the straight-line rate (200 percent  
declining-balance).  
Keystrokes  
Display  
10,000.00  
500.00  
10000$  
500M  
5n  
Enters original cost.  
Enters salvage value.  
5.00  
Enters expected useful life.  
Enters declining-balance factor.  
Depreciation in first year.  
200.00  
200¼  
1f#  
~
4,000.00  
5,500.00  
Remaining depreciable value after  
first year.  
2,400.00  
2f#  
Depreciation in second year.  
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Section 4: Additional Financial Functions  
85  
Keystrokes  
Display  
~
3,100.00  
Remaining depreciable value after  
second year.  
1,440.00  
1,660.00  
3f#  
Depreciation in third year.  
~
Remaining depreciable value after  
third year.  
To calculate depreciation and the remaining depreciable value when the  
acquisition date of the asset does not coincide with the beginning of the fiscal  
accounting year, refer to the procedures in Section 13. That section also includes a  
procedure for depreciation calculations when changing from the declining-balance  
method to the straight-line method, and a procedure for calculating excess  
depreciation.  
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Section 5  
Additional Operating  
Features  
Continuous Memory  
The calculator’s Continuous Memory contains the data storage registers, the  
financial registers, the stack and LAST X registers, program memory, and status  
information such as display format, date format, and payment mode. All  
information in Continuous Memory is preserved even while the calculator is turned  
off. Furthermore, information in Continuous Memory is preserved for a short time  
when the batteries are removed, so that you can change the batteries without  
losing your data and programs.  
Continuous Memory may be reset if the calculator is dropped or otherwise  
traumatized, or if power is interrupted. You can also manually reset Continuous  
Memory as follows:  
1. Turn the calculator off.  
2. Hold down the - key, and press ;.  
When Continuous Memory is reset:  
z
All registers are cleared.  
z
Program memory consists of eight program lines, each containing the  
instruction g(000.  
z
z
z
z
Display format is set to the standard format with two decimal places.  
Date format is set to month-day-year.  
Payment mode is set to End.  
Arithmetic operation is set to RPN mode.  
Whenever Continuous Memory has been reset, the display will show Pr Error.  
Pressing any key will clear this message from the display.  
86  
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Section 5: Additional Operating Features  
87  
The Display  
Status Indicators  
Nine indicators that appear along the bottom of the display signify the status of the  
calculator for certain operations. These status indicators are described elsewhere  
in this handbook where the relevant operation is discussed.  
Number Display Formats  
When the calculator is first turned on after coming from the factory or after  
Continuous Memory has been reset, answers are displayed with two decimal  
places.  
Keystrokes  
Display  
(RPN mode)  
19.87  
14.87  
19.8745632\  
5-  
Keystrokes  
(ALG mode)  
Display  
19.87  
14.87  
19.8745632-  
5}  
Although you see only two decimal places, all calculations in your hp 12c  
platinum are performed with full 10-digit numbers.  
When only two decimal places are displayed, numbers are rounded to two  
decimal places: if the third digit is 5 through 9, the second digit is increased by  
one; if the third digit is 0 through 4, the second digit is not affected. Rounding  
occurs regardless of how many decimal places are displayed.  
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88 Section 5: Additional Operating Features  
Several options are provided for controlling how numbers appear in the display.  
But regardless of which display format or how many displayed decimal places you  
specify, the number inside the calculator — which appears altered in the  
display — is not altered unless you use the B, !, V, Ý, or # functions.  
Standard Display Format. The number 14.87 now in your calculator is  
currently being displayed in the standard display format with two decimal places  
shown. To display a different number of decimal places, press f followed by a  
digit key (0 through 9) specifying the number of decimal places. In the following  
examples, notice how the displayed form of the number inside the calculator —  
14.87456320 — is rounded to the specified number of digits.  
Keystrokes  
Display  
f4  
f1  
f0  
f9  
14.8746  
14.9  
15.  
14.87456320  
Although nine decimal places were  
specified after f, only eight are  
displayed since the display can  
show a total of only 10 digits.  
The standard display format, plus the specified number of decimal places, remain  
in effect until you change them; they are not reset each time the calculator is turned  
on. However, if Continuous Memory is reset, when the calculator is next turned on  
numbers will be displayed in the standard display format with two decimal places  
shown.  
If a calculated answer is either too small or too large to be displayed in the  
standard display format, the display format automatically switches to scientific  
notation (described below). The display returns to the standard display format for  
all numbers that can be displayed in that format.  
Scientific Notation Display Format  
In scientific notation, a number is displayed with its mantissa at the left and a  
two-digit exponent at the right. The mantissa is simply the first seven digits in the  
number, and has a single, nonzero digit to the left of the decimal point. The  
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Section 5: Additional Operating Features  
89  
exponent is simply how many decimal places you would move the decimal point in  
the mantissa before writing down the number in standard format. If the exponent is  
negative (that is, there is a minus sign between it and the mantissa), the decimal  
point should be moved to the left; this occurs for any number less than 1. If the  
exponent is positive (that is, there is a blank space between it and the mantissa),  
the decimal point should be moved to the right; this occurs for any number greater  
than or equal to 1.  
To set the display format to scientific notation, press f.. For example (assuming  
the display still shows 14.87456320 from the preceding example):  
Keystrokes  
Display  
f.  
1.487456 01  
The exponent in this example indicates that the decimal point should be moved  
one decimal place to the right, giving the number 14.87456, which is the first  
seven digits of the number previously in the display.  
To set the display back to standard display format, press f followed by the  
desired number of decimal places. Scientific notation display format remains in  
effect until you change to the standard display format; it is not reset each time the  
calculator is turned on. However, if Continuous Memory is reset, when the  
calculator is next turned on the standard display format, with two decimal places,  
will be used.  
Mantissa Display Format. Because both the standard display format and  
scientific notation display format often show only a few digits of a number, you  
may occasionally want to see all 10 digits — the full mantissa — of the number  
inside the calculator. To do so, press fCLEARX and hold down the X key.  
The display will show all 10 digits of the number as long as you hold down the  
X key; after you release the key, the number will again be displayed in the  
current display format. For instance, if the display still contains the result from the  
preceding example:  
Keystrokes  
Display  
fCLEARX  
1487456320  
All 10 digits of the number inside  
the calculator.  
1.487456 01  
14.87  
Display returns to its former  
contents when the X key is  
released.  
f2  
Returns display to standard format.  
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90 Section 5: Additional Operating Features  
Special Displays  
Running. Certain functions and many programs may take several seconds or  
more to produce an answer. During these calculations, the word running flashes  
in the display to let you know that the calculator is running.  
Overflow and Underflow. If a calculation results in a number whose  
magnitude is greater than 9.999999999 ×1099, the calculation is halted and the  
calculator displays 9.999999 99 (if the number is positive) or –9.999999 99  
(if the number is negative).  
If a calculation results in a number whose magnitude is less than 10–99, the  
calculation is not halted, but the value 0 is used for that number in subsequent  
calculations.  
Errors. If you attempt an improper operation — such as division by zero — the  
calculator will display the word Error followed by a digit (0 through 9). To clear  
the Error display, press any key. This does not execute that key’s function, but  
does restore the calculator to its condition before the improper operation was  
attempted. Refer to Appendix D for a list of error conditions.  
Pr Error. If power to the calculator is interrupted, the calculator will display Pr  
Error when next turned on. This indicates that Continuous Memory — which  
contains all data, program, and status information — has been reset.  
The  
Key in RPN Mode  
Suppose you need to subtract $25.83 from $144.25, and you (mistakenly) key in  
25.83 as the first number and then key in 144.25 as the second number. But then  
you realize that when written down on paper, the desired calculation reads  
144.25 – 25.83, so that you have unfortunately keyed in the second number first.  
To correct this mistake, merely exchange the first and second numbers by pressing  
~, the exchange key.  
Keystrokes  
Display  
(RPN mode)  
144.25  
25.83  
25.83\144.25  
Oops! You mistakenly keyed in the  
second number first.  
~
Exchanges the first and second  
numbers. The first number keyed in  
is now in the display.  
-
118.42  
The answer is obtained by pressing  
the operation key.  
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Section 5: Additional Operating Features  
91  
The ~ key is also useful for checking the first number entered to make sure you  
keyed it in correctly. Before pressing the operation key or equals key, however,  
you should press ~ again to return the second number entered to the display.  
Regardless of how many times you press ~, the calculator considers the number  
in the display to be the second number entered.  
The  
Key in RPN Mode  
Occasionally you may want to recall to the display the number that was there  
before an operation was performed. (This is useful for doing arithmetic calculations  
with constants and for recovering from errors in keying in numbers.) To do so,  
press gF (LAST X). This section describes how to use gF in RPN mode.  
Arithmetic Calculations With Constants  
Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15,  
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.  
Keystrokes  
Display  
(RPN mode)  
15.00  
4.38  
65.70  
75.  
15\  
4.38  
§
Keys first quantity into calculator.  
Keys unit cost into display.  
Cost of a package of 15.  
75  
Keys second quantity into display.  
gF  
4.38  
Recalls unit cost — which was last  
number in display before § was  
pressed — into display.  
§
328.50  
250.  
Cost of a package of 75.  
250  
Keys third quantity into display.  
Recalls unit cost into display again.  
Cost of a package of 250.  
gF  
§
4.38  
1,095.00  
Another method for doing arithmetic calculations with constants is described on  
page 235.  
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92 Section 5: Additional Operating Features  
Recovering From Errors in Digit Entry  
Example: Suppose you want to divide the total annual production for one of your  
firm’s products (429,000) by the number of retail outlets (987) in order to  
calculate the average number distributed by each outlet. Unfortunately, you  
mistakenly key in the number of outlets as 9987 rather than as 987. It’s easy to  
correct:  
Keystrokes  
Display  
(RPN mode)  
429,000.00  
9,987.  
429000\  
9987  
You haven’t noticed your mistake  
yet.  
z
42.96  
About 43 products per outlet — but  
that seems too low!  
gF  
9,987.00  
Recalls to the display the number  
that was there before you press z.  
You see that you keyed it in wrong.  
429,000.00  
434.65  
429000\  
Begins the problem over.  
The correct answer.  
987z  
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Section 6  
Statistics Functions  
Accumulating Statistics  
The hp 12c platinum can perform one- or two-variable statistical calculations. The  
data is entered into the calculator using the _ key, which automatically calculates  
and stores statistics of the data into storage registers R1, through R6. (These  
registers are therefore referred to as the “statistics registers.”)  
Before beginning to accumulate statistics for a new set of data, you should clear  
the statistics registers by pressing fCLEAR².  
*
In one-variable statistical calculations, to enter each data point — referred to as an  
x-value” — key the x-value into the display, then press _.  
In two-variable statistical calculations, to enter each data pair — referred to as the  
x and y-values”:  
1. Key the y-value into the display.  
2. Press \.  
3. Key the x-value into the display.  
4. Press _.  
Each time you press _, the calculator does the following:  
z
z
z
z
z
z
The number in R1 is increased by 1, and the result is copied into the display.  
The x-value is added to the number in R2.  
The square of the x-value is added to the number in R3.  
The y-value is added to the number in R4.  
The square of the y-value is added to the number in R5.  
The product of the x and y-values is added to the number in R6.  
This also clears the stack registers and the display.  
*
93  
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94 Section 6: Statistics Functions  
The table below shows where the accumulated statistics are stored.  
Register  
Statistic  
n: number of data pairs accumulated.  
Σx: summation of x-values.  
R1 (and display)  
R2  
R3  
R4  
R5  
R6  
Σx2: summation of squares of x-values.  
Σy: summation of y-values.  
Σy2 summation of squares of y-values.  
Σxy: summation of products of x-values and y-values.  
Correcting Accumulated Statistics  
If you discover you have entered data incorrectly, the accumulated statistics can  
easily be corrected. Simply key in the incorrect data point or data pair again as if  
it were new, but press g^ instead of _. Then enter the correct data point or  
data pair and press _.  
Mean  
Pressing calculates the means (arithmetic averages) of the x-values ( x ) and  
y
of the y-values ( ). The mean of the x-values appears in the display after is  
pressed; to display the mean of the y-values, press ~.  
Example: A survey of seven salespersons in your company reveals that they work  
the following hours a week and sell the following dollar volumes each month. How  
?
many hours does the average salesperson work each week How much does the  
?
average salesperson sell each month  
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Section 6: Statistics Functions  
95  
Salesperson Hours/Week Sales/Month  
1
2
3
4
5
6
7
32  
40  
45  
40  
38  
50  
35  
$17,000  
$25,000  
$26,000  
$20,000  
$21,000  
$28,000  
$15,000  
To find the average workweek and sales of this sample:  
Keystrokes  
Display  
fCLEAR²  
0.00  
Clears statistics registers.  
First entry.  
32.00  
1.00  
32\  
17000_  
40.00  
2.00  
40\  
25000_  
Second entry.  
Third entry.  
45.00  
3.00  
45\  
26000_  
40.00  
4.00  
40\  
20000_  
Fourth entry.  
Fifth entry.  
38.00  
5.00  
38\  
21000_  
50.00  
6.00  
50\  
28000_  
Sixth entry.  
35.00  
7.00  
35\  
15000_  
Total number of entries in the  
sample.  
gÖ  
~
21,714.29  
40.00  
Mean dollar sales per month ( ).  
x
Mean workweek in hours ( ).  
y
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96 Section 6: Statistics Functions  
Standard Deviation  
Pressing gv calculates the standard deviation of the x-values (sx) and of the  
y-values (sy). (The standard deviation of a set of data is a measure of the dispersion  
around the mean.) The standard deviation of the x-values appears in the display  
after gv is pressed; to display the standard deviation of the y-values, press  
~.  
Example: To calculate the standard deviations of the x-values and of the y-values  
from the preceding example:  
Keystrokes  
Display  
gv  
~
4,820.59  
6.03  
Standard deviation of sales.  
Standard deviation of hours  
worked.  
The formulas used in the hp 12c platinum for calculating sx and sy give best  
estimates of the population standard deviation based on a sample of the  
population. Thus, current statistical convention calls them sample standard  
deviations. So we have assumed that the seven salespersons are a sample of the  
population of all salespersons, and our formulas derive best estimates of the  
population from the sample.  
What if the seven salespersons constituted the whole population of salespersons.  
Then we wouldn’t need to estimate the population standard deviation. We can  
find the true population standard deviation (σ) when the data set equals the total  
population, using the following keystrokes.  
*
Keystrokes  
gÖ  
Display  
21,714.29  
8.00  
Mean (dollars)  
_
Number of entries + 1.  
gv  
4,463.00  
σx  
~
5.58  
σy  
It turns out that if you sum the mean of the population into the set itself and find the new s,  
*
computed using the formulas on page 257, that s will be the population standard deviation,  
σ, of the original set.  
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Section 6: Statistics Functions  
97  
To continue summing data pairs, press gÖg^ before entering more data.  
Note: In some cases involving data values that differ by a relatively small  
amount, the calculator cannot compute the standard deviation or the linear  
estimation accurately because such calculations would exceed the precision  
of the calculator. For instance, while the standard deviation of the values  
1,999,999; 2,000,000 and 2,000,001 is 1; the standard deviation  
returned by the hp 12c platinum is 0 due to the effect of roundoff. This will  
not happen, however, if you normalize the data by keying only the  
difference between each value and the mean or approximate mean of the  
values. In the preceding example, the correct result can be obtained using  
the values –1, 0 and 1 instead. Just remember to add the difference  
(2,000,000) back to the calculation of the average.  
Linear Estimation  
With two-variable statistical data accumulated in the statistics registers, you can  
ˆ
y
ˆ
x
estimate a new y-value ( ) given a new x-value, and estimate a new x-value (  
given a new y-value.  
)
ˆ
y
To calculate  
and Q  
1. Key in a new x-value.  
2. Press gR.  
ˆ
x
To calculate  
:
1. Key in a new y-value.  
2. Press gQ.  
Example: Using the accumulated statistics from the preceding problem, estimate  
the amount of sales delivered by a new salesperson working 48 hours per week.  
Keystrokes  
Display  
28,818.93  
48gQ  
Estimated sales for a 48 hour  
workweek.  
The reliability of a linear estimate depends upon how closely the data pairs would,  
if plotted on a graph, lie in a straight line. The usual measure of this reliability is  
ˆ
y
the correlation coefficient, r. This quantity is automatically calculated whenever  
ˆ
~
. A correlation coefficient close to 1  
or  
is calculated; to display it, press  
x
or –1 indicates that the data pairs lie very close to a straight line. On the other  
hand, a correlation coefficient close to 0 indicates that the data pairs do not lie  
closely to a straight line; and a linear estimate using this data would not be very  
reliable.  
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98 Section 6: Statistics Functions  
Example: Check the reliability of the linear estimate in the preceding example by  
displaying the correlation coefficient.  
Keystrokes  
Display  
~
0.90  
The correlation coefficient is close  
to 1, so the sales calculated in the  
preceding example is a good  
estimate.  
To graph the regression line, calculate the coefficients of the linear equation  
y = A + Bx.  
1. Press 0gR to compute the y-intercept (A).  
2. To compute the slope of the line (B) in RPN mode, press  
1gR~d~-. To compute the slope of the line (B) in ALG mode,  
press these keys: 1gR~d-~}.  
Example: Compute the slope and intercept of the regression line in the preceding  
example.  
Keystrokes  
Display  
(RPN mode)  
15.55  
0.001  
0gR  
y-intercept (A); projected value for x  
= 0.  
1 gR~d~-  
Slope of the line (B); indicates the  
change in the projected values  
caused by an incremental change  
in the x value.  
Keystrokes  
(ALG mode)  
Display  
15.55  
0gR  
y-intercept (A); projected value for x  
= 0.  
0.001  
1gR~d-~}  
Slope of the line (B); indicates the  
change in the projected values  
caused by an incremental change  
in the x value.  
The equation that describes the regression line is:  
y = 15.55 + 0.001x  
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Section 6: Statistics Functions  
99  
Weighted Mean  
You can compute the weighted mean of a set of numbers if you know the  
corresponding weights of the items in question.  
1. Press fCLEAR².  
2. Key in the value of the item and press \, then key in its weight and press  
_. Key in the second item’s value, press \, key in the second weight,  
and press _. Continue until you have entered all the values of the items and  
their corresponding weights. The rule for entering the data is “item \  
weight _.”  
3. Press g to calculate the weighted mean of the items.  
Example: Suppose that you stop during a vacation drive to purchase gasoline at  
four stations as follows: 15 gallons at $1.16 per gallon, 7 gallons at $1.24 per  
gallon, 10 gallons at $1.20 per gallon, and 17 gallons at $1.18 per gallon. You  
want to find the average cost per gallon of gasoline purchased. If you purchased  
the same quantity at each station, you could determine the simple arithmetic  
average or mean using the keys. But since you know the value of the item  
(gasoline) and its corresponding weight (number of gallons purchased), use the  
g keys to find the weighted mean:  
Keystrokes  
Display  
fCLEAR²  
1.16\15_  
1.24\7_  
1.2\10_  
1.18\17_  
g  
0.00  
1.00  
2.00  
3.00  
4.00  
1.19  
Clears statistics registers.  
First item and weight.  
Second item and weight.  
Third item and weight.  
Fourth item and weight.  
Weighted mean cost per gallon.  
A procedure for calculating the standard deviation and standard error (as well as  
the mean) of weighted or grouped data is included in the hp 12c platinum  
Solutions Handbook.  
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Section 7  
Mathematics and  
Number-Alteration Functions  
The hp 12c platinum provides several keys for mathematical functions and for  
altering numbers. These functions are useful for specialized financial calculations  
as well as for general mathematics calculations.  
One-Number Functions  
Most of the mathematics functions require that only one number be in the  
calculator (that is, the number in the display) before the function key is pressed.  
Pressing the function key then replaces the number in the display by the result.  
Reciprocal. Pressing y calculates the reciprocal of the number in the display —  
that is, it divides 1 by the number in the display.  
Square. Pressing calculates the square of the number in the display.  
Square Root. Pressing gr calculates the square root of the number in the  
display.  
Logarithm. Pressing calculates the natural logarithm (that is, the  
logarithm to the base e) of the number in the display. To calculate the common  
logarithm (that is, the logarithm to the base 10) of the number in the display,  
calculate the natural logarithm, then press 10g°z in RPN mode and  
z10g°} in ALG mode.  
Exponential. Pressing g> calculates the exponential of the number in the  
display — that is, it raises the base e to the number in the display.  
Factorial. Pressing ge calculates the factorial of the number in the display —  
that is, it calculates the product of the integers from 1 to n, where n is the number  
in the display.  
Round. The display format specifies to how many decimal places a number  
inside the calculator is rounded when it appears in the display; but the display  
format alone does not affect the number itself inside the calculator. Pressing  
fB, however, changes the number inside the calculator to match its displayed  
version. Thus, to round a number in the display to a given number of decimal  
places, temporarily set the display format (as described on page 87) to show the  
desired number of decimal places, then press fB.  
100  
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Section 7: Mathematics and Number-Alteration Functions 101  
Integer. Pressing replaces the number in the display by its integer  
portion — that is, it replaces each digit to the right of the decimal point by 0. The  
number is changed inside the calculator as well as in the display. In RPN mode,  
the original number can be recalled to the display by pressing gF.  
Fractional. Pressing gT replaces the number in the display by its fractional  
portion — that is, it replaces all digits to the left of the decimal point by 0. Like  
, gT changes the number inside the calculator as well as its displayed  
version. In RPN mode, the original number can be recalled to the display by  
pressing gF.  
All of the above functions are used basically in the same way. For example, to find  
the reciprocal of 0.258:  
Keystrokes  
Display  
0.258  
3.88  
.258  
Keys the number into the display.  
y
The reciprocal of 0.258, the  
original number.  
Any of the above functions can be done with a number in the display resulting  
from a previous calculation, as well as with a number you have just keyed in. The  
examples below indicate how gF can recall the original number for further  
use in RPN mode.  
Keystrokes  
Display  
(RPN mode)  
fCLEARX  
3875968992 Displays all 10 digits of the number  
inside the calculator.  
3.88  
3.88  
Display returns to normal format  
when X key is released.  
fB  
The number now in the display  
appears the same as before, but …  
fCLEARX  
3880000000 Displaying all 10 digits of the  
number inside the calculator shows  
fB has changed the number to  
match its displayed version.  
3.88  
3.00  
Display returns to normal format.  
gÑ  
gF  
gT  
The integer portion of the number  
previously displayed.  
3.88  
0.88  
Recalls the original number to the  
display in RPN mode only.  
The fractional portion of the number  
previously displayed.  
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102 Section 7: Mathematics and Number-Alteration Functions  
The Power Function in RPN Mode  
Pressing q calculates a power of a number — that is, yx. Like the arithmetic  
function +, q requires two numbers:  
1. Key in the base number (which is designated by the y on the key).  
2. Press \ to separate the second number (the exponent) from the first (the  
base).  
3. Key in the exponent (which is designated by the x on the key).  
4. Press q to calculate the power.  
To Calculate Keystrokes  
(RPN mode)  
Display  
21.4  
2\1.4q  
2.64  
0.38  
–8.00  
1.26  
2–1.4  
(–2)3  
2\1.4Þq  
2Þ\3q  
2\3yq  
or 21/3  
3
2
The Power Function in ALG Mode  
To calculate a power of a number, that is, yx, in ALG mode, do the following:  
1. Key in the base number (which is designated by the y on the key).  
2. Press q and key in the exponent (which is designated by the x on the key)  
3. Press } to calculate the power.  
Keystrokes  
(ALG mode)  
To Calculate  
Display  
21.4  
2q1.4}  
2.64  
0.38  
–8.00  
2–1.4  
(–2)3  
2q1.4Þ}  
2Þq3}  
or 21/3  
2q3y}  
3
1.26  
2
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Part II  
Programming  
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Section 8  
Programming Basics  
?
Why Use Programs  
A program is simply a sequence of keystrokes that is stored in the calculator.  
Whenever you have to calculate with the same sequence of keystrokes several  
times, you can save a great deal of time by incorporating these keystrokes in a  
program. Instead of pressing all the keys each time, you press just one key to start  
the program: the calculator does the rest automatically!  
Creating a Program  
Creating a program consists simply of writing the program, then storing it:  
1. Write down the sequence of keystrokes that you would use to calculate the  
quantity or quantities desired.  
2. Select the mode you want to use (by pressing f] or f[).  
Note: Programs or steps created and saved in RPN mode should only be  
executed in RPN mode, and programs or steps created and saved in ALG  
mode should only be executed in ALG mode. (You can also create steps in  
your program to switch to the appropriate mode.)  
3. Press fs to set the calculator to Program mode. When the calculator is  
in Program mode, functions are not executed when they are keyed in, but  
instead are stored inside the calculator. The PRGM status indicator in the  
display is lit when the calculator is in Program mode.  
4. Press fCLEARÎ to erase any previous programs that may be stored  
inside the calculator. If you want to create a new program without erasing a  
program already stored, skip this step and proceed as described in Section  
11, Multiple Programs.  
5. Key in the sequence of keystrokes that you wrote down in step 1. Skip the  
beginning keystrokes that enter data, which would differ each time the  
program is used.  
104  
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Section 8: Programming Basics 105  
Example: Your office supplies dealer is selling selected stock at 25% off. Create  
a program that calculates the net cost of an item after the discount is subtracted  
and the $5 handling charge is added.  
First, we’ll manually calculate the net cost of an item listing for $200.  
Keystrokes  
Display  
(RPN mode)  
200.  
200  
Keys in cost of item.  
\
200.00  
Separates cost of item from  
percentage to be keyed in next.  
50.00  
150.00  
5.  
25b  
Amount of discount.  
Price less discount.  
Handling charge.  
-
5
+
155.00  
Net cost (price less discount plus  
handling charge).  
Keystrokes  
(ALG mode)  
Display  
200.  
200  
Keys in cost of item.  
-
200.00  
Separates cost of item from  
percentage to be keyed in next.  
50.00  
150.00  
5.  
25b  
Amount of discount.  
Price less discount.  
Handling charge.  
+
5
}
155.00  
Net cost (price less discount plus  
handling charge).  
Next, set the calculator to Program mode and erase any program(s) already  
stored:  
Keystrokes  
Display  
fs  
Sets calculator to Program mode.  
Clears program(s).  
fCLEARÎ  
000,  
Finally, press the keys that we used above to solve the problem manually. Do not  
key in 200; this number will vary each time the program is used. Don’t be  
concerned right now about what appears in the display as you press the keys;  
we’ll discuss that later in this section.  
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106 Section 8: Programming Basics  
Keystrokes  
Display  
(RPN mode)  
\
001,  
002,  
003,  
004,  
005,  
006,  
007,  
36  
2
2
5
5
b
-
25  
30  
5
5
+
40  
Keystrokes  
(ALG mode)  
Display  
-
001,  
002,  
003,  
004,  
005,  
006,  
007,  
30  
2
2
5
5
b
+
25  
40  
5
5
}
36  
Running a Program  
To run (sometimes called “execute”) a program:  
1. Press fs to set the calculator back to Run mode. If the calculator is  
already in Run mode (that is, the PRGM status indicator in the display is not  
lit), skip this step.  
2. Key any required data into the calculator, just as if you were calculating  
manually. When a program is run, it uses the data already keyed into the  
display and the registers inside the calculator.  
3. Press t to begin program execution.  
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Section 8: Programming Basics 107  
Example: Run the program created above to calculate the net cost of a typewriter  
listing for $625 and an executive chair listing for $159.  
Keystrokes  
Display  
(RPN mode)  
fs  
155.00  
Sets calculator to Run mode. Display  
shows number previously calculated.  
f]  
155.00  
625.  
Sets RPN mode.  
625  
Keys in price of typewriter.  
Net cost of typewriter.  
Keys in list price of chair.  
Net cost of chair.  
t
473.75  
159.  
159  
t
124.25  
Keystrokes  
(ALG mode)  
Display  
fs  
155.00  
Sets calculator to Run mode. Display  
shows number previously calculated.  
f[  
155.00  
625.  
Sets ALG mode.  
625  
Keys in price of typewriter.  
Net cost of typewriter.  
Keys in list price of chair.  
Net cost of chair.  
t
473.75  
159.  
159  
t
124.25  
That’s all there is to creating and running simple programs! But if you want to use  
programs frequently, you’ll want to know more about programming — such as  
how to check what keystrokes are stored in program memory, how many  
keystrokes can be stored in program memory, how to correct or otherwise modify  
programs, how to skip keystrokes when running a program, and so on. Before you  
can understand these aspects of programming, we need to briefly discuss how  
keystrokes are treated by the calculator when they are stored in Program mode  
and when they are executed in Run mode.  
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108 Section 8: Programming Basics  
Program Memory  
Keystrokes entered into the calculator in Program mode are stored in program  
memory. Each digit, decimal point, or function key is called an instruction and is  
stored in one line of program memory — usually referred to simply as a program  
line. Keystroke sequences beginning with the f, g, ?, :, and i prefix  
keys are considered to comprise a complete instruction and are stored in only one  
program line.  
When a program is run, each instruction in program memory is executed — that is,  
the keystroke in that program line is performed, just as if you were pressing the key  
manually — beginning with the current line in program memory and proceeding  
sequentially with the higher-numbered program lines.  
Whenever the calculator is in Program mode (that is, whenever the PRGM status  
indicator in the display is lit), the display shows information about the program line  
to which the calculator is currently set. At the left of the display is the number of the  
program line within program memory. The remaining digits in the display comprise  
a code that indicates what instruction has been stored in that program line. No  
code is shown for program line 000, since no regular instruction is stored there.  
Identifying Instructions in Program Lines  
Each key on the hp 12c platinum keyboard — except for the digit keys 0 through  
9 — is identified by a two-digit “keycode” that corresponds to the key’s position  
on the keyboard. The first digit in the keycode is the number of the key row,  
counting from row 1 at the top; the second digit is the number of the key in that  
row, counting from 1 for the first key in the row through 9 for the ninth key in the  
row and 0 for the tenth key in the row. The keycode for each digit key is simply  
the digit on the key. Thus, when you keyed the instruction b into program  
memory, the calculator displays a line number and a keycode  
004,  
25  
This indicates that the key for the instruction in program line 004 is in the second  
row on the keyboard and is the fifth key in that row: the b key. When you keyed  
the instruction + into program memory, the calculator displays a line number and  
keycode as  
007,  
40  
This indicates that the key for the instruction in program line 007 is in the fourth  
row on the keyboard and is the tenth key in that row: the + key. When you  
keyed the digit 5 into program memory, the keycode displayed was only the digit  
5.  
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Section 8: Programming Basics 109  
Since keystroke sequences beginning with f, g, ?, :, and i are stored  
in only one program line, the display of that line would show the keycodes for all  
the keys in the keystroke sequence.  
Instruction  
gÒ  
Keycode  
nnn,  
43 26  
?=0  
nnn,44 40 0  
nnn,43,33,000  
gi000  
Displaying Program Lines  
Pressing fs to set the calculator from Run mode to Program mode displays the  
line number and keycode for the program line to which the calculator is currently  
set.  
Occasionally you’ll want to check several or all of the instructions stored in  
program memory. The hp 12c platinum enables you to review program instructions  
either forward or backward through program memory:  
z
Pressing Ê (single step) while the calculator is in Program mode advances  
the calculator to the next line in program memory, then displays that line  
number and the keycode of the instruction stored there.  
z
Pressing (back step) while the calculator is in Program mode sets the  
calculator back to the previous line in program memory, then displays that  
line number and the keycode of the instruction stored there.  
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110 Section 8: Programming Basics  
For example, to display the first two lines of the program now stored in program  
memory, set the calculator to Program mode and press Ê twice:  
Keystrokes  
Display  
(RPN mode)  
fs  
000,  
Sets calculator to Program  
mode and displays current line  
of program memory  
Ê
Ê
001,  
002,  
36  
2
\
Program line 001:  
Program line 002: digit 2.  
Keystrokes  
(ALG mode)  
Display  
fs  
000,  
Sets calculator to Program  
mode and displays current line  
of program memory  
Ê
Ê
001,  
002,  
30  
2
-
Program line 001:  
Program line 002: digit 2.  
Pressing does the reverse:  
Keystrokes  
Display  
(RPN mode)  
gÜ  
gÜ  
001,  
000,  
36  
30  
Program line 001.  
Program line 000.  
Keystrokes  
(ALG mode)  
Display  
gÜ  
gÜ  
001,  
000,  
Program line 001.  
Program line 000.  
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Section 8: Programming Basics 111  
If either the Ê key or the Ü key is held down, the calculator displays all of the  
lines in program memory. Press Ê again now, but this time hold it down until  
program line 007 is displayed.  
Keystrokes  
Display  
(RPN mode)  
Ê
001,  
36  
40  
Program line 001  
.
.
.
.
.
.
007,  
(Release Ê)  
Program line 007  
Keystrokes  
(ALG mode)  
Display  
Ê
001,  
30  
36  
Program line 001  
.
.
.
.
.
.
007,  
(Release Ê)  
Program line 007  
Program line 007 contains the last instruction you keyed into program memory.  
However, if you press Ê again, you’ll see that this is not the last line stored in  
program memory:  
Keystrokes  
Display  
Ê
008,43,33,000  
Program line 008  
As you should now be able to tell from the keycodes displayed, the instruction in  
program line 008 is gi000.  
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112 Section 8: Programming Basics  
The  
000 Instruction and Program Line 000  
Whenever you run the program now stored in program memory, the calculator  
executes the instruction in line 008 after executing the seven instructions you keyed  
in. This i000 instruction — as its name implies — tells the calculator to “go to”  
program line 000 and execute the instruction in that line. Although line 000 does  
not contain a regular instruction, it does contain a “hidden” instruction that tells the  
calculator to halt program execution. Thus, after each time the program is run, the  
calculator automatically goes to program line 000 and halts, ready for you to key  
in new data and run the program again. (The calculator is also automatically set to  
program line 000 when you press fs to set the calculator from Program mode  
to Run mode or when fCLEARÎ is pressed in run mode.)  
The i000 instruction was already stored in line 008 — in fact, in all program  
lines — before you keyed in the program. If no instructions have been keyed into  
program memory, if Continuous Memory is reset, or if fCLEARÎ is pressed (in  
Program mode), the instruction i000 is automatically stored in program lines  
001 through 008. As you key each instruction into program memory, it replaces  
the i000 instruction in that program line.  
If your program should consist of exactly eight instructions, there would be no  
i000 instructions remaining at the end of program memory. Nevertheless, after  
such a program is executed the calculator automatically returns to program line  
000 and halts, just as if there were a i000 instruction following the program.  
If you key in more than eight instructions, program memory automatically expands  
to accommodate the additional instructions.  
Expanding Program Memory  
If no instructions have been keyed into program memory, if Continuous Memory  
has been reset, or if fCLEARÎ has been pressed (in Program mode), program  
memory consists of 8 program lines, and there are 20 storage registers available  
for storage of data.  
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Section 8: Programming Basics 113  
To determine at any time how many program lines (including those containing  
gi000) are currently in program memory, press gN (memory). The  
calculator will respond with a display like the following:  
If you find yourself creating long programs, you should create your programs so  
that they don’t use up program lines unnecessarily, since program memory is  
limited to 400 program lines. One way to minimize program length is to replace  
numbers consisting of more than just one digit — like the number 25 in lines 002  
and 003 of the program keyed in above — by a : instruction, and then storing  
the number in the designated storage register before running the program. In this  
case, this would save one program line, since the : instruction requires only  
one program line, not two as are required by the number 25. Of course, doing so  
uses up data storage registers that you might want to save for other data. As in  
many business and financial decisions, there is a trade off involved; here it is  
between program lines and data storage registers.  
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114 Section 8: Programming Basics  
Setting the Calculator to a Particular Program Line  
There will be occasions when you’ll want to set the calculator directly to a  
particular program line — such as when you’re storing a second program in  
program memory or when you’re modifying an existing program. Although you  
can set the calculator to any line by using Ç as described above, you can do so  
more quickly as follows:  
z
With the calculator in Program mode, pressing gi. followed by three  
digit keys sets the calculator to the program line specified by the digit keys,  
and then displays that line number and the keycode of the instruction stored  
there.  
z
With the calculator in Run mode, pressing gi followed by three digit  
keys sets the calculator to the program line specified by the digit keys. Since  
the calculator is not in Program mode, the line number and keycode are not  
displayed.  
The decimal point is not necessary if the calculator is in Run mode, but it is  
necessary if the calculator is in Program mode.  
For example, assuming the calculator is still in Program mode, you can set it to  
program line 000 as follows:  
Keystrokes  
Display  
gi.000  
000,  
Program line 000  
Executing a Program One Line at a Time  
Pressing Ç repeatedly with the calculator in Program mode (as described earlier)  
enables you to verify that the program you have stored is identical to the program  
you wrote — that is, to verify that you have keyed the instructions in correctly.  
However, this does not ensure that the program you wrote calculates the desired  
results correctly: even programs created by the most experienced programmers  
often do not work correctly when they are first written.  
To help you verify that your program works correctly, you can execute the program  
one line at a time, using the Ç key. Pressing Ç while the calculator is in Run  
mode advances the calculator to the next line in program memory, then displays  
that line’s number and the keycode of the instruction stored there, just as in  
Program mode. In Run mode, however, when the Ç key is released the  
instruction in the program line just displayed is executed and the display then  
shows the result of executing that line.  
For example, to execute the program stored in the calculator one line at a time:  
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Section 8: Programming Basics 115  
Keystrokes  
(RPN mode)  
Display  
fs  
124.25  
Sets calculator to Run mode  
and to line 000 in program  
memory. (Display shown  
assumes results remain from  
previous calculation.)  
625.  
625  
Keys in price of typewriter.  
Ç
001,  
36  
2
\
Program line 001:  
625.00  
Result of executing program  
line 001.  
Ç
Ç
Ç
Ç
Ç
Ç
002,  
2.  
Program line 002: 2.  
Result of executing program  
line 002.  
003,  
25.  
5
Program line 003: 5.  
Result of executing program  
line 003.  
004,  
25  
30  
5
b
Program line 004:  
156.25  
Result of executing program  
line 004.  
005,  
-
Program line 005:  
468.75  
Result of executing program  
line 005.  
006,  
5.  
Program line 006: 5  
Result of executing program  
line 006.  
007,  
40  
+
Program line 007:  
473.75  
Result of executing program  
line 007 (the last line of the  
program).  
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116 Section 8: Programming Basics  
Keystrokes  
Display  
(ALG mode)  
fs  
124.25  
Sets calculator to Run mode  
and to line 000 in program  
memory. (Display shown  
assumes results remain from  
previous calculation.)  
625.  
625  
Keys in price of typewriter.  
Ç
001,  
30  
2
-
Program line 001:  
625.00  
Result of executing program  
line 001.  
Ç
Ç
Ç
Ç
Ç
Ç
002,  
2.  
Program line 002: 2.  
Result of executing program  
line 002.  
003,  
25.  
5
Program line 003: 5.  
Result of executing program  
line 003.  
004,  
25  
40  
5
b
Program line 004:  
156.25  
Result of executing program  
line 004.  
005,  
+
Program line 005:  
468.75  
Result of executing program  
line 005.  
006,  
5.  
Program line 006: 5  
Result of executing program  
line 006.  
007,  
36  
}
Program line 007:  
473.75  
Result of executing program  
line 007 (the last line of the  
program).  
Pressing while the calculator is in Run mode sets the calculator to the  
previous line in program memory, then displays that line’s number and the  
keycode of the instruction stored there, just as in Program mode. In Run mode,  
however, when the Ü key is released the display again shows the same number  
as it did before was pressed: no instruction in program memory is  
executed.  
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Section 8: Programming Basics 117  
Interrupting Program Execution  
Occasionally you’ll want a program to stop executing so that you can see an  
intermediate result or enter new data. The hp 12c platinum provides two functions  
for doing so: gu (pause) and t (run/stop).  
Pausing During Program Execution  
When a running program executes a gu instruction, program execution halts  
for about 1 second, then resumes. During the pause, the calculator displays the last  
result calculated before the gu instruction was executed.  
If you press any key during a pause, program execution is halted indefinitely. To  
resume program execution at the program line following that containing the  
gu instruction, press t.  
Example: Create a program that calculates the entries in the AMOUNT, TAX,  
and TOTAL columns for each item on the jewelry distributor’s invoice shown on the  
next page, and also calculates the total in each of these columns for all items on  
the invoice. Assume the sales tax is 6.75%.  
To conserve lines of program memory, instead of keying in the tax rate before the  
b instruction we’ll store it in register R0 and recall it before the b instruction.  
Before storing the program in program memory, we’ll calculate the required  
amounts for the first item on the invoice manually. The keystroke sequence will use  
storage register arithmetic (described on page 29) in registers R1, R2, and R3 to  
calculate the column sums. Since these registers are cleared when fCLEAR² is  
pressed, we’ll press those keys before beginning the manual calculation — and  
also later, before running the program — to ensure that the column sums are  
“initialized” to zero. (Pressing fCLEARH would clear registers R1 through R3,  
but would also clear R0, which will contain the tax rate.)  
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118 Section 8: Programming Basics  
Pressing the gu keys is not necessary when we do the calculations manually,  
since in Run mode the result of every intermediate calculation is displayed  
automatically; but we’ll include gu instructions in the program so that the  
intermediate results AMOUNT and TAX are automatically displayed when the  
program is executed.  
Keystrokes  
Display  
(RPN mode)  
6.75  
0.00  
6.75?0  
Stores tax rate in R0.  
fCLEAR²  
Clears the registers in R1  
through R6.  
13.  
13  
Keys in quantity of item.  
\
13.00  
Separates quantity of item from  
cost of item to be keyed in  
next.  
68.5  
68.5  
Keys in cost of item.  
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Section 8: Programming Basics 119  
Keystrokes  
(RPN mode)  
Display  
§
890.50  
890.50  
AMOUNT.  
?+1  
Adds AMOUNT to sum of  
AMOUNT entries in register R1.  
:0  
6.75  
Recalls tax rate to display.  
TAX.  
b
60.11  
60.11  
?+2  
Adds TAX to sum of TAX entries  
in register R2.  
+
950.61  
950.61  
TOTAL.  
?+3  
Adds TOTAL to sum of TOTAL  
entries in register R3.  
Keystrokes  
(ALG mode)  
Display  
6.75  
0.00  
6.75?0  
Stores tax rate in R0.  
fCLEAR²  
Clears the registers in R1  
through R6.  
13.  
13  
Keys in quantity of item.  
§
13.00  
Separates quantity of item from  
cost of item to be keyed in  
next.  
68.5  
68.5  
Keys in cost of item.  
AMOUNT.  
}
890.50  
890.50  
?+1  
Adds AMOUNT to sum of  
AMOUNT entries in register R1.  
+
890.50  
6.75  
Prepares to add tax.  
Recalls tax rate to display.  
TAX.  
:0  
b
60.11  
?+2  
60.11  
Adds TAX to sum of TAX entries  
in register R2.  
}
950.61  
950.61  
TOTAL.  
?+3  
Adds TOTAL to sum of TOTAL  
entries in register R3.  
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120 Section 8: Programming Basics  
Now, we’ll store the program in program memory. Do not key in the quantity and  
cost of each item; these numbers will vary each time the program is run.  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program  
mode.  
fCLEARÎ  
§
000,  
001,  
002,  
Clears program memory.  
20  
gu  
43 31  
Pauses to display AMOUNT.  
?+1  
:0  
b
003,44 40 1  
004,  
005,  
006,  
45 0  
25  
gu  
43 31  
Pauses to display TAX.  
?+2  
007,44 40 2  
008, 40  
+
?+3  
009,44 40 3  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program  
mode.  
fCLEARÎ  
§
000,  
Clears program memory.  
001,  
002,  
003,  
004,  
20  
34  
~
}
36  
gu  
43 31  
Pauses to display AMOUNT.  
?+1  
005,44 40 1  
=
006,  
007,  
008,  
009,  
40  
45 0  
25  
:0  
b
gu  
43 31  
Pauses to display TAX.  
?+2  
010,44 40 2  
011, 36  
}
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Section 8: Programming Basics 121  
Keystrokes  
(ALG mode)  
Display  
012,44 40 3  
?+3  
Note: The procedure used in the ALG program in steps 1 through 3 allows  
the algebraic program to run in the same manner as the RPN version. In the  
instructions below, the \ key is the same as the } key in ALG mode.  
Now, to run the program, first set the appropriate mode by pressing  
f] or f[ and then do the following:  
Keystrokes  
Display  
fs  
950.61  
0.00  
Sets calculator to Run mode.  
Clears registers R1– R6.  
Stores tax rate.  
fCLEAR²  
6.75?0  
13\68.5  
68.5  
Enters quantity and price of first  
item on invoice.  
t
890.50  
60.11  
950.61  
72.9  
AMOUNT for first item.  
TAX for first item.  
TOTAL for first item.  
18\72.9  
Enters quantity and price of  
second item on invoice.  
t
1,312.20  
88.57  
AMOUNT for second item.  
TAX for second item.  
1,400.77  
85.  
TOTAL for second item.  
24\85  
Enters quantity and price of  
third item on invoice.  
t
2,040.00  
137.70  
2,177.70  
345.  
AMOUNT for third item.  
TAX for third item.  
TOTAL for third item.  
5\345  
Enters quantity and price of  
fourth item on invoice.  
t
1,725.00  
116.44  
AMOUNT for fourth item.  
TAX for fourth item.  
1,841.44  
5,967.70  
TOTAL for fourth item.  
Sum of AMOUNT column.  
:1  
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122 Section 8: Programming Basics  
Keystrokes  
Display  
:2  
402.82  
Sum of TAX column.  
:3  
6,370.52  
Sum of TOTAL column.  
If the duration of the pause is not long enough to write down the number displayed,  
you can prolong it by using more than one gu instruction. Alternatively, you  
can have the program automatically stop as described next.  
Stopping Program Execution  
Stopping Program Execution Automatically. Program execution is  
automatically halted when the program executes a t instruction. To resume  
executing the program from the program line at which execution was halted, press  
t.  
Example: Replace the program above by one containing t instructions  
instead of gu instructions.  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program mode.  
Clears program memory.  
fCLEARÎ  
000,  
001,  
002,  
§
20  
31  
t
Stops program execution to display  
AMOUNT.  
?+1  
:0  
b
003,44 40 1  
004,  
005,  
006,  
45 0  
25  
t
31  
Stops program execution to display  
TAX.  
?+2  
007,44 40 2  
008, 40  
+
?+3  
009,44 40 3  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program mode.  
Clears program memory.  
fCLEARÎ  
000,  
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Section 8: Programming Basics 123  
Keystrokes  
(ALG mode)  
Display  
§
001,  
002,  
003,  
20  
34  
36  
~
}
t
004,  
31  
Stops program execution to display  
AMOUNT.  
?+1  
005,44 40 1  
=
006,  
007,  
40  
:0  
45 0  
b
008,  
009,  
25  
31  
t
Stops program execution to display  
TAX.  
?+2  
010,44 40 2  
011, 36  
012,44 40 3  
}
?+3  
Now, to run the program, first set the appropriate mode by pressing f] or  
f[ and then do the following:  
Keystrokes  
Display  
fs  
6,370.52  
0.00  
Sets calculator to Run mode.  
Clears registers R1 through R6.  
First item.  
fCLEAR²  
13\68.5  
t
68.5  
890.50  
60.11  
AMOUNT for first item.  
TAX for first item.  
t
t
950.61  
72.9  
TOTAL for first item.  
Second item.  
18\72.9  
t
1,312.20  
88.57  
AMOUNT for second item.  
TAX for second item.  
TOTAL for second item.  
Third item.  
t
t
1,400.77  
85.  
24\85  
t
2,040.00  
AMOUNT for third item.  
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124 Section 8: Programming Basics  
Keystrokes  
t
Display  
137.70  
TAX for third item.  
t
2,177.70  
345.  
TOTAL for third item.  
Fourth item.  
5\345  
t
1,725.00  
116.44  
AMOUNT for fourth item.  
TAX for fourth item.  
TOTAL for fourth item.  
Sum of AMOUNT column.  
Sum of TAX column.  
Sum of TOTAL column.  
t
t
1,841.44  
5,967.70  
402.82  
:1  
:2  
:3  
6,370.52  
Program execution is also automatically halted when the calculator overflows (refer  
to page 90) or attempts an improper operation that results in an Error display.  
Either of these conditions signifies that the program itself probably contains an  
error.  
To determine at which program line execution has halted (in order to locate the  
error), press any key to clear the Error display, then press fs to set the  
calculator to Program mode and display that program line.  
You may also want to display the current program line (by pressing fs) if  
your program has halted at one of several t instructions in your program and  
you want to determine which one that is. To continue executing the program  
afterward:  
1. Press fs to set the calculator back to Run mode.  
2. If you want to resume execution from the program line at which execution  
halted rather than from line 000, press gi followed by three digit keys  
that specify the program line desired.  
3. Press t to resume execution.  
Stopping Program Execution Manually. Pressing any key while a program  
is running halts program execution. You may want to do this if the calculated  
results displayed by a running program appear to be incorrect (indicating that the  
program itself is incorrect).  
To halt program execution during a pause in a running program (that is, when  
gu is executed), press any key.  
After stopping program execution manually, you can determine at which program  
line execution has halted and/or resume program execution as described above.  
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Section 9  
Branching and Looping  
Although the instructions in a program normally are executed in order of their  
program line numbers, in some situations it is desirable to have program execution  
transfer or “branch” to a program line that is not the next line in program memory.  
Branching also makes it possible to automatically execute portions of a program  
more than once — a process called “looping.”  
Simple Branching  
The i (go to) instruction is used in a program to transfer execution to any  
program line. The program line desired is specified by keying its three-digit line  
number into the program line containing the i instruction. When the i  
instruction is executed, program execution branches or “goes to” the program line  
specified and then continues sequentially as usual.  
You have already seen a common use of branching: the gi000 instruction  
(that is stored in program memory after the program you key in) transfers execution  
to program line 000. A i instruction can be used to branch not only backward  
in program memory — as in the case of gi000 and as illustrated above —  
but also forward in program memory. Backward branching is typically done to  
create loops (as described next); forward branching is typically done in  
conjunction with a go or gm instruction for conditional branching (as  
described afterward).  
125  
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126 Section 9: Branching and Looping  
Looping  
If a i instruction specifies a lower-numbered line in program memory, the  
instructions in the program lines between the specified line and the i instruction  
will be executed repeatedly. As can be seen in the illustration above under Simple  
Branching, once the program begins executing the “loop” it will execute it again  
and again.  
If you want to terminate the execution of a loop, you can include a go or  
gm instruction (described below) or an t instruction within the loop. You  
can also terminate execution by pressing any key while the loop is being  
executed.  
Example: The following program automatically amortizes the payments on a  
home mortgage without requiring you to press f! for each payment. It will  
amortize one month’s payments each time or one year’s payments each time the  
loop is executed, depending on whether the number 1 or 12 is in the display  
when you start running the program. Before running the program, we’ll “initialize”  
it by storing the required data in the financial registers — just as we would do if  
we were amortizing a single payment manually. We’ll run the program for a  
$150,000 mortgage at 4.75% for 30 years, and we’ll key 1 into the display just  
before running it in order to amortize monthly payments. For the first two “passes”  
through the loop we’ll execute the program one line at a time, using Ç, so that  
we can see the looping occurring; then we’ll use t to execute the entire loop a  
third time before terminating execution.  
Keystrokes  
Display  
fs  
Sets calculator to Program mode.  
Clears program memory  
fCLEARÎ  
?0  
000,  
001,  
44 0 Stores the number from the display  
into register R0. This number will be  
the number of payments to be  
amortized.  
:0  
002,  
45 0 Recalls the number of payments to  
be amortized. This program line is  
the one to which program  
execution will later branch. It is  
included because after the first time  
the loop is executed, the number in  
the “display” is replaced by the  
*
result of f!.  
More precisely, the number in the X-register.  
*
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Section 9: Branching and Looping 127  
Keystrokes  
Display  
f!  
gu  
003,  
004,  
42 11  
43 31  
Amortizes payment(s).  
Pauses to display amount of  
payment(s) applied to interest.  
~
005,  
006,  
34  
Brings amount of payment(s)  
applied to principal into  
“display.”*  
gu  
43 31  
Pauses to display amount of  
payment(s) applied to principal.  
gi002  
007,43,33,002 Transfers program execution to line  
002, so that the number of  
payments to be amortized can be  
recalled to the display before the  
f! instruction in line 003 is  
executed.  
fs  
0.00  
Sets calculator to Run mode.  
(Display shown assumes no results  
remain from previous calculations.)  
fCLEARG  
30gA  
4.75gC  
150000$  
g  
0.00  
Clears financial registers.  
Enters n.  
360.00  
0.40  
Enters i.  
150,000.00  
150,000.00  
–782.47  
0.00  
Enters PV.  
Sets payment to End.  
Calculates the monthly payment.  
Reset n to zero.  
P
0n  
1.  
1
Keys 1 into the display to amortize  
monthly payments.  
Ê
Ê
001,  
44 0  
?
Line 001:  
0.  
1.00  
002,  
45 0  
:
Line 002:  
0. This is the  
beginning of the first pass through  
the loop.  
1.00  
003,  
Ê
42 11  
f!  
.
Line 003:  
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128 Section 9: Branching and Looping  
Keystrokes  
Display  
–593.75  
Portion of first month’s payment  
applied to interest.  
Ê
Ê
004,  
43 31  
34  
gu  
.
Line 004:  
–593.75  
005,  
Line 005:  
~
.
–188.72  
Portion of first month’s payment  
applied to principal.  
Ê
Ê
006,  
43 31  
gu  
Line 006:  
.
–188.72  
007,43,33,002  
gi  
Line 007:  
002. This is the  
end of the first pass through the  
loop.  
–188.72  
Ê
Ê
002,  
45 0  
:
0. Program  
Line 002:  
execution has branched to the  
beginning of the loop for the  
second pass through it.  
1.00  
003,  
42 11  
Line 003: .  
f!  
–593.00  
Portion of second month’s payment  
applied to interest.  
Ê
Ê
004,  
43 31  
34  
gu  
.
Line 004:  
–593.00  
005,  
Line 005:  
~
.
–189.47  
Portion of second month’s payment  
applied to principal.  
Ê
Ê
006,  
43 31  
gu  
Line 006:  
.
–189.47  
007,43,33,002  
–189.47  
gi  
Line 007:  
002.  
This is the end of the second pass  
through the loop.  
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Section 9: Branching and Looping 129  
Keystrokes  
Display  
t
–592.25  
Portion of third month’s payment  
applied to interest.  
–190.22  
–190.22  
Portion of third month’s payment  
applied to principal.  
t(or any key)  
Halts program execution.  
Conditional Branching  
Often there are situations when it is desirable for a program to be able to branch  
to different lines in program memory, depending on certain conditions. For  
example, a program used by an accountant to calculate taxes might need to  
branch to different program lines depending on the tax rate for the particular  
income level.  
The hp 12c platinum provides two conditional test instructions that are used in  
programs for conditional branching:  
z
g o tests whether the number in the X-register (represented by the x in the  
key symbol) is less than or equal to the number in the Y-register (represented  
by the y in the key symbol). As discussed in Appendix A, the number in the  
X-register is simply the number that would, if the calculator were in Run mode,  
be currently in the display; and the number in the Y-register is the number  
that would, if the calculator were in Run mode, have been in the display  
when \ was pressed. For example, pressing 4\5 would place the  
number 4 in the Y-register and the number 5 in the X-register.  
z
g m tests whether the number in the X-register is equal to zero.  
The possible results of executing either of these instructions are:  
z
If the condition tested for is true when the instruction is executed, program  
execution continues sequentially with the instruction in the next line of  
program memory.  
z
If the condition tested for is false when the instruction is executed, program  
execution skips the instruction in the next line of program memory and  
continues with the instruction in the following line.  
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130 Section 9: Branching and Looping  
These rules can be summarized as “DO if TRUE”.  
The program line immediately following that containing the conditional test  
instruction can contain any instruction; however, the most commonly used  
instruction there is i. If a i instruction follows a conditional test instruction,  
program execution branches elsewhere in program memory if the condition is true  
and continues with the next line in program memory if the condition is false.  
Example: The following program calculates income tax at a rate of 20% on  
incomes of $20,000 or less and 25% on incomes of more than $20,000. To  
conserve program lines, the program assumes that the test value — 20,000 — has  
been stored in register R0 and the tax rates — 20 and 25 — have been stored in  
registers R1 and R2, respectively.  
Note: If a program requires that certain numbers be in the X- and  
Y-registers when instructions such as go are executed, it is extremely  
helpful when writing the program to show the quantities in each register after  
each instruction is executed, as in the following diagram (which shows an  
RPN mode program, although it works in a similar way in ALG mode.).  
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Section 9: Branching and Looping 131  
RPN program notes: We’ll key the income into the display before running the  
program so that it will be in the X-register when the :0 instruction in program  
line 001 is executed. This instruction will place the test value 20,000 in the  
X-register and (as explained in Appendix A) move the income into the Y-register.  
The ~ instruction in program line 002 will exchange the numbers in the X- and  
Y-registers (as also explained in Appendix A): that is, it will place the income back  
into the X-register and place the test value into the Y-register. This is necessary  
because when either the :2 instruction in line 005 or the :1 instruction in  
line 007 is executed, the number in the X-register is moved into the Y-register; if the  
~ instruction were not included, the test value 20,000, rather than the income,  
would be in the Y-register when the b instruction in line 008 is executed.  
Keystrokes  
Display  
(RPN mode)  
f]  
fs  
007,43,33,002  
Sets calculator to Program mode.  
(Display shows program line at  
which execution was halted at  
end of preceding example.)  
fCLEARÎ  
000,  
Clears program memory.  
:0  
001,  
002,  
45 0 Recalls test value into X-register  
and places income in Y-register.  
~
34  
Places income in X-register and  
test value in Y-register.  
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132 Section 9: Branching and Looping  
Keystrokes  
Display  
(RPN mode)  
go  
003,  
43 34  
Tests whether number in X-register  
(income) is less than or equal to  
number in Y-register (20,000).  
gi007  
004,43,33,007 If condition is true, branches to  
program line 007.  
:2  
005,  
45 2 If condition is false, recalls 25%  
tax rate to X-register.  
gi008  
:1  
006,43,33,008 Branches to program line 008.  
007,  
45 1 Recalls 20% tax rate to X-register.  
b
008,  
25  
Calculates tax.  
fs  
–190.22  
Sets calculator to Run mode.  
(Display shows results of running  
of previous program.)  
ALG program notes: We’ll key the income into the display before running the  
program. We’ll store it in R9 so it will be available for the examples in the next  
chapter. By keying the income into the display before running the program, we  
ensure that it will be in the X-register when the :0 instruction in program line  
002 is executed. This instruction will place the test value 20,000 in the X-register  
and move the income into the Y-register. The ~ instruction in program line 003  
will exchange the numbers in the X- and Y-registers: that is, it will place the income  
back into the X-register and place the test value into the Y-register. This is  
necessary because when either the :2 instruction in line 007 or the :1  
instruction in line 009 is executed, the number in the X-register is moved into the  
Y-register; if the ~ instruction were not included, the test value 20,000, rather  
than the income, would be in the Y-register when the b instruction in line 010 is  
executed.  
Keystrokes  
Display  
(ALG mode)  
f[  
fs  
007,43,33,002  
Sets calculator to Program mode.  
(Display shows program line at  
which execution was halted at  
end of preceding example.)  
fCLEARÎ  
000,  
Clears program memory.  
?9  
001,  
44 9 Stores income into register R9.  
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Section 9: Branching and Looping 133  
Keystrokes  
(ALG mode)  
Display  
:0  
002,  
45 0 Recalls test value into X-register  
and places income in Y-register.  
~
003,  
34  
Places income in X-register and  
test value in Y-register.  
§
004,  
005,  
20  
Prepares for multiplication.  
go  
43 34  
Tests whether number in X-register  
(income) is less than or equal to  
number in Y-register (20,000).  
gi009  
006,43,33,009 If condition is true, branches to  
program line 009.  
:2  
007,  
45 2 If condition is false, recalls 25%  
tax rate to X-register.  
gi010  
:1  
b
008,43,33,010 Branches to program line 010.  
009,  
45 1 Recalls 20% tax rate to X-register.  
010,  
25  
36  
Divides tax rate by 100.  
Calculates tax.  
}
011,  
fs  
–190.22  
Sets calculator to Run mode.  
(Display shows results of running  
of previous program.)  
Now, we'll store the required numbers in registers R0, R1, and R2, then we’ll run the  
program, using Ç so that we can check that the branching occurs properly. It’s  
good practice with programs containing conditional test instructions to check that  
the program branches correctly for all possible conditions: in this case, if the  
income is less than, equal to, or greater than the test value.  
Keystrokes  
Display  
(RPN mode)  
20,000.00  
20.00  
20000?0  
20?1  
25?2  
15000  
Stores test value in register R0.  
Stores 20% tax rate in register R1.  
Stores 25% tax rate in register R2.  
25.00  
15,000.  
Keys income less than test value  
into display and X-register.  
Ê
001,  
45 0  
:
0.  
Line 001:  
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134 Section 9: Branching and Looping  
Keystrokes  
Display  
(RPN mode)  
20,000.00  
Test value has been recalled to  
X-register, moving income to  
Y-register.  
Ê
002,  
34  
~
Line 002:  
15,000.00  
Income has been placed in  
X-register and test value has been  
placed in Y-register.  
Ê
Ê
003,  
43 34  
Line 003:  
go  
15,000.00  
004,43,33,007  
o
Condition tested by  
was true,  
so program execution continued  
with line 004: gi007.  
15,000.00  
Ê
Ê
007,  
45 1  
:
1.  
Line 007:  
20.00  
20% tax rate has been recalled to  
X-register, moving income to  
Y-register.  
008,  
25  
b
.
Line 008:  
3,000.00  
20,000.  
20% of 15,000 = 3,000.  
20000  
Keys income equal to test value  
into display and X-register.  
Ê
001,  
45 0  
:
0.  
Line 001:  
20,000.00  
Test value has been recalled to  
X-register, moving income to  
Y-register.  
Ê
Ê
002,  
34  
~
.
Line 002:  
20,000.00  
Income has been placed in  
X-register and test value has been  
placed in Y-register.  
003,  
43 34  
Line 003 .  
go  
20,000.00  
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Section 9: Branching and Looping 135  
Keystrokes  
(RPN mode)  
Display  
Ê
Ê
Ê
004,43,33,007  
o
Condition tested by  
was true,  
so program execution continued  
with line 004: gi007.  
20,000.00  
007,  
45 1  
:
1.  
Line 007:  
20.00  
20% tax rate has been recalled to  
X-register, moving income to  
Y-register.  
008,  
25  
b
.
Line 008:  
4,000.00  
25,000.  
20% of 20,000 = 4,000.  
25000  
Keys income greater than test value  
into display and X-register.  
Ê
001,  
45 0  
:
0.  
Line 001:  
20,000.00  
Test value has been recalled to  
X-register, moving income to  
Y-register.  
Ê
002,  
34  
~
.
Line 002:  
25,000.00  
Income has been placed in  
X-register and test value has been  
placed in Y-register.  
Ê
Ê
003,  
43 34  
Line 003: .  
go  
25,000.00  
005,  
45 2  
o
Condition tested by  
was false,  
so program execution skipped the  
next line and continued at line  
005: :2.  
25.00  
25% tax rate has been recalled to  
X-register, moving income to  
Y-register.  
Ê
Ê
006,43,33,008  
25.00  
gi  
008.  
Line 006:  
008,  
25  
b
.
Line 008:  
6,250.00  
25% of 25,000 = 6,250.  
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136 Section 9: Branching and Looping  
Keystrokes  
Display  
(ALG mode)  
20,000.00  
20.00  
20000?0  
20?1  
25?2  
15000  
Stores test value in register R0.  
Stores 20% tax rate in register R1.  
Stores 25% tax rate in register R2.  
25.00  
15,000.  
Keys income less than test value  
into display and X-register.  
Ê
Ê
001,  
44 9  
?
9.  
Line 001:  
15,000.00  
Stores income into register R9.  
002,  
45 0  
:
0.  
Line 002:  
20,000.00  
Test value has been recalled to  
X-register, moving income to  
Y-register.  
Ê
003,  
34  
~
Line 003:  
15,000.00  
Income has been placed in  
X-register and test value has been  
placed in Y-register.  
Ê
Ê
Ê
004,  
20  
§
Line 004:  
15,000.00  
005,  
43 34  
go  
Line 005:  
15,000.00  
006,43,33,009  
o
Condition tested by  
was true,  
so program execution continued  
with line 006: gi009.  
15,000.00  
Ê
009,  
45 1  
:
1.  
Line 009:  
20.00  
20% tax rate has been recalled to  
X-register, moving income to  
Y-register.  
Ê
Ê
010,  
0.20  
011,  
25  
36  
b
.
Line 010:  
Divides tax rate by 100.  
Line 011:  
}
.
3,000.00  
20% of 15,000 = 3,000.  
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Section 9: Branching and Looping 137  
Keystrokes  
(ALG mode)  
Display  
Ê
012,43,33,000  
3,000.00  
gi  
000.  
Line 012:  
20,000.  
20000  
Keys income equal to test value  
into display and X-register.  
Ê
001,  
44 9  
?
9.  
Line 001:  
20,000.00  
Stores income into register R9.  
Ê
002,  
45 0  
:
0.  
Line 002:  
20,000.00  
Test value has been recalled to  
X-register, moving income to  
Y-register.  
Ê
003,  
34  
20  
~
.
Line 003:  
20,000.00  
Income has been placed in  
X-register and test value has been  
placed in Y-register.  
Ê
Ê
Ê
004,  
§
Line 004:  
20,000.00  
005,  
43 34  
go  
Line 005:  
.
20,000.00  
006,43,33,009  
o
Condition tested by  
was true,  
so program execution continued  
with line 006: gi009.  
20,000.00  
Ê
009,  
45 1  
:
1.  
Line 009:  
20.00  
20% tax rate has been recalled to  
X-register, moving income to  
Y-register.  
Ê
Ê
Ê
010,  
0.20  
011,  
25  
36  
b
.
Line 010:  
Divides tax rate by 100.  
Line 011:  
20% of 20,000 = 4,000.  
gi  
}
.
4,000.00  
012,43,33,000  
4,000.00  
Line 012:  
000.  
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138 Section 9: Branching and Looping  
Keystrokes  
Display  
(ALG mode)  
25,000.  
25000  
Keys income greater than test value  
into display and X-register.  
Ê
001,  
44 9  
?
9.  
Line 001:  
25,000.00  
Stores income into register R9.  
Ê
Ê
002,  
45 0  
:
0.  
Line 002:  
20,000.00  
Test value has been recalled to  
X-register, moving income to  
Y-register.  
003,  
34  
20  
~
.
Line 003:  
25,000.00  
Income has been placed in  
X-register and test value has been  
placed in Y-register.  
Ê
Ê
Ê
004,  
§
.
Line 004:  
25,000.00  
005,  
43 34  
go  
.
Line 005:  
25,000.00  
007,  
45 2  
o
Condition tested by  
was false,  
so program execution skipped the  
next line and continued at line  
007: :2.  
25.00  
25% tax rate has been recalled to  
X-register, moving income to  
Y-register.  
Ê
Ê
Ê
008,43,33,010  
25.00  
gi  
010.  
Line 008:  
010,  
25  
b
.
Line 010:  
0.25  
Divides tax rate by 100.  
011,  
36  
}
.
Line 011:  
6,250.00  
25% of 25,000 = 6,250.  
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Section 10  
Program Editing  
There are various reasons why you might want to modify a program you have  
stored in Program memory: to correct a program that turns out to have errors; to  
insert new instructions such as ? to store intermediate results or u to display  
intermediate results; or to replace a u instruction by an t instruction.  
Rather than clearing program memory and keying in the modified program, you  
can modify the program already stored in the calculator. This is called program  
editing.  
Changing the Instruction in a Program Line  
To change a single instruction in program memory:  
1. Press fs to set the calculator to Program mode.  
2. Use Ç, Ü, or i. to set the calculator to the program line preceding  
the line containing the instruction to be changed.  
3. Key in the new instruction.  
For example, to change the instruction stored in program line 005, press  
gi.004, then key in the new instruction that is to be stored in program line  
005. The instruction previously stored in line 005 will be replaced; it is not  
automatically “bumped” into line 006.  
Example: With the last program from the preceding section still stored in the  
calculator, suppose you wanted to use register R2 for some other purpose, and so  
you needed to replace the :2 instruction in program line 005 in the RPN  
program (line 007 in the ALG program) with, say, :6. You could change the  
instruction in line 005 as follows:  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program mode.  
gi.004  
004,43,33,007  
Sets calculator to program line  
preceding that containing the  
instruction to be changed.  
:6  
005,  
45 6  
Keys new instruction into program  
line 005, replacing the :2  
instruction previously there.  
139  
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140 Section 10: Program Editing  
Keystrokes  
Display  
(RPN mode)  
Ê
006,43,33,008  
6,250.00  
Shows that instruction in program  
line 006 has not been changed.  
fs  
Sets calculator back to Run mode.  
(Display shown assumes results  
remain from last example in  
preceding section.)  
:2?6  
25.00  
Copies tax rate from R2 into R6.  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program mode.  
gi.006  
006,43,33,009  
Sets calculator to program line  
preceding that containing the  
instruction to be changed.  
:6  
007,  
45 6  
Keys new instruction into program  
line 007, replacing the :2  
instruction previously there.  
Ê
008,43,33,010  
6,250.00  
Shows that instruction in program  
line 008 has not been changed.  
fs  
Sets calculator back to Run mode.  
(Display shown assumes results  
remain from last example in  
preceding section.)  
:2?6  
25.00  
Copies tax rate from R2 into R6.  
Adding Instructions at the End of a Program  
To add one or more instructions at the end of the last program stored in program  
memory:  
1. Press fs to set the calculator to Program mode.  
2. Press gi. followed by three digits that specify the last line you keyed  
into program memory (that is, the highest numbered line, not necessarily the  
line most recently keyed in).  
3. Key in the new instruction or instructions.  
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Section 10: Program Editing 141  
Note: To add one or more instructions at the end of a program that is not  
the last program stored in program memory, use the procedure described  
below under Adding Instructions within a Program.  
Example: With the last program from the preceding section stored in the  
calculator, suppose you wanted to calculate the net income after taxes. In the RPN  
program, you could add a - instruction at the end in order to calculate the net  
income after taxes. In the ALG program, the tax computed would need to be  
subtracted from the income previously stored in R9 (and this will be done by  
changing the sign of the tax to make it negative and then adding it to the income).  
You could do this as follows:  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program mode.  
gi.008  
008,  
009,  
25 Sets calculator to last line keyed  
into program memory.  
-
30  
Keys new instruction into  
program line 009.  
fs  
25.00  
Sets calculator back to Run mode.  
12,000.00  
15000t  
Net income after 20% tax is  
subtracted from $15,000  
income.  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program mode.  
gi.011  
011,  
012,  
013,  
36 Sets calculator to last line keyed  
into program memory.  
Þ
+
16  
40  
Keys new instruction into  
program line 012.  
Keys new instruction into  
program line 013.  
:9  
}
014,  
015,  
25.00  
45 9 Keys new instruction into  
program line 014.  
36  
Keys new instruction into  
program line 015.  
fs  
Sets calculator back to Run mode.  
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142 Section 10: Program Editing  
Keystrokes  
Display  
(ALG mode)  
12,000.00  
15000t  
Net income after 20% tax is  
subtracted from $15,000  
income.  
Adding Instructions within a Program  
If an instruction is to be added within a program, simply keying it in will replace  
the instruction previously stored in that program line, as described above; the  
contents of all higher-numbered program lines remain unchanged.  
To add instructions within a program, you could simply key in the new instructions,  
beginning at the proper program line, followed by the original instructions from  
that program line through the end of the program. This method is described below  
under Adding Instructions by Replacement. When instructions must be added in the  
middle of a long program, however, using this method will require you to key in  
numerous instructions — namely, the original instructions from the point at which  
the new instructions are added through the end of program memory. Since keying  
in these instructions may require a significant amount of time, in such situations you  
may prefer to use the method described below under Adding Instructions by  
Branching.  
That method basically involves branching to the new instructions which are stored  
at the end of program memory, then branching back to the program line  
immediately following the line from which you branched out. Adding instructions  
by branching is not so simple as adding instructions by replacement; however, it  
generally will require fewer keystrokes whenever there are more than four program  
lines between (and including) the first line to be executed after the new instruction(s)  
and the last line you keyed into program memory. Furthermore, if program  
memory includes branches to program lines following the point at which the new  
instruction(s) are being added, adding instructions by branching will not require  
that you change the line numbers specified in the i instructions, which may be  
necessary when you add instructions by replacement.  
Adding Instructions by Replacement  
1. Press fs to set the calculator to Program mode.  
2. Press gi. followed by three digits that specify the last program line to  
be executed before the added instruction(s). This sets the calculator to the  
proper program line for adding the new instruction(s) in the next step.  
3. Key in the new instruction or instructions.  
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Section 10: Program Editing 143  
4. Key in the original instruction or instructions, beginning with the first  
instruction to be executed after the added instruction(s), and continuing  
through the last instruction you keyed into program memory.  
Note: If program memory includes branches to program lines following that  
at which the first new instruction is being added, remember to change the  
line number(s) specified in the i instruction(s) — as described above  
under Changing the Instruction in a Program Line — to the actual new line  
number(s).  
Example: Assuming you have made the program modifications as in the  
preceding example, suppose you now wanted to insert a t instruction before  
the program calculates net income after tax so that the program will display the  
amount of the tax before displaying the net income after tax. The program should  
be modified by making the changes below:  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program mode.  
gi.008  
008,  
25 Sets calculator to last program  
line to be executed, which  
contains the b instruction.  
t
-
009,  
010,  
31  
30  
Keys in new instruction.  
Keys in original instruction, which  
was replaced by new instruction  
added.  
fs  
12,000.00  
3,000.00  
Sets calculator back to Run mode.  
15000t  
Twenty percent tax on $15,000  
income.  
t
12,000.00  
Net income after tax.  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program mode.  
gi.011  
011,  
012,  
36 Sets calculator to last line keyed  
into program memory for original  
program.  
t
31  
Keys new instruction into  
program line 012.  
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144 Section 10: Program Editing  
Keystrokes  
Display  
(ALG mode)  
Þ
013,  
014,  
015,  
016,  
16  
40  
Keys new instruction into  
program line 013.  
+
Keys new instruction into  
program line 014.  
:9  
45 9 Keys new instruction into  
program line 015.  
}
36  
Keys new instruction into  
program line 016.  
fs  
12,000.00  
3,000.00  
Sets calculator back to Run mode.  
15000t  
Twenty percent tax on $15,000  
income.  
t
12,000.00  
Net income after 20% tax is  
subtracted from $15,000  
income.  
Adding Instructions by Branching  
1. Press fs to set the calculator to Program mode.  
2. Press gi. followed by three digits that specify the program line  
immediately preceding the point at which the new instruction(s) are being  
added — usually, the last program line to be executed before the added  
instruction(s). This sets the calculator to the proper program line for inserting  
a i instruction in the next step. This i instruction will replace whatever  
instruction was already stored there, but that instruction will be keyed back  
into program memory, to be executed just after the new instructions, in step  
7.  
3. Press gi followed by three digits that specify the second line after the  
last line you keyed into program memory. (Branching to the second line  
rather than to the first is necessary because the first line following the last  
program in program memory must contain a i000 instruction. The  
i000 instruction ensures that program execution will branch to line 000  
and halt after the program is run.) For example, if the last line you keyed into  
program memory was line 010, you would press gi012 at this step,  
preserving the gi000 in line 011.  
4. Press gi. followed by three digits that specify the last line you keyed  
into program memory.  
5. Press gi000. This automatically converts a data storage register into  
seven additional lines of program memory (if there was not already a  
gi000 instruction remaining at the end of program memory), and it  
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Section 10: Program Editing 145  
ensures that program execution will branch to line 000 after the program is  
run.  
6. Key in the instruction(s) being added.  
7. Key in the instruction that originally immediately followed the point at which  
the new instruction(s) are being added — that is, the first instruction to be  
executed after the added instruction(s). (This instruction was replaced by the  
i instruction keyed in at step 3.)  
8. Press gi followed by three digits that specify the second line following  
the point at which the new instruction(s) are being added. This i  
instruction will cause program execution to branch back to the proper line  
within the original program.  
Example: Continuing with the preceding example, suppose incomes less than or  
equal to $7,500 were not to be taxed. You could modify the program to check for  
this condition and stop at line 000, displaying the original income keyed in, by  
storing 7,500 in register R3 and adding the following instructions between lines  
000 and 001 (the added lines are the same in RPN and ALG modes):  
:3~gogi000. Since there are more than four instructions between  
(and including) the first line to be executed after the added instructions (line 001)  
and the last line you keyed into program memory (line 010 in RPN and line 016 in  
ALG), it will require fewer keystrokes to add the new instructions by branching  
than to add them by replacement.  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program mode.  
gi.000  
000,  
Sets calculator to program line  
immediately preceding point at  
which new instructions are being  
added. (In this particular example,  
this step could have been skipped  
since calculator was already set at  
the proper program line.)  
gi012  
001,43,33,012 Branches to program line 012, the  
second line after last line of  
program.  
gi.010  
010,  
30 Sets calculator to last line of  
program so that the gi000  
instruction keyed in next will be  
stored as the last line of the current  
program.  
gi000  
011,43,33,000 Ends the current program with a  
gi000.  
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146 Section 10: Program Editing  
Keystrokes  
Display  
(RPN mode)  
:3  
~
012,  
013,  
014,  
45 3  
34  
Added instructions.  
go  
43 34  
gi000  
015,43,33,000  
:0  
016,  
45 0 Keys in instruction immediately  
following point at which new  
instructions are being added. (This  
instruction was replaced in line  
001 by gi012 instruction.)  
gi002  
017,43,33,002 Branches back to second line (line  
002) following point at which new  
instructions are being added.  
fs  
12,000.00  
7,500.00  
6,500.00  
Sets calculator back to Run mode.  
Stores test value in register R3.  
7500?3  
6500t  
Runs program for income less than  
$7,500. Display shows original  
income keyed in, indicating that tax  
is zero.  
3,000.00  
15000t  
Tax on $15,000 income.  
t
12,000.00  
Net income after tax. This shows  
program still works for an income  
greater than $7,500 and less than  
$20,000.  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program mode.  
gi.000  
000,  
Sets calculator to program line  
immediately preceding point at  
which new instructions are being  
added. (In this particular example,  
this step could have been skipped  
since calculator was already set at  
the proper program line.)  
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Section 10: Program Editing 147  
Keystrokes  
(ALG mode)  
Display  
gi018  
001,43,33,018 Branches to program line 018, the  
second line after last line of  
program.  
gi.016  
016,  
36 Sets calculator to last line of  
program so that the gi000  
instruction keyed in next will be  
stored as the last line of the current  
program.  
gi000  
017,43,33,000 Ends the current program with a  
gi000.  
:3  
~
018,  
019,  
020,  
45 3  
34  
Added instructions.  
go  
43 34  
gi000  
021,43,33,000  
?9  
022,  
44 9 Keys in instruction immediately  
following point at which new  
instructions are being added. (This  
instruction was replaced in line  
001 by gi018 instruction.)  
gi002  
023,43,33,002 Branches back to second line (line  
002) following point at which new  
instructions are being added.  
fs  
12,000.00  
7,500.00  
6,500.00  
Sets calculator back to Run mode.  
Stores test value in register R3.  
7500?3  
6500t  
Runs program for income less than  
$7,500. Display shows original  
income keyed in, indicating that tax  
is zero.  
3,000.00  
15000t  
Tax on $15,000 income.  
t
12,000.00  
Net income after tax. This shows  
program still works for an income  
greater than $7,500 and less than  
$20,000.  
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148 Section 10: Program Editing  
The following illustration of the edited RPN program shows how program  
execution branches to the instructions added at the end of program memory, then  
branches back. While the actual program in ALG mode is different, the illustration  
does indicate the method used.  
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Section 11  
Multiple Programs  
You can store multiple programs in program memory, provided that you separate  
them by instructions that will halt program execution after each program is run and  
return to the beginning of the program if it is run again. You can run programs  
after the first one stored in program memory by setting the calculator to the first  
line of the program using i before pressing t.  
Storing Another Program  
To store a program after another program is already stored in program memory:  
1. Press fs to set the calculator to Program mode. Do not clear program  
memory.  
2. Press gi. followed by three digits that specify the number of the last  
line you keyed into program memory.  
Note: If this is the second program to be stored in program memory, you  
will need to ensure that a i000 instruction separates it from the first  
program by doing step 3. If there are already two or more programs stored  
in program memory, skip step 3 and proceed with step 4.  
3. Press gi000. This automatically converts a data storage register into  
seven additional lines of program memory (if there was not already a  
i000 instruction remaining at the end of program memory), and it  
ensures that program execution will branch to line 000 after the first  
program is run.  
4. Key the program into program memory. If you are storing a program that  
you originally had written to be stored at the beginning of program memory  
and the program contains a i instruction, be sure to change the line  
number specified in the instruction so that the program will branch to the  
actual new line number.  
Note: The next two steps are included so that program execution will halt  
after this program is run and will return to the beginning of the program if it  
is run again. If the program ends with a loop, you should skip steps 5 and 6  
since the instructions in those steps would serve no purpose and never be  
executed.  
5. Press t. This halts program execution at the end of the program.  
6. Press gi followed by three digit keys that specify the first line number of  
your new program. This transfers program execution to the beginning of the  
new program when the program is run again.  
149  
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150 Section 11: Multiple Programs  
Example 1: Assuming that program memory still contains the last program from  
the preceding section (which consisted of 17 program lines in RPN mode and 23  
program lines in ALG mode), store after that program the office-supplies program  
from Section 8 (page 104). Since this is the second program to be stored in  
program memory, we’ll ensure that a i000 instruction separates it from the first  
program by doing step 3 in the procedure above. Furthermore, since this program  
does not end with a loop, we’ll do steps 5 and 6 too.  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program mode.  
gi.017  
017,43,33,002 Sets calculator to last line keyed  
into program memory.  
gi000  
018,43,33,000 Ensures that second program is  
separated from first by i000.  
\
019,  
020,  
021,  
022,  
023,  
024,  
025,  
026,  
36  
2
2
5
5
b
-
25  
30  
5
Keys in program.  
5
+
t
40  
31  
Halts program execution.  
gi019  
027,43,33,019 Branches to beginning of program.  
fs  
12,000.00  
Sets calculator back to Run mode.  
(Display shown assumes results  
remain from running program in  
previous example.)  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program mode.  
gi.023  
023,43,33,002 Sets calculator to last line keyed  
into program memory.  
gi000  
024,43,33,000 Ensures that second program is  
separated from first by i000.  
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Section 11: Multiple Programs 151  
Keystrokes  
(ALG mode)  
Display  
-
025,  
026,  
027,  
028,  
029,  
030,  
031,  
032,  
30  
2
5
2
5
b
+
25  
40  
5
Keys in program.  
5
}
t
36  
31  
Halts program execution.  
gi025  
033,43,33,025 Branches to beginning of program.  
fs  
12,000.00  
Sets calculator back to Run mode.  
(Display shown assumes results  
remain from running program in  
previous example.)  
Example 2: With the two programs now stored in program memory from the  
preceding examples (occupying 27 program lines in RPN mode and 33 lines in  
ALG mode), store the amortization program from Section 9(page 125). Since there  
are already two programs stored in program memory, we’ll skip step 3 in the  
procedure above. Furthermore, since the amortization program ends with a loop,  
we’ll skip steps 5 and 6. When the amortization program was stored at the  
beginning of program memory, the i instruction at the end of the program  
branched to the :0 instruction in line 002. In the RPN program, since the :0  
instruction is now in line 029, we’ll specify that line number with the i  
instruction in line 034. In the ALG program, since the :0 instruction is now in  
line 035, we’ll specify that line number with the i instruction in line 041.  
Keystrokes  
Display  
(RPN mode)  
fs  
Sets calculator to Program  
mode.  
gi.027  
027,43,33,019 Sets calculator to last line  
keyed into program memory.  
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152 Section 11: Multiple Programs  
Keystrokes  
Display  
(RPN mode)  
?0  
028,  
029,  
030,  
031,  
032,  
033,  
44 0  
45 0  
42 11  
43 31  
34  
:0  
f!  
gu  
~
Keys in program  
gu  
43 31  
gi029  
034,43,33,029  
Keystrokes  
(ALG mode)  
Display  
fs  
Sets calculator to Program  
mode.  
gi.033  
033,43,33,025 Sets calculator to last line  
keyed into program memory.  
?0  
034,  
035,  
036,  
037,  
038,  
039,  
44 0  
45 0  
42 11  
43 31  
34  
:0  
f!  
gu  
~
Keys in program  
gu  
43 31  
gi035  
040,43,33,035  
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Section 11: Multiple Programs 153  
Running Another Program  
To run a program that does not begin with program line 001:  
1. Press fs to set the calculator to Run mode. If the calculator is already in  
Run mode, skip this step.  
2. Press gi followed by three digits that specify the first line of the  
program.  
3. Press t.  
Example: Run the office-supplies program, now stored in the calculator  
beginning at program line 019 in RPN mode and line 025 in ALG mode, for the  
typewriter listing for $625.  
Keystrokes  
Display  
(RPN mode)  
fs  
12,000.00  
12,000.00  
473.75  
Sets calculator to Program  
mode.  
gi019  
625t  
Sets calculator to first line of  
program to be executed.  
Net cost of typewriter.  
Keystrokes  
(ALG mode)  
Display  
fs  
12,000.00  
Sets calculator to Program  
mode.  
gi025  
625t  
12,000.00  
473.75  
Sets calculator to first line of  
program to be executed.  
Net cost of typewriter.  
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Part III  
Solutions  
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Section 12  
Real Estate and Lending  
Annual Percentage Rate Calculations With Fees  
Borrowers are usually charged fees in connection with the issuance of a mortgage,  
which effectively raises the interest rate. The actual amount received by the  
borrower (PV) is reduced, while the periodic payments remain the same. Given the  
life or term of the mortgage, the interest rate, the mortgage amount, and the basis  
of the fee charge (how the fee is calculated), the true Annual Percentage Rate (APR)  
may be calculated. Information is entered as follows:  
1. Press and fCLEARG.  
2. Calculate and enter the periodic payment amount of the loan.  
a. Key in the total number of payment periods; press n.  
b. Key in the periodic interest rate (as a percentage); press ¼.  
c. Key in the mortgage amount; press $.  
*
d. To obtain the periodic payment amount, press P.*  
3. Calculate and key in the actual net amount disbursed.  
*
RPN Mode:  
z
If fees are stated as a percentage of the mortgage amount (points),  
recall the mortgage amount (:$); key in the fee (percentage)  
rate; press b-$.  
z
z
If fees are stated as a flat charge, recall the mortgage amount  
(:$); key in the fee amount (flat charge); press -$.  
If fees are stated as a percentage of the mortgage amount plus a flat  
charge, recall the mortgage amount (:$); key in the fee  
(percentage) rate, press b-; key in the fee amount (flat charge);  
press -$.  
Positive for cash received; negative for cash paid out.  
*
156  
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Section 12: Real Estate and Lending 157  
ALG Mode:  
z
If fees are stated as a percentage of the mortgage amount (points),  
recall the mortgage amount (:$); press -; key in the fee  
(percentage) rate; press b$.  
z
z
If fees are stated as a flat charge, recall the mortgage amount  
(:$); press -; key in the fee amount (flat charge); press $.  
If fees are stated as a percentage of the mortgage amount plus a flat  
charge, recall the mortgage amount (:$); press -; key in the  
fee (percentage) rate, press b-; key in the fee amount (flat  
charge); press $.  
4. Press ¼ to obtain the interest rate per compounding period.  
5. RPN: To obtain the annual nominal percentage rate, key in the number  
of periods per year, then press µ.  
5. ALG: To obtain the annual nominal percentage rate, press µ. Key in the  
number of periods per year, then press ³.  
Example 1: A borrower is charged 2 points for the issuance of his mortgage. If  
the mortgage amount is $160,000 for 30 years and the interest rate is 5.5% per  
year, with monthly payments, what true annual percentage rate is the borrower  
?
paying (One point is equal to 1% of the mortgage amount.)  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
30gA  
5.5gC  
fCLEARG  
30gA  
5.5gC  
360.00  
0.46  
Months (into n)  
% monthly interest rate  
(into i).  
160,000.00  
–908.46  
160000$  
160000$  
Loan amount (into PV).  
P
P
Monthly payment  
(calculated).  
:$2b-  
Actual amount received  
by borrower (into PV).  
:$-2b  
156,800.00  
0.47  
$
$
¼
¼
% monthly interest rate  
(calculated).  
5.68  
12§  
Annual percentage rate.  
§12³  
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158 Section 12: Real Estate and Lending  
Example 2: Using the same information as given in example 1, calculate the  
APR if the mortgage fee is $750 instead of a percentage.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
30gA  
5.5gC  
fCLEARG  
30gA  
5.5gC  
360.00  
0.46  
Months (into n)  
Percent monthly interest  
rate (into i).  
160,000.00  
–908.46  
160000$  
160000$  
Loan amount (into PV).  
P
P
Monthly payment  
(calculated).  
:$750-  
Effective mortgage  
amount (into PV).  
:$-750  
159,250.00  
0.46  
$
$
¼
¼
Monthly interest rate  
(calculated).  
5.54  
12§  
Annual percentage rate.  
§12³  
Example 3: Again using the information given in example 1, what is the APR if  
?
the mortgage fee is stated as 2 points plus $750  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
30gA  
5.5gC  
fCLEARG  
30gA  
5.5gC  
360.00  
0.46  
Months (into n)  
Percent monthly interest  
rate (into i).  
160,000.00  
–908.46  
160000$  
160000$  
Loan amount (into PV).  
P
P
Monthly payment  
(calculated).  
:$2b- :$-2b  
750-$  
-750$  
Effective mortgage  
amount (into PV).  
156,050.00  
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Section 12: Real Estate and Lending 159  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
¼
¼
0.48  
5.73  
Monthly interest rate  
(calculated).  
12§  
§12³  
Annual percentage rate.  
Price of a Mortgage Traded at a Discount or Premium  
Mortgages may be bought and/or sold at prices lower (discounted) or higher (at a  
premium) than the remaining balance of the loan at the time of purchase. Given  
the amount of the mortgage, the periodic payment, the timing and amount of the  
balloon or prepayment, and the desired yield rate, the price of the mortgage may  
be found. It should be noted that the balloon payment amount (if it exists) occurs  
coincident with, and does not include, the last periodic payment amount.  
Information is entered as follows:  
1. Press and fCLEARG.  
2. Key in the total number of periods until the balloon payment or prepayment  
occurs; press n. (If there is no balloon payment, key in total number of  
payments and press n.)  
3. Key in the desired periodic interest rate (yield) and press ¼.  
4. Key in the periodic payment amount; press P.  
*
5. Key in the balloon payment amount and press M. (If there is no balloon  
*
payment, go to step 6.)  
6. Press $ to obtain the purchase price of the mortgage.  
Example 1: A lender wishes to induce the borrower to prepay a low interest rate  
loan. The interest rate is 5% with 72 payments remaining of $137.17 and a  
balloon payment at the end of the sixth year of $2,000. If the lender is willing to  
discount the future payments at 9%, how much would the borrower need to prepay  
?
the note  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
fCLEARG  
72n  
g  
fCLEARG  
72n  
72.00  
Months (into n).  
Positive for cash received; negative for cash paid out.  
*
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 159 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
160 Section 12: Real Estate and Lending  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
0.75  
9gC  
Discount rate (into i).  
9gC  
*
137.17  
137.17P  
Monthly payments (into  
PMT).  
137.17P  
*
–8,777.61  
2000M$  
Amount necessary to  
prepay the note.  
2000M$  
Example 2: A 6.5% mortgage with 26 years remaining and a remaining  
balance of $249,350 is available for purchase. Determine the price to pay for this  
mortgage if the desired yield is 12%. (Since the payment amount is not given, it  
must be calculated.)  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
26gA  
fCLEARG  
26gA  
312.00  
0.54  
Months (into n).  
6.5gC  
6.5gC  
Percent monthly interest  
rate (into i).  
249350Þ$ 249350Þ$  
Monthly payment to be  
received (calculated).  
1,657.97  
1.00  
P
P
12gC  
12gC  
Desired monthly interest  
rate (into i).  
$
$
–158,361.78  
Purchase price to achieve  
the desired yield  
(calculated).  
Note that the payments are positive because this problem is in seen from the viewpoint of the  
lender who will be receiving payments. The negative PV indicates money that was lent out.  
*
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 160 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 12: Real Estate and Lending 161  
Yield of a Mortgage Traded at a Discount or Premium  
The annual yield of a mortgage bought at a discount or premium can be  
calculated given the original mortgage amount, interest rate, and periodic  
payment, as well as the number of payment periods per year, the price paid for  
the mortgage, and the balloon payment amount (if it exists).  
Information is entered as follows:  
1. Press and fCLEARG.  
2. Key in the total number of periods until the balloon payment occurs and  
press n. (If there is no balloon payment, key in the total number of periods  
and press n.)  
3. Key in the periodic payment amount then press P.  
*
4. Key in the purchase price of the mortgage then press $.  
*
5. Key in the balloon payment amount then press M. (If there is no balloon  
*
payment, go to step 6.)  
6. Press ¼ to obtain the yield per period.  
7. RPN: Key in the number of periods per year and press § to obtain the  
nominal annual yield.  
7. ALG: Press §. Key in the number of periods per year and press ³ to  
obtain the nominal annual yield.  
Example 1: An investor wishes to purchase a $300,000 mortgage taken out at  
6% for 21 years. Since the mortgage was issued, 42 monthly payments have been  
made. What would be the annual yield if the purchase price of the mortgage is  
?
$250,000 (Since PMT was not given, it must be calculated).  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
fCLEARG  
21gA  
g  
fCLEARG  
21gA  
Enter the number of  
periods (into n).  
252.00  
0.50  
6gC  
6gC  
Monthly interest rate  
(into i).  
–300,000.00  
300000Þ$ 300000Þ$  
Mortgage amount (into  
PV; negative to indicate  
money paid out).  
Positive for cash received; negative for cash paid out.  
*
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 161 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
162 Section 12: Real Estate and Lending  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
P
P
2,096.57  
Payment received  
(calculated).  
:n  
42-n  
:n  
-42n  
252.00  
210.00  
Recall number of  
periods.  
Number of periods left  
after mortgage is  
bought (into n).  
–250,000.00  
250000Þ$ 250000Þ$  
Input price of mortgage  
(into PV; negative to  
indicate money paid  
out).  
¼
¼
0.60  
7.20  
Yield per month  
(calculated).  
12§  
§12³  
Percent annual yield.  
Example 2: Using the same information given in example 1, calculate the annual  
yield if the loan is to be paid in full at the end of the fifth year (from original  
issuance). (In this case both the payment amount and the balloon must be  
calculated since they are not given.)  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
fCLEARG  
21gA  
g  
fCLEARG  
21gA  
Input the number of  
periods (into n).  
252.00  
0.50  
6gC  
6gC  
Monthly interest rate  
(into PV).  
–300,000.00  
2,096.57  
300000Þ$ 300000Þ$  
Mortgage amount (into  
PV).  
P
P
Payment (calculated).  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 162 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 12: Real Estate and Lending 163  
Calculate the remaining balance of the loan after five years.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
60.00  
5gA  
Number of periods to  
be amortized.  
5gA  
M
258,377.24  
Remaining balance of  
M
the loan after five years.  
:n  
60.00  
18.00  
:n  
42-n  
New life of loan.  
-42n  
250000Þ$  
¼
Percent monthly yield.  
(calculated).  
250000Þ$  
¼
1.01  
12.11  
12§  
Percent annual yield.  
§12³  
The Rent or Buy Decision  
The question of whether to rent or purchase a residence is not always easy to  
answer, especially when the time period over which you would own or rent a  
house is short. This program performs an analysis which could be helpful in  
reaching a decision. Essentially, it calculates a yield or rate of return on the  
proposed investment. This yield may be compared with the yield obtained by  
renting a residence and investing the down payment and monthly payment  
differences in a savings account or other investment opportunity. This program  
takes into account the tax advantages obtained by a home owner on property  
taxes and mortgage interest.  
First the program computes the Net Cash Proceeds upon Resale (NCPR), next the  
*
yield on the investment in the house and then the value of the hypothetical savings  
account at the end of the investment period. A comparison of the NCPR and the  
final balance of the savings account and a comparison of the yields should aid in  
determining whether to rent or buy.  
The Net Cash Proceeds upon Resale (NCPR = sales price – commission – mortgage balance),  
*
is the pre-tax proceeds. The program assumes that the buyer reinvests in like property and is  
not subject to capital gains tax.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 163 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
164 Section 12: Real Estate and Lending  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
000,  
DISPLAY  
000,  
(ALG mode)  
fCLEARÎ  
M
fCLEARÎ  
001,  
002,  
15  
15  
001,  
002,  
15  
15  
M
M
M
*
*
003,  
16  
1
003,  
16  
1
Þ
Þ
004,44 48  
004,44 48  
?.1  
:n  
?0  
:$  
fCLEARG  
:1  
-
?.1  
:n  
?0  
005, 45 11  
006, 44  
005, 45 11  
006, 44  
0
0
007, 45 13  
008, 42 34  
007, 45 13  
008, 42 34  
:$  
fCLEARG  
-
009, 45  
010,  
1
30  
13  
2
009,  
30  
1
010, 45  
011,  
:1  
$
011,  
13  
2
$
012, 45  
012, 45  
:2  
gA  
:3  
gC  
P
:2  
gA  
:3  
gC  
P
013, 43 11  
014, 45  
013, 43 11  
014, 45  
3
3
015, 43 12  
015, 43 12  
016,  
14  
0
016,  
14  
0
017,  
017,  
0
0
018,  
11  
0
018,  
11  
0
n
n
019, 45  
020,  
019, 45  
020,  
:0  
1
:0  
§
1
20  
1
021,  
2
021,  
2
1
* FV is repeated in the program twice to ensure that it is computed and not stored.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 164 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 12: Real Estate and Lending 165  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
022,  
(ALG mode)  
20  
022,  
2
§
2
023, 42 11  
024, 16  
025, 45 11  
023, 42 11  
f!  
Þ
f!  
Þ
z
024,  
025,  
16  
10  
:n  
z
026,  
10  
4
026, 45 11  
:n  
+
027, 45  
028,  
027,  
40  
4
:4  
+
40  
0
028, 45  
029,  
:4  
029,45 48  
030,  
20  
0
§
:.0  
25  
4
030,45 48  
031,  
b
:.0  
b
031, 45  
032,  
25  
30  
4
:4  
-
30  
5
032,  
-
033, 45  
034,  
033, 45  
034,  
:5  
-
:4  
-
30  
8
30  
5
035, 45  
036,  
035, 45  
036,  
:8  
+
:5  
+
40  
40  
8
037, 45 14  
037, 45  
038,  
:P  
+
:8  
+
038,  
40  
14  
1
40  
039,  
039, 45 14  
P
:P  
P
040,45 48  
041, 45  
042,  
040,  
14  
1
:.1  
:7  
b
7
041,45 48  
042,  
:.1  
-
25  
30  
30  
7
043,  
043, 45  
044,  
-
:7  
b
044, 45 13  
045, 30  
25  
30  
:$  
-
045,  
-
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 165 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
166 Section 12: Real Estate and Lending  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
046,  
DISPLAY  
(ALG mode)  
:$  
M
15  
31  
1
046, 45 13  
M
047,  
047,  
15  
31  
1
t
048, 45  
049, 45  
050,  
048,  
t
:1  
:6  
+
6
049, 45  
050,  
:1  
Þ
40  
16  
13  
12  
16  
30  
6
051,  
051,  
Þ
-
052,  
052, 45  
053,  
$
:6  
$
053,  
13  
12  
¼
054,45,43 12  
054,  
:gC  
t
¼
055,  
31  
9
055,45,43 12  
:gC  
t
056, 45  
056,  
31  
9
:9  
gC  
M
057, 43 12  
058, 15  
057, 45  
:9  
gC  
M
058, 43 12  
059,  
15  
fs  
fs  
REGISTERS  
PV: Price  
n: Period  
i: Apprec.  
PMT: Used  
R2: Life  
FV: Used  
R0: Period  
R4: Taxes/Mo  
R8: Rent  
R1: Dwn Pmt  
R3: i(Mtg)  
R5: Improve./mo  
R9: Savings i  
R6: Closing C.  
R.0: Tax Bracket  
R7: % Comm.  
R.1: Market V.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 166 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 12: Real Estate and Lending 167  
1. Key in the program.  
2. Key in the estimated down payment then press ?1.  
3. Key in the life of the mortgage then press ?2.  
4. Key in the annual mortgage interest rate then press ?3.  
5. Key in the estimated monthly taxes then press ?4.  
6. Key in the total amount estimated for monthly repairs, improvements,  
incremental insurance, utility costs, and other expenses, then press ?5.  
7. Key in the closing costs then press ?6.  
8. Key in the selling cost as a percentage of the selling price. This should  
include sales commission, escrow fees, etc. then press ?7.  
9. Key in the monthly rent for the alternative housing then press ?8.  
10.Key in the savings or alternative investment annual interest rate as a  
percentage then press ?9.  
11.Key in the combined State and Federal marginal tax rate as a percentage  
*
then press ?.0.  
12.Press and fCLEARG then key in the number of years involved in  
the investment; press n.  
13.Key in the estimated rate of yearly appreciation as a percentage then press  
¼.  
14.Key in the price of the house under consideration then press $.  
15.Press t to compute the net proceeds from the sale of the house. (A  
negative value indicates money lost.)  
16.Press t to compute the yield on your investment in the house.  
17.Press t to compute the value of a savings account or other investment.  
18.Compare the value of the hypothetical savings account to the net proceeds of  
the sale of the house. Examine the sign and magnitude of the yield to arrive  
at your decision.  
19.To change data and repeat the calculations, store the changed values in the  
appropriate registers and go to step 12.  
The user should key in the total marginal income tax — Federal plus State — to obtain  
*
calculations which reflect the tax advantages of home ownership. Because of the complexities  
of tax laws and different financial and tax considerations for each individual, this program  
should only serve as a guide in considering an investment of this type. For more specific,  
detailed information, consult a tax accountant or qualified tax advisor.  
If the calculator displays a negative result or Error 5 when solving for yield then your  
investment has resulted in a loss. The amount of interest earned on the alternative investment  
is not taken into account in this calculation.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 167 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
168 Section 12: Real Estate and Lending  
Example: You are being transferred for 4 years to a distant city and are faced  
with the decision of whether to rent or to buy a house. A quick survey of the  
housing market indicates that you can purchase an acceptable house for  
$270,000 with a $7,000 down payment on a 30-year mortgage at 6% interest.  
The closing costs would be about $3,700. Selling costs include a 6% commission  
for resale and miscellaneous other fees that amount to another 2% of the sale price.  
Housing in the area is appreciating 5% per year. Property taxes would be about  
$300 per month, and you estimate that maintenance would cost an additional  
$165 per month.  
An alternative would be to rent a similar dwelling at $900 per month and to invest  
the difference between the purchase cost and rent at 3% interest. Your personal  
income tax rate (marginal) is 25% Federal and 5% State. Which alternative is  
?
more financially attractive  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARH  
7000?1  
30?2  
fCLEARH  
7000?1  
30?2  
0.00  
7,000.00  
30.00  
Down payment.  
Life of mortgage.  
Interest rate.  
6.00  
6?3  
6?3  
300.00  
165.00  
3,700.00  
8.00  
300?4  
165?5  
3700?6  
8?7  
300?4  
165?5  
3700?6  
8?7  
Property taxes.  
Monthly expenses.  
Closing costs.  
Resale costs (as a  
percentage).  
900.00  
3.00  
900?8  
3?9  
900?8  
3?9  
Rent.  
Savings interest rate.  
Tax bracket.  
30.00  
30?.0  
fCLEARG  
4n  
30?.0  
fCLEARG  
4n  
30.00  
Clear financial registers.  
Years in investment.  
Yearly appreciation rate.  
House price.  
4.00  
5.00  
5¼  
5¼  
270,000.00  
53,095.65  
270000$  
t
270000$  
t
NCPR (calculated).  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 168 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 12: Real Estate and Lending 169  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
t
t
t
t
8.57  
Yield.  
46,048.61  
Balance in savings.  
By purchasing a house, you would gain $7,047.04 (53,095.65 – 46,048.61)  
over an alternate investment at 3% interest.  
Deferred Annuities  
Sometimes transactions are established where payments do not begin for a  
specified number of periods; the payments are deferred. The technique for  
calculating NPV may be applied assuming zero for the first cash flow. Refer to  
pages 73 through 77.  
Example 1: You have just inherited $20,000 and wish to put some of it aside for  
your daughter’s college education. You estimate that when she is of college age, 9  
years from now, she will need $7,000 at the beginning of each year for 4 years  
for college tuition and expenses. You wish to establish a fund which earns 6%  
annually. How much do you need to deposit in the fund today to meet your  
?
daughter’s educational expenses  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARH  
0gJ  
fCLEARH  
0gJ  
0.00  
0.00  
Initialize.  
First cash flow.  
0.00  
8.00  
0gK  
8ga  
0gK  
8ga  
Second through ninth  
cash flows.  
7,000.00  
4.00  
7000gK  
4ga  
7000gK  
4ga  
Tenth through thirteenth  
cash flows.  
6.00  
6¼  
6¼  
Interest.  
NPV.  
fl  
fl  
15,218.35  
Leases often call for periodic contractual adjustments of rental payments. For  
example, a 2-year lease calls for monthly payments (at the beginning of the month)  
of $500 per month for the first 6 months, $600 per month for the next 12 months,  
and $750 per month for the last 6 months. This situation illustrates what is called a  
“step-up” lease. A “step-down” lease is similar, except that rental payments are  
decreased periodically according to the lease contract. Lease payments are made  
at the beginning of the period.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 169 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
170 Section 12: Real Estate and Lending  
In the example cited, the rental payment stream for months 7 through 24 are  
“deferred annuities,” as they start at some time in the future. The cash flow  
diagram from the investor’s viewpoint looks like this:  
To find today’s present value of the cash flows assuming a desired yield, the NPV  
technique may be used. (Refer to pages 73 through 77.)  
Example 2: A 2-year lease calls for monthly payments (at the beginning of the  
month) of $500 per month for the first 6 months, $600 per month for the next 12  
months, and $750 per month for the last 6 months. If you wish to earn 13.5%  
annually on these cash flows, how much should you invest (what is the present  
?
value of the lease)  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARH  
500gJ  
fCLEARH  
500gJ  
0.00  
Initialize.  
500.00  
First cash flow.  
gK  
5ga  
gK  
5ga  
500.00  
5.00  
Second through sixth cash  
flows.  
600.00  
12.00  
600gK  
12ga  
600gK  
12ga  
Next twelve cash flows.  
750.00  
6.00  
750gK  
6ga  
750gK  
6ga  
Last six cash flows.  
1.13  
13.5gC  
13.5gC  
Monthly interest rate.  
fl  
fl  
12,831.75  
Amount to invest to  
achieve a 13.5% yield.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 170 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13  
Investment Analysis  
Partial-Year Depreciation  
For both income tax purposes and financial analyses, it is valuable to calculate  
depreciation based on a calendar or fiscal accounting year. When the acquisition  
date of an asset does not coincide with the start of the year — which is the rule  
rather than the exception — the amounts of depreciation in the first and last years  
are computed as fractions of a full year’s depreciation.  
Straight-Line Depreciation  
The following hp 12c platinum program calculates the straight-line depreciation for  
the year desired with the acquisition date occurring at any time during the year.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
000,  
fCLEARÎ  
fCLEARÎ  
z
001,  
1
2
001,  
10  
1
1
002,  
002,  
2
1
z
003,  
10  
1
003,  
2
2
³
004, 44  
005,  
004,  
36  
1
?1  
~
34  
2
005, 44  
006,  
?1  
~
006, 44  
007,  
34  
2
?2  
1
1
007, 44  
008,  
?2  
-
-
008,  
30  
0
30  
1
009, 44  
010,  
009,  
?0  
1
1
³
1
010,  
36  
0
fV  
011, 42 23  
011, 44  
?0  
171  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 171 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
172 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
(RPN mode)  
012, 45  
013,  
1
20  
3
012,  
1
:1  
§
1
fV  
§
013, 42 23  
014, 44  
014,  
20  
1
?3  
:$  
015, 45 13  
015, 45  
:1  
~
³
016,  
017,  
018,  
34  
30  
13  
016,  
36  
3
-
017, 44  
?3  
:$  
-
$
018, 45 13  
:n  
:1  
-
019, 45 11  
019,  
020,  
021,  
30  
34  
13  
~
020, 45  
021,  
1
30  
11  
0
$
n
:n  
-
022,  
022, 45 11  
023, 45  
023,  
30  
1
:0  
gm  
024, 43 35  
025,43,33,035  
024, 45  
025,  
:1  
n
11  
0
gi035  
:2  
026, 45  
027, 43 31  
028, 45  
029, 42 23  
2
026, 45  
:0  
gu  
:0  
gm  
gi038  
:2  
027, 43 35  
028,43,33,038  
0
fV  
t
029, 45  
030, 43 31  
031, 45  
032, 42 23  
2
gu  
:0  
030,  
31  
1
031,  
0
1
fV  
t
032,44 40  
033,44 40  
0
?=0  
?=2  
gi026  
:2  
2
033,  
31  
1
034,43,33, 026  
035, 45  
034,  
1
2
035,44 40  
0
?=0  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 172 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 173  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
gu  
:$  
:M  
-
036, 43 31  
037, 45 13  
038, 45 15  
036,44 40  
037,43,33, 029  
038, 45  
2
?=2  
gi029  
:2  
2
gu  
:$  
-
039,  
30  
3
039, 43 31  
040, 45 13  
040, 45  
:3  
041,43,33, 030  
041,  
30  
gi030  
fs  
:M  
³
042, 45 15  
043,  
36  
3
044, 45  
:3  
045,43,33, 033  
gi033  
fs  
REGISTERS  
n: Life  
i: Unused  
PV: Dep. Value  
R1: #Mos./12  
PMT: Unused  
R2: Counter  
FV: Salvage  
R3: 1st Yr. Dep.  
R0: Used  
R4–R.4: Unused  
1. Key in the program.  
2. Press fCLEARG.  
3. Key in the book value then press $.  
4. Key in the salvage value then press M.  
5. Key in the life in years (an integer) then press n.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 173 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
174 Section 13: Investment Analysis  
RPN Mode:  
6. Key in the year desired then press \.  
7. Key in the number of months in the first year and press t. The display  
*
will show the amount of depreciation for the desired year. If desired, press  
~ to see the remaining depreciable value then press  
:$:3=~-:M- to find the total depreciation from the  
first year through the current year.  
ALG Mode:  
6. Key in the year desired then press ³.  
7. Key in the number of months in the first year and press t.* The display  
will show the amount of depreciation for the desired year. If desired, press  
~ to see the remaining depreciable value then press  
:$=:3-~-:M³ to find the total depreciation from  
the first year through the current year.  
8. Press t for the amount of depreciation and remaining depreciable value  
for the next year. Repeat this step for the following years.  
9. For a new case, press gi000 and return to step 2.  
Note: If the number of months in the first calendar year is less than 12, the  
amount of depreciation in the 1st year will be less than a full year’s  
depreciation. The actual number of years that depreciation will occur is  
equal to the life +1. For example, a drill has a life of 3 years and is  
purchased 3 months before the year-end. The following time diagram shows  
that depreciation will occur over 4 calendar years.  
Example 1: A property has just been purchased for $150,000. The purchase  
price is allocated between $25,000 for land and $125,000 for improvements  
(building). The remaining useful life of the building is agreed to be 25 years. There  
is no salvage value forecasted at the end of the useful life of the building. Thus, the  
depreciable value and book value is $125,000.  
The building was acquired 4 months before the end of the year. Using straight-line  
depreciation, find the amount of depreciation and remaining depreciable value for  
?
the 1st, 2nd, 25th, and 26th years. What is the total depreciation after 3 years  
The display will pause showing the year number before showing the amount of depreciation  
*
for that year.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 174 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 175  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARG  
Salvage value = 0 so FV  
= 0; set to 0 by  
fCLEARG  
CLEARG.  
125,000.00  
25.00  
125000$  
25n  
125000$  
25n  
Book value.  
Life.  
1.00  
1\  
1³  
Year desired.  
1.00  
1,666.67  
123,333.33  
4t  
4t  
First year:  
depreciation,  
remaining depreciable  
value.  
~
~
t
~
t
~
2.00  
5,000.00  
118,333.33  
Second year:  
depreciation,  
remaining depreciable  
value.  
t
t
3.00  
5,000.00  
Third year:  
depreciation.  
~:$=  
:3-~³  
gi000  
~:$:3  
+~-  
gi000  
11,666.67  
Total depreciation through  
third year.  
fCLEARG  
125000$  
25n  
fCLEARG  
125000$  
25n  
11,666.67  
125,000.00  
25.00  
Book value.  
Life.  
25.00  
25\  
25³  
Year desired.  
25.00  
5,000.00  
3,333.33  
4t  
4t  
Twenty-fifth year:  
depreciation,  
remaining depreciable  
value.  
~
~
t
~
t
~
26.00  
3,333.33  
0.00  
Twenty-sixth year:  
depreciation,  
remaining depreciable  
value.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 175 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
176 Section 13: Investment Analysis  
Example 2: A used car was purchased for $6,730 with 4.5 months remaining in  
the year. If the expected life of the car is 5 years, what is the amount of  
?
depreciation in the first year  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
gi000  
fCLEARG  
gi000  
fCLEARG  
6,730.00  
5.00  
6730$  
5n  
6730$  
5n  
Book value.  
Life.  
1.00  
1\  
1³  
1.00  
4.5t  
4.5t  
First year:  
504.75  
depreciation.  
Declining-Balance Depreciation  
The following hp 12c platinum program calculates the declining-balance  
depreciation for the year desired with the acquisition date occurring at any time  
during the year.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
000,  
fCLEARÎ  
fCLEARÎ  
z
001,  
1
2
001,  
10  
1
1
002,  
002,  
2
1
z
003,  
10  
1
003,  
2
2
³
004, 44  
005,  
004,  
36  
1
?1  
~
34  
2
005, 44  
006,  
?1  
~
006, 44  
007,  
34  
2
?2  
1
1
007, 44  
008,  
?2  
-
-
008,  
30  
0
30  
1
009, 44  
009,  
?0  
1
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 176 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 177  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
³
010,  
1
010,  
36  
0
1
f#  
011, 42 25  
011, 44  
012,  
?0  
1
012, 45  
013,  
1
20  
3
1
:1  
§
f#  
§
013, 42 25  
014, 44  
014,  
20  
1
?3  
:$  
~
015, 45 13  
015, 45  
016,  
:1  
³
016,  
34  
30  
13  
0
36  
3
-
017,  
017, 44  
?3  
:$  
-
$
018,  
018, 45 13  
019, 45  
019,  
30  
34  
13  
0
:0  
gm  
~
020, 43 35  
021,43,33,031  
020,  
$
021,  
gi031  
:2  
022, 45  
023, 43 31  
024, 45  
025, 42 25  
2
022, 45  
:0  
gu  
gm  
023, 43 35  
024,43,33,034  
0
:0  
f#  
t
gi034  
:2  
025, 45  
026, 43 31  
027, 45  
028, 42 25  
2
gu  
:0  
026,  
31  
1
027,  
0
1
f#  
t
028,44 40  
029,44 40  
0
?+0  
?+2  
gi022  
:2  
2
029,  
31  
1
030,43,33, 022  
031, 45  
030,  
1
2
031,44 40  
032,44 40  
0
?+0  
?+2  
gi025  
gu  
:$  
032, 43 31  
033, 45 13  
2
033,43,33, 025  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 177 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
178 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
(RPN mode)  
:M  
-
034, 45 15  
034, 45  
2
:2  
gu  
:$  
-
035,  
30  
3
035, 43 31  
036, 45 13  
036, 45  
:3  
037,43,33, 026  
gi026  
fs  
037,  
30  
:M  
³
038, 45 15  
039,  
36  
040, 45  
3
:3  
041,43,33, 029  
gi029  
fs  
REGISTERS  
n: Life  
i: Factor  
PV: Dep. Value  
R1: #Mos./12  
PMT: Unused  
R2: Counter  
FV: Salvage  
R3:1st Yr. Dep.  
R0: Used  
R4–R.4: Unused  
1. Key in the program.  
2. Press fCLEARG.  
3. Key in the book value then press $.  
4. Key in the salvage value then press M.  
5. Key in the declining-balance factor as a percentage then press ¼.  
6. Key in the life in years (an integer) then press n.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 178 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 179  
RPN Mode:  
7. Key in the year desired then press \.  
8. Key in the number of months in first year and press t. The display  
*
will show the amount of depreciation for the desired year. Press ~ to see  
the remaining depreciable value. If desired, press  
:$:3=~-:M- to find the total depreciation through  
the current year.  
ALG Mode:  
7. Key in the year desired then press ³.  
8. Key in the number of months in first year* and press t.† The display will  
show the amount of depreciation for the desired year. Press ~ to see the  
remaining depreciable value. If desired, press  
:$=:3-~-:M³ to find the total depreciation  
through the current year.  
9. Press t for the amount of depreciation then, if desired, press ~ for the  
remaining depreciable value for the next year. Repeat this step for the  
following years.  
10.For a new case press gi000 and return to step 2.  
Example: An electron beam welder which costs $50,000 is purchased 4 months  
before the end of the accounting year. What will the depreciation be during the  
first full accounting year (year 2) if the welder has a 6-year depreciable life, a  
salvage value of $8,000 and is depreciated using the declining-balance  
?
depreciation method The declining-balance factor is 150%.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
fCLEARG  
50000$  
8000M  
150¼  
f[  
fCLEARG  
50000$  
8000M  
150¼  
50,000.00  
8,000.00  
150.00  
6.00  
Book value.  
Salvage value.  
Declining-balance factor.  
Life.  
6n  
6n  
2.00  
2\  
2³  
Year desired.  
Second year:  
2.00  
4t  
4t  
Refer to straight-line depreciation instruction note, page 174.  
*
The display will pause showing the year number before showing the amount of depreciation  
for that year.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 179 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
180 Section 13: Investment Analysis  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
11,458.33  
depreciation.  
Sum-of-the-Years-Digits Depreciation  
The following hp 12c platinum program calculates the sum-of-the-years-digits  
depreciation for the year desired with the acquisition date occurring at any time  
during the year.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
000,  
fCLEARÎ  
fCLEARÎ  
z
001,  
1
2
001,  
10  
1
1
002,  
002,  
2
1
z
003,  
10  
1
003,  
2
2
³
004, 44  
005,  
004,  
36  
1
?1  
~
34  
2
005, 44  
006,  
?1  
~
006, 44  
007,  
34  
2
?2  
1
1
007, 44  
008,  
?2  
-
-
008,  
30  
0
30  
1
009, 44  
010,  
009,  
?0  
1
1
³
1
010,  
36  
0
fÝ  
011, 42 24  
011, 44  
012,  
?0  
1
012, 45  
013,  
1
20  
3
1
:1  
§
fÝ  
§
013, 42 24  
014, 44  
014,  
20  
1
?3  
:$  
~
015, 45 13  
015, 45  
016,  
:1  
³
016,  
017,  
34  
30  
36  
3
-
017, 44  
?3  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 180 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 181  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
$
:$  
-
018,  
13  
018, 45 13  
:n  
:1  
-
019, 45 11  
019,  
020,  
021,  
30  
34  
13  
~
020, 45  
021,  
1
30  
11  
0
$
n
:n  
-
022,  
022, 45 11  
023, 45  
023,  
30  
1
:0  
gm  
024, 43 35  
025,43,33, 035  
024, 45  
025,  
:1  
n
11  
0
gi035  
:2  
026, 45  
027, 43 31  
028, 45  
029, 42 24  
2
026, 45  
:0  
gu  
gm  
027, 43 35  
028,43,33, 038  
0
:0  
fÝ  
t
gi038  
:2  
029, 45  
030, 43 31  
031, 45  
032, 42 24  
2
gu  
:0  
030,  
31  
1
031,  
0
1
fÝ  
t
032,44 40  
033,44 40  
0
?=0  
?=2  
gi026  
:2  
2
033,  
31  
1
034,43,33, 026  
035, 45  
034,  
1
2
035,44 40  
036,44 40  
0
?=0  
?=2  
gi029  
:2  
gu  
:$  
:M  
-
036, 43 31  
037, 45 13  
038, 45 15  
2
037,43,33, 029  
038, 45  
2
gu  
:$  
-
039,  
30  
3
039, 43 31  
040, 45 13  
040, 45  
:3  
041,43,33, 030  
041,  
30  
gi030  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 181 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
182 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
(RPN mode)  
fs  
:M  
³
042, 45 15  
043,  
36  
3
044, 45  
:3  
045,43,33, 033  
gi033  
fs  
REGISTERS  
n: Life  
i: Unused  
PV: Dep. Value  
R1: #Mos./12  
PMT: Unused  
R2: Counter  
FV: Salvage  
R3: 1st Yr. Dep.  
R0: Used  
R4–R.4: Unused  
1. Key in the program.  
2. Press fCLEARG.  
3. Key in the book value then press $.  
4. Key in the salvage value then press M.  
5. Key in the life in years (an integer) then press n.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 182 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 183  
RPN Mode:  
6. Key in the year desired then press \.  
7. Key in the number of months in first year then press t. The display  
*
will show the amount of depreciation for the desired year. If desired,  
press ~ to see the remaining depreciable value, then press  
:$:3=~-:M- to find the total depreciation through  
the current year.  
ALG Mode:  
6. Key in the year desired then press ³.  
7. Key in the number of months in first year* then press t.† The display  
will show the amount of depreciation for the desired year. If desired,  
press  
~
to see the remaining depreciable value, then press  
:$=:3-~-:M³ to find the total depreciation  
through the current year.  
8. Press t for the amount of depreciation then, if desired, press ~ for the  
remaining depreciable value for the next year. Repeat this step for the  
following years.  
9. For a new case press gi000 and return to step 2.  
Example: A commercial movie camera is purchased for $12,000. If maintained  
properly, the camera has a useful life expectancy of 25 years with $500 salvage  
value. Using the sum-of-the-years-digits method, what is the amount of depreciation  
?
and the remaining depreciable value for the 4th and 5th years Assume the first  
depreciation year is 11 months long.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARG  
12000$  
500M  
25n  
fCLEARG  
12000$  
500M  
25n  
12,000.00  
500.00  
25.00  
Book value.  
Salvage value.  
Life.  
4.00  
4\  
4³  
Year desired.  
Refer to straight-line depreciation instruction note, page 174.  
*
The display will pause showing the year number before showing the amount of depreciation  
for that year.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 183 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
184 Section 13: Investment Analysis  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
4.00  
781.41  
8,238.71  
11t  
11t  
Fourth year:  
depreciation,  
remaining depreciable  
value.  
~
~
t
~
t
~
5.00  
746.02  
7,492.69  
Fifth year:  
depreciation,  
remaining depreciable  
value.  
Full- and Partial-Year Depreciation with Crossover  
When calculating declining-balance depreciation it is often advantageous for tax  
purposes to switch from declining balance to straight-line depreciation at some  
point. This hp 12c platinum program calculates the optimum crossover point and  
automatically switches to straight-line depreciation at the appropriate time. The  
crossover point is the end of the year in which the declining-balance depreciation  
last exceeds or equals the amount of straight-line depreciation. The straight-line  
depreciation is determined by dividing the remaining depreciable value by the  
remaining useful life.  
Given the desired year and the number of months in the first year, this program  
calculates the depreciation for the desired year, the remaining depreciable value,  
and the total depreciation through the current year.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
000,  
fCLEARÎ  
fCLEARÎ  
z
001,  
1
2
001,  
10  
1
1
002,  
002,  
2
1
z
003,  
10  
6
003,  
2
2
³
004, 44  
004,  
36  
6
?6  
:n  
~
005, 45 11  
005, 44  
?6  
:n  
-
006,  
007,  
34  
30  
006, 45 11  
007, 30  
-
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 184 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 185  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
~
³
?4  
d
008, 44  
009,  
4
33  
0
008,  
34  
36  
4
?4  
d
009,  
010, 44  
011,  
010, 44  
011,  
?0  
1
1
33  
33  
0
d
012,44 30  
013, 44  
014, 44  
0
012,  
?-0  
?2  
?3  
f#  
2
013, 44  
014,  
?0  
1
3
1
015, 42 25  
015,44 30  
016, 44  
017, 44  
0
?-0  
?2  
?3  
f#  
§
016, 45  
017,  
6
20  
1
2
:6  
§
3
018, 44  
018, 42 25  
?1  
:$  
~
019, 45 13  
019,  
20  
6
020,  
021,  
022,  
023,  
34  
30  
13  
36  
020, 45  
021,  
:6  
³
-
36  
1
$
022, 44  
?1  
:$  
-
\
023, 45 13  
gF  
~
024, 43 40  
025, 34  
026, 45 15  
024,  
025,  
026,  
30  
34  
13  
~
:M  
$
-
027,  
30  
34  
0
027, 45  
1
:1  
~
:0  
1
:$  
-
028,  
028, 45 13  
029, 30  
030, 45 15  
029, 45  
030,  
:M  
1
go  
³
031, 43 34  
031,  
36  
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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
186 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
032,  
(RPN mode)  
~
032,43,33, 039  
34  
0
gi039  
d
d
033,  
034,  
035,  
33  
33  
1
033, 45  
034,  
:0  
1
1
go  
035, 43 34  
036,43,33, 043  
1
gu  
d
036, 43 31  
gi043  
d
037,  
33  
31  
1
037,  
038,  
039,  
33  
33  
1
t
d
038,  
039,  
1
1
gu  
d
040,44 40  
041,44 30  
2
040, 43 31  
?+2  
?-0  
f#  
?+1  
?5  
:$  
:M  
-
0
041,  
33  
31  
1
t
042, 42 25  
042,  
043,44 40  
044, 44  
1
5
043,  
1
044,44 40  
045,44 30  
2
?+2  
?-0  
f#  
?+1  
?5  
045, 45 13  
046, 45 15  
0
046, 42 25  
047,  
30  
4
047,44 40  
048, 44  
1
5
048, 45  
049,  
:4  
z
:$  
-
10  
049, 45 13  
050, 30  
051, 45 15  
go  
050, 43 34  
051,43,33, 053  
052,43,33, 065  
:M  
z
gi053  
gi065  
d
052,  
10  
4
053,  
33  
0
053, 45  
054,  
:4  
³
054,  
36  
0
go  
055, 45  
0
055, 43 34  
:0  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 186 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 187  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
go  
gi086  
:$  
:5  
056, 43 34  
057,43,33, 086  
058, 45 13  
056,43,33, 058  
057,43,33, 070  
gi058  
gi070  
d
058,  
33  
0
059, 45  
060,  
5
30  
13  
1
059,  
0
-
060, 45  
0
:0  
go  
$
061,  
061, 43 34  
062,43,33, 091  
063, 45 13  
062,  
1
gi091  
:$  
-
063,44 30  
4
?-4  
gi040  
:4  
n
064,43,33, 040  
064,  
30  
5
065, 45  
066,  
4
11  
0
065, 45  
066,  
:5  
$
13  
1
067,  
067,  
0
1
068, 44  
069,  
6
068,44 30  
4
?6  
1
?-4  
gi044  
:4  
n
1
069,43,33, 044  
070,44 30  
071,44 40  
072, 45  
073,44 30  
074, 45  
2
070, 45  
071,  
4
11  
0
?-2  
?=0  
:5  
?-1  
:3  
fV  
?+1  
1
0
5
072,  
0
1
073, 44  
074,  
6
?6  
1
3
1
075, 42 23  
075,44 30  
076,44 40  
077, 45  
078,44 30  
079, 45  
2
?-2  
?=0  
:5  
?-1  
:3  
076,44 40  
077,  
1
1
0
2
0
5
078,44 30  
079,44 40  
1
?-0  
?+2  
3
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 187 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
188 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
(RPN mode)  
fV  
?+1  
1
080,44 40  
081,  
3
33  
0
080, 42 23  
?+3  
d
081,44 40  
082,  
1
1
082, 45  
083,  
:0  
1
1
083,44 30  
084,44 40  
085,44 40  
086,  
0
?-0  
?+2  
?+3  
d
go  
084, 43 34  
085,43,33, 074  
2
3
gi074  
d
d
086,  
33  
33  
2
33  
0
087,  
087, 45  
088,  
:0  
1
088, 45  
1
:2  
gu  
d
go  
089, 43 31  
089, 43 34  
090,43,33, 079  
090,  
33  
31  
6
gi079  
t
d
d
091,  
091,  
33  
33  
2
092, 45  
092,  
:6  
gm  
093, 43 35  
094,43,33, 074  
095,43,33, 058  
093, 45  
:2  
gu  
d
094, 43 31  
gi074  
gi058  
fs  
095,  
33  
31  
6
t
096,  
097, 45  
:6  
gm  
098, 43 35  
099,43,33, 079  
100,43,33, 063  
gi079  
gi063  
fs  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 188 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 189  
REGISTERS  
PV: Dep. Value  
n: Life  
i: Factor  
R0: Used  
R4: Used  
PMT: Unused  
R2: Counter  
R6: Used  
FV: Salvage  
R3: Used  
R1: Dep.  
R5: Used  
1. Key in the program.  
2. Press fCLEARH.  
3. Key in the book value then press $.  
4. Key in the salvage value then press M.  
5. Key in the life in years (an integer) then press n.  
6. Key in the declining-balance factor as a percentage then press ¼.  
7. RPN: Key in the desired year and press \.  
7. ALG: Key in the desired year and press ³.  
8. Key in the number of months in the first year then press t to calculate  
*
the amount of depreciation for the desired year.  
9. If desired, press ~ to see the remaining depreciable value.  
10.If desired, press :1 to see the total depreciation through the current year.  
11.Continue pressing t to find the amount of depreciation for the successive  
*
years. Steps 9 and 10 may be repeated for each year.  
12.For a new case press gi000 and return to step 2.  
Example: An electronic instrument is purchased for $11,000, with 6 months  
remaining in the current fiscal year. The instrument’s useful life is 8 years and the  
salvage value is expected to be $500. Using a 200% declining-balance factor,  
generate a depreciation schedule for the instrument’s complete life. What is the  
?
remaining depreciable value after the first year What is the total depreciation  
?
after the 7th year  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARH  
11000$  
fCLEARH  
11000$  
0.00  
11,000.00  
Book value.  
Refer to straight-line depreciation note page 174.  
*
The display will pause with the year number before displaying the amount of depreciation for  
that year.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 189 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
190 Section 13: Investment Analysis  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
500.00  
8.00  
500M  
8n  
500M  
8n  
Salvage value.  
Life.  
200.00  
1.00  
200¼  
1\  
200¼  
1³  
Declining-balance factor.  
First year depreciation  
desired.  
1.00  
6t  
6t  
First year:  
1,375.00  
9,125.00  
depreciation,  
remaining depreciable  
value.  
~
~
t
t
t
t
t
t
t
t
t
t
t
t
2.00  
Second year:  
depreciation.  
2,406.25  
3.00  
Third year:  
depreciation.  
1,804.69  
4.00  
Fourth year:  
depreciation.  
1,353.51  
5.00  
Fifth year:  
depreciation.  
1,015.14  
6.00  
Sixth year:  
depreciation.  
*
761.35  
7.00  
Seventh year:  
depreciation.  
713.62  
:1  
:1  
9,429.56  
Total depreciation through  
the seventh year.  
t
t
8.00  
Eight year:  
713.63  
depreciation  
t
t
9.00  
Ninth year:  
356.81  
depreciation.  
By observation the crossover was year 6. Years 7, 8, and 9 use straight-line depreciation.  
*
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 190 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 191  
Excess Depreciation  
When accelerated depreciation is used, the difference between total depreciation  
charged over a given period of time and the total amount that would have been  
charged under straight-line depreciation is called excess depreciation. To obtain  
excess depreciation:  
RPN Mode:  
1. Calculate the total depreciation then press \.  
2. Key in the depreciable amount (cost less salvage) then press \. Key in  
the useful life of the asset in years then press z. Key in the number of  
years in the income projection period then press § to get the total  
straight-line depreciation charge.  
3. Press - to get the excess depreciation.  
ALG Mode:  
1. Calculate the total depreciation then press -gØ.  
2. Key in the depreciable amount (cost less salvage) then press z. Key in  
the useful life of the asset in years then press §. Key in the number of  
years in the income projection period then press to get the total  
straight-line depreciation charge.  
3. Press ³ to get the excess depreciation.  
Example: What is the excess depreciation in the previous example over 7  
?
calendar years (Because of the partial first year, there are 6.5 years depreciation  
in the first 7 calendar years.)  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
9,429.56  
9429.56\  
9429.56-gØ  
Total depreciation through  
seventh year.  
10,500.00  
1,312.50  
10500\  
10500z  
Depreciable amount.  
8z  
8§  
Yearly straight-line  
depreciation.  
8,531.25  
898.31  
6.5§  
6.5 gÙ  
Total straight-line  
depreciation.  
-
³
Excess depreciation  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 191 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
192 Section 13: Investment Analysis  
Modified Internal Rate of Return  
The traditional Internal Rate of Return (IRR) technique has several drawbacks which  
hamper its usefulness in some investment applications. The technique implicitly  
assumes that all cash flows are either reinvested or discounted at the computed  
yield rate. This assumption is financially reasonable as long as the rate is within a  
realistic borrowing and lending range (for example, 10% to 20%). When the IRR  
becomes significantly greater or smaller, the assumption becomes less valid and  
the resulting value less sound as an investment measure.  
IRR also is limited by the number of times the sign of the cash flow changes  
(positive to negative or vice versa). For every change of sign, the IRR solution has  
the potential for an additional answer. The cash flow sequence in the example that  
follows has three sign changes and hence up to three potential internal rates of  
return. This particular example has three positive real answers: 1.86, 14.35, and  
29. Although mathematically sound, multiple answers probably are meaningless  
as an investment measure.  
This Modified Internal Rate of Return procedure (MIRR) is one of several IRR  
alternatives which avoids the drawbacks of the traditional IRR technique. The  
procedure eliminates the sign change problem and the reinvestment (or  
discounting) assumption by utilizing user stipulated reinvestment and borrowing  
rates.  
Negative cash flows are discounted at a safe rate that reflects the return on an  
investment in a liquid account. The figure generally used is a short-term security  
(T-Bill) or bank passbook rate.  
Positive cash flows are reinvested at a reinvestment rate which reflects the return on  
an investment of comparable risk. An average return rate on recent market  
investments might be used.  
The steps in the procedure are:  
1. Calculate the future value of the positive cash flows (NFV) at the reinvestment  
rate.  
2. Calculate the present value of the negative cash flows (NPV) at the safe rate.  
3. Knowing n, PV, and FV, solve for i.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 192 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 193  
Example: An investor has the following unconventional investment opportunity.  
The cash flows are:  
Group  
# of Months  
Cash Flow ($)  
–180,000  
100,000  
–100,000  
0
0
1
2
3
4
1
5
5
9
1
200,000  
Calculate the MIRR using a safe rate of 6% and a reinvestment (risk) rate of 10%.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARH  
0gJ  
fCLEARH  
0gJ  
0.00  
0.00  
First cash flow.  
100,000.00  
5.00  
100000gK 100000gK  
5ga 5ga  
Second through sixth  
cash flows.  
5.00  
0gK5ga 0gK5ga  
0gK9ga 0gK9ga  
200000gK 200000gK  
10gCfl 10gCfl  
Next five cash flows.  
Next nine cash flows.  
Last cash flow.  
9.00  
200,000.00  
657,152.37  
NPV of positive cash  
flows.  
Þ$  
Þ$  
-657,152.37  
775,797.83  
20nM  
20nM  
NFV of positive cash  
flows.  
180000Þg 180000Þg  
J0gK5g J0gK5g  
a100000Þ a100000Þ  
gK5ga6 gK5ga  
NPV of negative cash  
flows.  
-660,454.55  
gCfl  
6gCfl  
0.81  
9.70  
20n¼  
20n¼  
Monthly MIRR  
12§  
Annual MIRR.  
§12³  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 193 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
194 Section 13: Investment Analysis  
Black-Scholes Formula for Valuing European Options  
This program implements the Black-Scholes formula which has been used  
extensively in option markets worldwide since its publication in the early 1970’s.  
The five inputs are simply keyed into the five financial variables and then t  
displays the call option value, and ~ shows the put option value. The option  
values produced are accurate to at least the nearest cent for asset and strike prices  
under $100.  
Reference: Tony Hutchins, 2003, Black-Scholes takes over the HP12C, HPCC  
(www.hpcc.org) Datafile, V22, N3, pp13-21.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fCLEARÎ  
:n  
:¼  
b
fs  
fCLEARÎ  
:n  
§
000,  
000,  
001, 45 11  
002, 20  
003, 45 12  
001, 45 11  
002, 45 12  
:¼  
b
003,  
004,  
25  
16  
Þ
004,  
005,  
006,  
25  
36  
16  
g>  
:M  
§
}
005, 43 22  
006, 45 15  
Þ
g>  
§
007,  
20  
4
007, 43 22  
008, 20  
009, 45 15  
008, 44  
009,  
?4  
~
:M  
}
34  
gr  
:P  
b
010, 43 21  
011, 45 14  
010,  
36  
4
011, 44  
?4  
:n  
gr  
§
012,  
25  
3
012, 45 11  
013, 43 21  
013, 44  
?3  
:$  
:4  
z
014, 45 13  
014,  
015, 45 14  
016, 25  
20  
:P  
b
015, 45  
016,  
4
10  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 194 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 195  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
g°  
~
}
017, 43 23  
017,  
36  
3
018,  
019,  
34  
10  
018, 44  
?3  
:$  
z
z
019, 45 13  
gF  
020, 43 40  
020,  
10  
4
021,  
2
5
021, 45  
022,  
2
:4  
}
022, 44  
023,  
36  
?5  
z
g°  
z
10  
40  
6
023, 43 23  
+
024,  
024,  
025,  
026,  
027,  
028,  
029,  
10  
34  
~
}
025, 44  
026, 45  
027,  
?6  
:3  
-
3
36  
30  
3
45 3  
10  
:3  
z
028, 44  
029,  
?3  
\
36  
20  
2
2
§
030,  
030, 44  
031,  
5
40  
34  
30  
6
?5  
+
gr  
gF  
031, 43 21  
032, 43 40  
~
-
032,  
033,  
034,  
035,  
2
10  
16  
033,  
2
z
034, 44  
035, 45  
036,  
?6  
:3  
}
Þ
g>  
~
3
036, 43 22  
36  
3
037,  
038,  
039,  
040,  
34  
3
037, 44  
?3  
g¡  
z
038, 43 20  
3
.
0
48  
0
039,  
040,  
10  
2
2
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 195 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
196 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
(RPN mode)  
}
041,  
042,  
043,  
044,  
045,  
046,  
047,  
0
6
041,  
042,  
36  
16  
0
Þ
6
z
g>  
:3  
g¡  
gr  
z
10  
1
043, 43 22  
044, 45  
3
1
+
40  
22  
20  
045, 43 20  
046, 43 21  
y
§
047,  
048,  
049,  
050,  
051,  
052,  
053,  
054,  
055,  
056,  
057, 44  
058,  
059,  
060,  
061,  
062,  
063,  
064,  
10  
3
gF  
gF  
048, 43 40  
049, 43 40  
3
.
48  
0
050,  
051,  
052,  
053,  
054,  
055,  
056,  
057,  
058,  
059,  
060,  
061,  
062,  
063,  
064,  
1
8
1
0
0
8
0
7
6
7
6
§
+
20  
2
40  
1
2
1
}
y
4
36  
22  
2
4
-
§
30  
20  
8
?2  
§
~
}
20  
34  
36  
1
8
7
7
+
§
.
40  
20  
48  
2
1
8
8
7
2
7
b
§
25  
20  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 196 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 197  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
065, 45  
066,  
3
34  
3
065, 45  
066,  
2
30  
2
:3  
~
:2  
-
067, 44  
068,  
067,  
?3  
O
2
35  
34  
068,  
4
4
~
§
:2  
+
069,  
069,  
20  
2
go  
070, 43 34  
071,43,33,077  
070, 45  
071,  
40  
8
g(077  
1
072,  
1
3
072,  
8
073,44 30  
074,  
073,  
7
?-3  
Þ
7
§
~
§
.
16  
3
074,  
20  
34  
20  
48  
2
075,44 20  
076,  
075,  
3  
~
34  
5
076,  
077, 45  
077,  
:5  
gm  
078, 43 35  
079,43,33, 089  
078,  
2
b
}
079,  
25  
36  
3
g(089  
:6  
080, 45  
081, 45  
082, 45  
083,  
6
3
080,  
081, 45  
082,  
:3  
:3  
~
4
34  
3
:4  
§
20  
6
083, 44  
084,  
?3  
O
084, 44  
085,  
35  
34  
?6  
O
~
35  
5
085,  
go  
g(093  
1
086, 44  
087,  
086, 43 34  
087,43,33,093  
?5  
~
34  
088,43,33,028  
088,  
1
g(028  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 197 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
198 Section 13: Investment Analysis  
KEYSTROKES  
DISPLAY  
KEYSTROKES  
(ALG mode)  
DISPLAY  
(RPN mode)  
~
089,  
34  
3
089,44 30  
090,  
3
16  
3
?-3  
Þ
090, 45  
:3  
:$  
?-4  
§
091, 45 13  
091,44 20  
092,  
3  
~
092,44 30  
093,  
4
20  
6
34  
5
093, 45  
:5  
gm  
094, 45  
095,  
094, 43 35  
095,43,33,106  
:6  
-
30  
4
g(106  
:6  
:3  
§
096, 45  
6
096,44 40  
097, 45  
098,  
?+4  
:4  
4
097, 45  
098,  
3
20  
4
~
34  
5
099, 44  
099, 45  
100,  
?5  
:4  
}
fs  
36  
6
101, 44  
102,  
?6  
O
35  
5
103, 44  
104,  
?5  
34  
~
105,43,33,037  
106, 34  
107, 45 13  
g(037  
~
:$  
108,44 30  
109,  
4
20  
3
?-4  
§
110, 45  
111,  
:3  
-
30  
6
112, 45  
:6  
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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 199  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
DISPLAY  
DISPLAY  
(ALG mode)  
113,  
36  
4
}
114,44 40  
115, 45  
116,  
?+4  
:4  
4
34  
5
~
117, 44  
?5  
118,43,33, 000  
g(000  
fs  
REGISTERS  
i: Interest rate (%) PV: Stock price  
n: Term to expiry  
FV: Strike price  
R3: N(d1)  
PMT: Volatility (%)  
R2: Unused  
R0: Unused  
R1: Unused  
R4: Put value  
R5: Call value  
R6: QxN(d2)  
R7-R.9: Unused  
Note: The n, i and PMT values must all be based on the same time unit (for  
example: n is measured in years or months and i and PMT are rates per year  
or per month). i is a continuous percentage rate. PMT is the standard  
deviation of the continuous percentage stock return (as observed over the  
time unit). For sensible output, all inputs should be positive. The PMT=0 case  
can be simulated by using a PMT arbitrarily close to 0.  
Program Instructions  
1. Key in the program.  
2. Enter the five inputs into the five financial registers. These values are  
preserved by the program.  
a. Key in the unexpired term of the option and press n.  
b. Key in the risk-free interest rate as a percentage and press ¼.  
c. Key in the current (or spot) stock price and press $.  
d. Key in the volatility assumption as a percentage and press P.  
e. Key in the strike price and press M.  
3. Press t. The Call value is displayed. Press ~ to see the Put value.  
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Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
200 Section 13: Investment Analysis  
Example 1: An option has 6 months to run and a strike price of $45. Find  
Call and Put values assuming a spot price of $52, return volatility of 20.54% per  
month and a risk-free interest rate of 0.5% per month. Show how to change the  
time scale of the inputs between monthly and annual values.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
6n  
f[  
6n  
6.00  
0.50  
Time to expiry (months).  
.5¼  
.5¼  
Interest rate (% per  
month).  
52.00  
20.54  
45.00  
14.22  
5.89  
52$  
52$  
Stock price.  
20.54P  
45M  
20.54P  
45M  
Volatility (% per month).  
Strike price.  
t
t
Call value.  
~
~
Put value.  
:gAn  
:gC¼  
:P  
:gAn  
:gC¼  
:P§  
0.50  
Years to expiry.  
Yearly interest rate %.  
6.00  
12gr§P 12grP  
71.15  
14.22  
6.00  
Yearly volatility %.  
t
t
Call value (unchanged).  
Months to expiry.  
:ngA  
:¼gC  
:P  
:ngA  
:¼gC  
:Pz  
0.50  
Monthly interest rate %.  
12grzP 12grP  
20.54  
Monthly volatility %.  
The next example is Example 12.7 from Options, Futures, and Other Derivatives  
(5th Edition) by John C. Hull (Prentice Hall, 2002).  
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Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 13: Investment Analysis 201  
Example 2: The stock price six months from the expiration of an option is $42,  
the exercise price of the option is $40, the risk-free interest rate is 10% per annum,  
and the volatility is 20% per annum. Find Call and Put values.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
0.50  
.5n  
10¼  
42$  
20P  
40M  
t
.5n  
10¼  
42$  
20P  
40M  
t
Time to expiry (years).  
Interest rate (% per year).  
Stock price.  
10.00  
42.00  
20.00  
40.00  
4.76  
Volatility (% per year).  
Strike price.  
Call value.  
~
~
0.81  
Put value.  
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Section 14  
Leasing  
Advance Payments  
Situations may exist where payments are made in advance (leasing is a good  
example). These agreements call for extra payments to be made when the  
transaction is closed.  
This first procedure finds the periodic payment amount necessary to achieve a  
desired yield when a number of payments are made in advance. And, given the  
periodic payment, the second procedure calculates the periodic yield.  
Solving for Payment  
To calculate the payment, information is entered as follows:  
1. Press and fCLEARG.  
RPN Mode:  
2. Key in the total number of payments in the lease then press \.  
3. Key in the total number of payments made in advance then press  
?0-n.  
4. Key in or calculate the periodic interest rate as a percentage then press  
¼.  
5. Press 1ÞP$:0+.  
6. Key in the initial loan amount then press ~z, to obtain the periodic  
payment to be received by the lessor.  
ALG Mode:  
2. Key in the total number of payments in the lease.  
3. Key in the total number of payments made in advance then press  
-?0n.  
4. Key in or calculate the periodic interest rate as a percentage then press  
¼.  
5. Press 1ÞP$+:0³.  
6. Key in the initial loan amount then press z~³, to obtain the  
periodic payment to be received by the lessor.  
202  
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Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 14: Leasing 203  
Example 1: Equipment worth $750 is leased for 12 months. The equipment is  
assumed to have no salvage value at the end of the lease. The lessee has agreed  
to make three payments at the time of closing. What monthly payment is necessary  
?
to yield the lessor 10% annually  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
12\  
fCLEARG  
12-  
12.00  
9.00  
Duration of lease.  
3?0-n  
3?0n  
Number of periodic  
payments.  
0.83  
10gC  
1ÞP  
10gC  
–1.00  
1ÞP  
$:0+  
750~z  
$+:0³ 11.64  
64.45  
750z~³  
Monthly payment to be  
received.  
If solving for the payment amount will be done repetitively, key in the following hp  
12c platinum program.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
001, 43  
002, 42 34  
000,  
001, 43  
002, 42 34  
f
CLEAR  
Î
f
CLEAR  
Î
g  
g  
8
8
f
CLEAR  
G
f
CLEAR  
G
003, 45  
004, 45  
005,  
0
1
003, 45  
004,  
0
30  
1
:0  
:1  
-
:0  
-
30  
11  
2
005, 45  
006,  
:1  
n
n
006,  
11  
2
007, 45  
007, 45  
:2  
:2  
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204 Section 14: Leasing  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
008,  
¼
¼
008,  
12  
1
12  
1
009,  
009,  
1
1
Þ
P
$
:1  
+
Þ
P
$
+
010,  
16  
14  
13  
1
010,  
16  
14  
13  
40  
1
011,  
011,  
012,  
012,  
013, 45  
014,  
013,  
40  
3
014, 45  
015,  
:1  
³
015, 45  
016,  
36  
3
:3  
~
34  
10  
016, 45  
017,  
:3  
z
z
017,  
10  
34  
36  
fs  
~
018,  
³
019,  
fs  
REGISTERS  
PV: Used  
R1: #Adv. Pmt.  
n: n–#Adv. Pmt.  
FV: 0  
i: i  
PMT: –1  
R2: i  
R0: n  
R3: Loan  
R4–R.7: Unused  
1. Key in the program.  
2. Key in the total number of payments in the lease then press ?0.  
3. Key in the total number of payments made in advance then press ?1.  
4. Key in the periodic interest rate as a percentage then press ?2.  
5. Key in the loan amount and press ?3; then press t to obtain the  
periodic payment to be received by the lessor.  
6. For a new case, return to step 2. The values changed from the previous case  
are the only values which need to be entered.  
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Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 14: Leasing 205  
Example 2: Using the preceding program, solve for the monthly payment using  
the information given in example 1. Then change the yearly interest to 15% and  
solve for the new payment amount.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
12?0  
3?1  
f[  
12?0  
3?1  
12.00  
3.00  
Duration of lease.  
Number of advance  
payments.  
0.83  
0.83  
64.45  
10\12z  
?2  
10z12³  
?2  
Periodic interest rate.  
750?3t  
750?3t  
Monthly payment to be  
received.  
1.25  
15\12z  
15z12³  
?2t  
?2t  
65.43  
Monthly payment to  
achieve a 15% yield.  
Example 3: Using the information from example 1, what monthly payment is  
necessary to yield the lessor 15% annually if one payment is due at the time of  
?
closing  
Assuming that the previous example was just solved, the keystrokes are as follows:  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
66.86  
1?1t  
Monthly payment to be  
received.  
1?1t  
Since this problem is an annuity due situation (one payment at the beginning of the  
period) the calculation could also be done as follows:  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
g×  
g×  
fCLEARG  
12n  
fCLEARG  
12n  
12.00  
1.25  
Duration of lease.  
15gC  
15gC  
Periodic interest rate (into i).  
66.86  
750Þ$P 750Þ$P  
Monthly payment to be  
received.  
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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
206 Section 14: Leasing  
Solving for Yield  
To calculate the periodic yield, information is entered as follows:  
1. Press and fCLEARG.  
RPN Mode:  
2. Key in the total number of payments in the lease then press \.  
3. Key in the total number of payments made in advance then press  
?0-n.  
4. Key in the periodic payment to be received then press P.  
5. Key in the total amount of the loan then press Þ:0:P§+$.  
6. Press ¼ to obtain the periodic yield.  
ALG Mode:  
2. Key in the total number of payments in the lease then press -.  
3. Key in the total number of payments made in advance then press  
?0n.  
4. Key in the periodic payment to be received then press P.  
5. Press :0§:P³+ Then key in the total amount of the loan and  
.
press Þ$.  
6. Press ¼ to obtain the periodic yield.  
Example 1: A lease has been written to run for 60 months. The leased  
equipment has a value of $25,000 with a $600 monthly payment. The lessee has  
agreed to make 3 payments at the time of closing ($1,800). What is the annual  
?
yield to the lessor  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
60\3  
fCLEARG  
60-3  
3.  
?0-n  
?0n  
57.00  
Number of periodic  
payments.  
600.00  
600P  
600P  
Monthly payment.  
PV.  
25000Þ: :0§:  
0:P§  
+$  
P+25000  
Þ$  
-23,200.00  
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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 14: Leasing 207  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
¼
¼
1.44  
Monthly yield  
(calculated).  
12§  
§12³  
17.33  
Annual yield (as a  
percentage).  
If solving for yield will be done repetitively, key in the following hp 12c platinum  
program:  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fCLEARÎ  
g  
fCLEARG  
:0  
fs  
000,  
001, 43  
002, 42 34  
000,  
001, 43  
002, 42 34  
fCLEARÎ  
g  
8
8
fCLEARG  
:0  
003, 45  
004, 45  
005,  
0
1
003, 45  
004,  
0
30  
1
-
:1  
-
30  
11  
2
005, 45  
006,  
:1  
n
n
006,  
11  
2
007, 45  
008,  
007, 45  
008,  
:2  
:2  
P
§
P
14  
3
14  
20  
1
009, 45  
010,  
009,  
:3  
Þ
:1  
:P  
§
16  
1
010, 45  
011,  
:1  
-
011, 45  
30  
3
012, 45 14  
012, 45  
013,  
:3  
$
013,  
014,  
015,  
016,  
20  
40  
13  
12  
13  
12  
+
¼
014,  
$
:gC  
fs  
015,45,43 12  
¼
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 207 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
208 Section 14: Leasing  
KEYSTROKES  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
(RPN mode)  
:gC  
fs  
017,45,43 12  
REGISTERS  
n: n–#Adv. Pmts.  
FV: 0  
i: i  
PV: Used  
PMT: Pmt.  
R2: Pmt.  
R0: n  
R1: Adv. Pmts.  
R3: Loan  
R4–R.7: Unused  
1. Key in the program.  
2. Key in the total number of payments in the lease then press ?0.  
3. Key in the total number of payments made in advance then press ?1.  
4. Key in the periodic payment to be received then press ?2.  
5. Key in the total amount of the loan, then press ?3; then press t to  
obtain the periodic yield.  
6. For a new case, return to step 2. The values changed from the previous case  
are the only values which need to be re-entered.  
Example 2: Using the program, solve for yield using the same information given  
in example 1. Then change the payment to $625 and solve for the yield.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
60?0  
3?1  
f[  
60?0  
3?1  
Number of payments.  
60.00  
3.00  
Number of advance  
payments.  
Periodic payment.  
600.00  
17.33  
600?2  
600?2  
Annual yield (as a  
percentage).  
25000?3t 25000?3t  
Annual yield (as a  
percentage) when PMT is  
increased $25.  
19.48  
625?2t  
625?2t  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 208 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 14: Leasing 209  
Advance Payments With Residual  
Situations may arise where a transaction has advance payments and a residual  
value (salvage value) at the end of the normal term.  
Solving for Payment  
The following program solves for the periodic payment amount necessary to  
achieve a desired yield.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
001, 43  
002, 42 34  
000,  
001, 43  
002, 42 34  
f
CLEAR  
Î
G
f
CLEAR  
Î
G
g  
g  
8
8
f
CLEAR  
f
CLEAR  
003, 45  
004,  
0
11  
1
003, 45  
004,  
0
11  
1
:0  
n
:0  
n
005, 45  
006,  
005, 45  
006,  
:1  
¼
:1  
¼
12  
3
12  
3
007, 45  
008,  
007, 45  
008,  
:3  
M
$
:2  
+
:3  
M
$
+
15  
13  
2
15  
13  
40  
2
009,  
009,  
010, 45  
011,  
010,  
40  
5
011, 45  
012,  
:2  
³
012, 44  
013,  
36  
5
?5  
0
0
013, 44  
014,  
?5  
0
M
014,  
15  
0
:n  
M
015, 45 11  
015,  
15  
:n  
-
016, 45  
017,  
4
016, 45 11  
017, 30  
:4  
-
30  
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210 Section 14: Leasing  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
n
018,  
11  
1
018, 45  
019,  
4
11  
1
:4  
n
019,  
1
Þ
P
$
020,  
16  
14  
13  
4
020,  
1
Þ
P
$
+
021,  
021,  
16  
14  
13  
40  
4
022,  
022,  
023, 45  
024,  
023,  
:4  
+
40  
5
024,  
025, 45  
026,  
025, 45  
026,  
:5  
~
z
:4  
³
34  
10  
36  
5
027,  
027, 45  
028,  
:5  
z
fs  
10  
34  
36  
~
029,  
³
030,  
fs  
REGISTERS  
n: Used.  
i: Interest  
PV: Used  
R1: Interest.  
R5: Used  
PMT: –1.  
FV: Residual  
R3: Residual  
R0: # Pmts (n)  
R2: Loan.  
R4: # Adv. Pmt.  
R6–R.6: Unused  
1. Key in the program.  
2. Key in the total number of payments then press ?0.  
3. Key in or calculate the periodic interest rate then press ?1.  
4. Key in the loan amount then press ?2.  
5. Key in the residual value then press ?3.  
6. Key in the total number of payments made in advance then press ?4.  
Then press t to obtain the payment amount received by the lessor.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 210 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Section 14: Leasing 211  
7. For a new case, return to step 2. The values changed from the previous case  
are the only values which need to be re-entered.  
Example 1: A copier worth $22,000 is to be leased for 48 months. The lessee  
has agreed to make 4 payments in advance, with a purchase option at the end of  
48 months enabling him to buy the copier for 30% of the purchase price. What  
monthly payment is necessary to yield the lessor 15% annually:  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
48.00  
48?0  
48?0  
Duration of lease.  
15.00  
15\  
15z  
1.25  
12z?1  
22000?2  
30b?3  
4?4t  
12³?1  
22000?2  
Monthly interest rate.  
22,000.00  
6,600.00  
487.29  
§
30b³?  
3
4?4t  
Monthly payment received  
by lessor.  
Example 2: Using the information from example 1, what would the monthly  
?
payments be if the lessor desired a yield of 18% annually  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
487.29  
1.50  
From previous example.  
Monthly interest rate.  
18\12z  
18z12³  
?1t  
?1t  
520.81  
Monthly payment received  
by lessor.  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 211 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
212 Section 14: Leasing  
Solving for Yield  
Solving for yield is essentially the same as solving for Internal Rate of Return (IRR).  
The keystrokes are as follows:  
1. Press fCLEARH.  
2. Key in the amount of the first cash flow then press gJ. This initial amount  
is the difference between the initial loan amount and any payments received  
at closing time. Observe the sign convention: positive for cash received and  
negative for cash paid out.  
3. Key in the amount of the first cash flow then press gK. Then key in the  
number of times that cash flow occurs then press ga.  
4. Key in 0gK then the number of advance payments minus one. Then  
press ga.  
5. Key in the residual then press gK. Then press fL to solve for  
periodic yield.  
Example: Equipment worth $5,000 is leased for 36 months at $145 per month.  
The lessee has agreed to pay the first and last month’s payments in advance. At  
the end of the lease, the equipment may be purchased for $1,500. What is the  
?
annual yield to the lessor if the equipment is purchased  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARH  
5000Þ\  
145\2§= 5000Þ  
gJ gJ  
fCLEARH  
145§2=  
Net amount of cash  
advanced.  
–4,710.00  
34.00  
145gK34g 145gK34g  
a
Thirty-four cash flows of  
$145.00.  
a
0.00  
0gK  
1500gK  
fL12§  
0gK  
1500gK  
Thirty-fifth cash flow.  
Thirty-sixth cash flow.  
Annual yield to lessor.  
1,500.00  
fL§12³ 18.10  
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Section 15  
Savings  
Nominal Rate Converted to Effective Rate  
Given a nominal interest rate and the number of compounding periods per year,  
this keystroke procedure computes the effective annual interest rate.  
1. Press and fCLEARG.  
RPN Mode:  
2. Key in the annual nominal rate as a percentage, then press \.  
3. Key in the number of compounding periods per year, then press nz¼.  
4. Press ÞPM to obtain the effective annual interest rate.  
ALG Mode:  
2. Key in the annual nominal rate as a percentage.  
3. Press z. Key in the number of compounding periods per year, then  
press ¼ÞP. Then key in the number of compounding periods per  
year and press n.  
4. Press M to obtain the effective annual interest rate.  
Example 1: What is the effective annual interest rate if the annual nominal rate  
?
of 5.25% is compounded quarterly  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
g  
g  
fCLEARG  
5.25\  
4nz¼  
fCLEARG  
5.25z  
4¼  
5.25  
1.31  
Nominal rate.  
Percent quarterly interest  
rate.  
ÞPM  
ÞP4nM 5.35  
Percent effective interest  
rate.  
213  
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214 Section 15: Savings  
For repeated calculations, the following hp 12c platinum program can be used:  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
001, 43  
002, 42 34  
000,  
001, 43  
002, 42 34  
f
CLEAR  
Î
G
f
CLEAR  
Î
G
g  
g  
8
8
f
CLEAR  
f
CLEAR  
n
n
003,  
004,  
005,  
006,  
007,  
008,  
11  
10  
12  
16  
14  
15  
003,  
004,  
005,  
006,  
007,  
008,  
009,  
010,  
11  
34  
10  
34  
12  
16  
14  
15  
z
~
z
¼
Þ
P
M
fs  
~
¼
Þ
P
M
fs  
REGISTERS  
i: Nom. Rate/n PV: 0  
R0–R.9: Unused  
n: # Periods.  
FV: Eff. Rate  
PMT: Used.  
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Section 15: Savings 215  
1. Key in the program.  
2. RPN: Key in the annual nominal rate as a percentage then press \.  
2. ALG: Key in the annual nominal rate as a percentage then press ³.  
3. Key in the number of compounding periods per year then press t to  
obtain the effective annual interest rate.  
4. For a new case return to step 2.  
Example 2: What is the effective annual rate of interest if the annual nominal  
?
rate of 5.25% is compounded monthly  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
5.25  
5.38  
5.25\  
5.25³  
12t  
12t  
Percent effective interest  
rate.  
Effective Rate Converted to Nominal Rate  
Given an effective interest rate and the number of compounding periods per year,  
this routine calculates the nominal interest rate.  
1. Press fCLEARG.  
2. Key in the number of periods per year then press n.  
3. Key in 100 then press $.  
RPN Mode:  
4. Key in the effective annual rate as a percentage then press +ÞM¼.  
5. Press :n§ to obtain the annual nominal rate.  
ALG Mode:  
4. Press +. Key in the effective annual rate as a percentage then press  
³ÞM¼.  
5. Press §:n³ to obtain the annual nominal rate.  
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Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
216 Section 15: Savings  
Example: Find the nominal rate compounded quarterly if the effective annual rate  
is 5.35%.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
fCLEARG  
4n100$  
5.35+Þ  
M¼  
fCLEARG  
4n100$  
+5.35³Þ  
M¼  
100.00  
–105.35  
1.31  
:n§  
§:n³  
5.25  
Percent nominal interest  
rate.  
Continuous Rate Converted to Effective Rate  
This procedure converts a continuous annual interest rate to the effective rate.  
1. RPN: Press 1\.  
1. ALG: Press 1³.  
2. Key in the continuous rate as a percentage then press b.  
3. Press g>à.  
Example: What is the effective rate resulting from a 5.25% passbook rate with  
?
continuous compounding  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
0.05  
1.05  
5.39  
1\5.25b  
g>  
1³5.25b  
g>  
à
à
Effective rate.  
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Section 16  
Bonds  
30/360 Day Basis Bonds  
A bond is a contract to pay interest, usually semiannually, at a given rate (coupon)  
and to pay the principal of the bond at some specified future date. A bond which  
is calculated on a 30/360 day basis is one in which the day count basis is  
computed using 30 days in a month and 360 days in a year.  
The following program solves for the price given the yield or for the yield given the  
price of a semiannual coupon bond which is calculated on a 30/360 day basis  
and is held for more than six months.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
001, 42 34  
000,  
001, 42 34  
f
CLEAR  
Î
CLEAR  
f Î  
fCLEARG  
g×  
fCLEARG  
g×  
:2  
002, 43  
003, 45  
004,  
7
2
002, 43  
003, 45  
004,  
7
2
:2  
2
10  
2
z
2
005,  
10  
14  
5
005,  
z
2
006,  
006,  
14  
40  
5
P
:5  
+
P
+
007, 45  
008,  
007,  
40  
15  
3
008, 45  
009,  
:5  
M
009,  
15  
3
M
010, 45  
011, 45  
010, 45  
011, 45  
:3  
:4  
gÒ  
d
:3  
:4  
gÒ  
d
4
4
012, 43 26  
013, 33  
012, 43 26  
013, 33  
217  
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218 Section 16: Bonds  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
014,  
014,  
015,  
016,  
017,  
018,  
1
8
10  
1
z
1
015,  
016,  
017,  
018,  
8
1
0
8
0
8
10  
11  
0
z
0
11  
n
n
019, 43 24  
019, 43 24  
gT  
1
gT  
1
020,  
021,  
022,  
1
34  
30  
020,  
021,  
022,  
023,  
1
30  
34  
20  
~
-
-
~
§
023, 45 14  
:P  
§
024,  
20  
6
024, 45 14  
:P  
}
025, 44  
026, 45  
025,  
36  
6
?6  
:0  
gm  
0
026, 44  
027, 45  
?6  
:0  
gm  
027, 43 35  
028,43,33,039  
0
028, 43 35  
029,43,33,041  
g(039  
2
029,  
2
10  
12  
13  
6
g(041  
030,  
030,  
10  
2
z
z
2
031,  
031,  
¼
032,  
032,  
12  
13  
6
$
¼
$
033, 45  
034,  
033,  
:6  
~
34  
16  
6
034, 45  
035,  
:6  
~
Þ
-
035,  
34  
16  
30  
6
Þ
036, 45  
037,  
036,  
:6  
-
30  
037,  
038,43,33,000  
038, 45  
g(000  
:6  
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Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Section 16: Bonds 219  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
039, 45  
040, 45  
041,  
1
6
039,  
36  
}
:1  
:6  
+
040,43,33,000  
g(000  
:1  
Þ
-
40  
16  
13  
12  
2
041, 45  
042,  
1
16  
30  
6
042,  
Þ
$
043,  
043,  
044,  
044, 45  
045,  
¼
:6  
$
045,  
13  
12  
20  
2
2
046,  
20  
046,  
§
¼
047,  
fs  
§
048,  
2
049,  
36  
}
fs  
REGISTERS  
PV: –Price  
n: days/180  
FV: Red+Cpn./2  
R3: Dset  
i: Yield/2  
R0: Yield  
R4: Dmat  
PMT: Coupon/2.  
R2: Coupon  
R1: Price.  
R5: Redemption  
R6: Accrued Int.  
R7–R.3: Unused  
1. Key in the program.  
2. If the C status indicator is not displayed, press .  
3. Key in the annual coupon interest rate as a percentage then press ?2.  
4. Key in the settlement date (MM.DDYYYY) then press ?3.  
*
5. Key in the maturity date (MM.DDYYYY)* then press ?4.  
6. Key in the redemption value as a percentage of par then press ?5.  
For information about date format see pages 37 to 38.  
*
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220 Section 16: Bonds  
7. If price is desired:  
a. Key in the desired yield to maturity as a percentage then press ?0.  
b. Press t to calculate price as a percentage of par value.  
c. RPN: Press ~ to display accrued interest due the seller. Press + to  
calculate the total price paid.  
c. ALG: Press +~ to display accrued interest due the seller and then  
press } to calculate the total price paid.  
For a new case return to step 3. Note that only those values which have been  
changed need to be reentered and stored.  
8. If yield is desired:  
a. Press 0?0.  
b. Key in the price as a percentage of par value and press ?1.  
c. Press t to compute annual yield to maturity.  
For a new case return to step 3. Note that only those values which have  
been changed need to be reentered and stored.  
Example 1: What price should you pay on August 28, 2004 for a 5.5% bond  
(computed with a 30/360 basis) that matures on June 1, 2008, if you want a  
?
?
yield of 4.75% What price should you pay for a yield of 4.5% This problem  
assumes a redemption value of 100.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
?Æ  
Set compound interest  
mode if the C indicator is  
not on.  
?Æ  
5.50  
8.28  
5.5?2  
5.5?2  
Coupon into R2.  
8.282004?3 8.282004?3  
Settlement date into  
register R3.  
6.01  
6.012008?4 6.012008?4  
Maturity date into R4.  
Redemption value into R5.  
Yield into R0.  
100.00  
4.75  
100?5  
4.75?0  
t
100?5  
4.75?0  
t
102.55  
1.33  
Price (calculated).  
~
~
Accrued interest  
(calculated).  
4.50  
4.5?0  
4.5?0  
New yield into R0.  
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Section 16: Bonds 221  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
t
~
+
t
103.41  
Price to yield 4.5%  
(calculated).  
+~  
³
1.33  
Accrued interest  
(calculated).  
104.74  
Total price paid.  
Example 2: The market is quoting 105% for the bond described in example 1.  
?
What yield will that provide What would be the yield to maturity if 104% were  
?
the quoted price  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
104.74  
0.00  
From previous example.  
0?0  
0?0  
4.05  
105?1t  
105?1t  
Yield at 105%  
(calculated).  
4.33  
104?1t  
104?1t  
Yield at 104%  
(calculated).  
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222 Section 16: Bonds  
Annual Coupon Bonds  
For bonds which have annual coupons, use the following hp 12c platinum  
program to evaluate price and accrued interest on an Actual/Actual day basis.  
This program may be modified for annual coupon bonds to be calculated on a  
30/360 day basis.  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
fs  
fs  
000,  
001, 42 34  
000,  
001, 42 34  
f
CLEAR  
CLEAR  
Î
G
f
CLEAR  
CLEAR  
Î
G
f
f
g  
:0  
n
g  
:0  
n
002, 43  
003, 45  
004,  
8
0
002, 43  
003, 45  
004,  
8
0
11  
2
11  
2
005, 45  
006,  
005, 45  
006,  
:2  
P
:2  
P
:1  
¼
14  
1
14  
1
007, 45  
008,  
007, 45  
008,  
:1  
¼
12  
3
12  
3
009, 45  
010,  
009, 45  
010,  
:3  
M
:3  
M
15  
13  
5
15  
13  
5
$
$
011,  
011,  
012, 45  
013,  
012, 45  
013,  
:5  
Æ
:5  
-
26  
6
30  
26  
6
Æ
014,  
014,  
6
Þ
-
015,  
16  
30  
6
015,  
6
Þ
³
016,  
016,  
16  
36  
6
017, 44  
018, 45  
017,  
?6  
:5  
5
018, 44  
?6  
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Section 16: Bonds 223  
KEYSTROKES  
(RPN mode)  
KEYSTROKES  
(ALG mode)  
DISPLAY  
DISPLAY  
gÒ  
?7  
:6  
:4  
gÒ  
:7  
z
019, 43 26  
019, 45  
5
:5  
gÒ  
020, 44  
021, 45  
022, 45  
7
6
4
020, 43 26  
021, 44  
022, 45  
023, 45  
7
6
4
?7  
:6  
:4  
gÒ  
z
023, 43 26  
024, 45  
025,  
7
10  
11  
0
024, 43 26  
025,  
10  
7
n
026,  
026, 45  
027,  
:7  
n
027,  
11  
0
0
P
M
028,  
14  
15  
16  
028,  
0
P
M
:n  
§
029,  
029,  
14  
15  
Þ
:n  
030,  
030,  
031, 45 11  
031, 45 11  
032, 45  
033,  
2
16  
20  
31  
30  
032,  
20  
2
:2  
Þ
§
033, 45  
034,  
:2  
Þ
+
034,  
16  
40  
31  
34  
36  
16  
t
-
035,  
035,  
t
~
³
036,  
036,  
fs  
037,  
038,  
Þ
fs  
039,  
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224 Section 16: Bonds  
REGISTERS  
PV: Used  
n: Used  
i: Yield  
PMT: Cpn. or 0  
R2: Coupon  
FV: Used  
R0: # Periods (n)  
R4: Settlement  
R8–R.5: Unused  
R1: Yield  
R3: Redemption  
R7: Used  
R5: Next Cpn.  
R6: Last Coupon  
For annual coupon bonds calculated on a 30/360 day basis, insert d after  
at steps 19 and 23 in the RPN mode program and after at steps  
20 and 24 in the ALG mode (making each program two steps longer).  
1. Key in the program and press if the C status indicator is not  
displayed.  
2. Key in the total number of coupons which are received and press ?0.  
3. Key in the annual yield as a percentage then press ?1.  
4. Key in the amount of the annual coupon then press ?2.  
*
5. Key in the redemption value then press ?3.  
*
6. Key in the settlement (purchase) datethen press ?4.  
7. Key in the date of the next coupon then press ?5.  
8. Press t to obtain the amount of accrued interest.  
9. Press t to determine the price of the bond.  
10.For a new case, return to step 2.  
Example: What is the price and accrued interest of a 20-year Eurobond with  
annual coupons of 6.5% purchased on August 15, 2004 to yield 7%. The next  
coupon is received on December 1, 2004.  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
f]  
f[  
?Æ  
?Æ  
Set compound interest  
mode if the C indicator is  
not on.  
20.00  
7.00  
6.50  
20?0  
7?1  
20?0  
7?1  
Total number of coupons.  
Annual yield.  
6.5?2  
6.5?2  
Annual coupon rate.  
Positive for cash received; negative for cash paid out.  
For information about date format see page 37.  
*
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Section 16: Bonds 225  
Keystrokes  
(RPN mode)  
Keystrokes  
(ALG mode)  
Display  
100.00  
8.15  
100?3  
100?3  
Redemption value.  
Settlement date.  
Next coupon date.  
Accrued interest.  
Purchase price.  
8.152004?4 8.152004?4  
12.01  
–4.58  
–94.75  
12.012004?5 12.012004?5  
t
t
t
t
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Appendices  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 227 of 275  
Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Appendix A  
RPN and the Stack  
In RPN mode, four special registers in the hp 12c platinum  
are used for storing numbers during calculations. To  
understand how these registers are used, they should be  
visualized as stacked on top of each other.  
(For this reason, they are generally referred to as the “stack registers” or  
collectively as “the stack.”) The stack registers are designated X, Y, Z, and T.  
Unless the calculator is in Program mode, the number shown in the display is the  
number in the X-register (modified according to the current display format).  
The number in the X-register — and, for two-number functions, the number in the  
Y-register — are the number(s) used in calculations. The Z- and T-registers are used  
primarily for the automatic retention of intermediate results during chain  
calculations, as described in section 1.  
Before we discuss the details of the stack operation, let’s take a quick look at how  
the stack is used in a simple arithmetic calculation and in a chain calculation. For  
each key pressed in the keystroke sequence, the diagram illustrating the  
calculation shows, above the key, the numbers in each of the stack registers after  
that key is pressed.  
First, let’s consider the calculation of 5 – 2:  
The diagram shows why we said in section 1 that the \ key separates the  
second number entered from the first number entered. Note also that this positions  
the 5 in the Y-register above the 2 in the X-register — just like they would be  
positioned if you wrote the calculation vertically on paper:  
228  
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Printed Date: 2005/8/1  
Dimension: 14.8 cm x 21 cm  
Appendix A: RPN and the Stack 229  
Now let’s see what happens in the stack during a chain calculation in RPN mode:  
(3× 4) + (5× 6)  
7
See how the intermediate results are not only displayed when they are calculated,  
but also automatically stored and available in the stack at just the right time!  
That’s basically how the stack operates. In the rest of this appendix, we’ll take a  
more detailed look at how numbers are entered into and rearranged within the  
stack, and the effect of the various hp 12c platinum functions on the numbers in the  
stack.  
Getting Numbers Into the Stack: The  
Key  
As discussed in earlier sections, if two numbers are being keyed in for a  
two-number function — such as + — you press \ between the numbers to  
separate them. The following diagram illustrates what happens in the stack when  
you enter the numbers 10 and 3 (to calculate, for example, 10 ÷ 3). (Assume that  
the stack registers have been already loaded with the numbers shown as the result  
of previous calculations).  
When a digit is keyed into the display, it is simultaneously entered into the  
X-register. As additional digit keys are pressed, the corresponding digits are  
appended (that is, added to the right of) those already in the displayed X-register  
until \ is pressed. As shown in the preceding diagram, pressing \ does the  
following:  
1. It copies the number from the displayed X-register into the Y-register. This  
process is part of the stack lift.  
2. It tells the calculator that the number in the displayed X-register is complete:  
that is, it terminates digit entry.  
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230 Appendix A: RPN and the Stack  
Termination of Digit Entry  
The first digit keyed in after digit entry has been terminated replaces the number  
already in the displayed X-register. Digit entry is automatically terminated when  
any key is pressed (except for digit entry keys — digit keys, ., Þ, and É —  
and prefix keys — f, g, ?, :, and i).  
Stack Lift  
When the stack lifts, the number in each stack register is copied into the register  
above, and the number formerly in the T-register is lost. The number formerly in the  
X-register is then contained in both the X-register and the Y-register.  
When a number is entered into the displayed X-register — either from the  
keyboard, from a storage register (using :), or from the LAST X register (using  
F) — the stack usually lifts first. The stack does not lift if the last key pressed  
before a number is entered was one of the following: \ , O, _ or ^. If  
*
one of these keys was the last key pressed, the number in the displayed X-register  
is replaced when a new number is entered.  
Rearranging Numbers in the Stack  
The  
Key  
Pressing ~ exchanges the numbers in the X- and  
Y-registers.  
Certain functions (Ò, Ï, !, E, V, Ý, #, Ö, v, R, and Q)  
return answers to the Y-register as well as to the displayed X-register. The ~ key,  
since it exchanges the number in the Y-register with that in the displayed X-register,  
is used to display the second number calculated.  
The  
Key  
When d (roll down) is pressed the number in each  
stack register is copied into the register below, and the  
number formerly in the X-register is copied into the  
T-register.  
Pressing d four times successively displays the numbers in the Y-, Z-, and  
T-registers and returns the numbers to their original registers.  
Note also that although the stack lifts when \ is pressed, it does not lift when a number is  
*
entered after \ is pressed.  
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Appendix A: RPN and the Stack 231  
One-Number Functions and the Stack  
One-number mathematics and number-alteration functions — y, r, °, >,  
¡, e, B, Ñ, and T — use only the number in the displayed X-register.  
When the key is pressed, the function is performed upon the number in the  
X-register, and the answer is then placed into the X-register. The stack does not lift,  
so the number formerly in the X-register does not get copied into the Y-register; but  
this number is copied into the LAST X register. The numbers in the Y-, Z-, and  
T-registers are not affected when a one number function is performed.  
Two-Number Functions and the Stack  
Two-number functions — +, -, §, z, q, b, à, and Z — use the  
numbers in both the X- and the Y-registers.  
Mathematics Functions  
To perform an arithmetic operation, the numbers are positioned in the X- and  
Y-registers just as you would write them vertically on paper: the number you would  
write on top goes in the Y-register, and the number you would write on the bottom  
goes in the X-register. For example, to do each of the four arithmetic calculations  
shown below, you would put the 8 in the Y-register (using \ and then key the 2  
into the displayed X-register.)  
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232 Appendix A: RPN and the Stack  
When an arithmetic operation or q is performed, the answer is placed in the  
X-register, the number formerly in the X-register is copied into the LAST X register,  
and the stack drops. When the stack drops, the number in the Z-register is copied  
into the Y-register, and the number in the T-register is copied into the Z-register but  
also remains in the T-register.  
The diagram on the next page illustrates the stack operation when 8 ÷ 2 is  
calculated. (Assume that the stack and LAST X registers have already been loaded  
with the numbers shown as the result of previous calculations.)  
Percentage Functions  
When any of the three percentage functions is performed, the answer is placed in  
the X-register, the number formerly in the X-register is copied into the LAST X  
register, but the stack does not drop. The numbers in the Y-, Z-, and T-registers are  
not changed when a percentage function is performed.  
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Appendix A: RPN and the Stack 233  
Calendar and Financial Functions  
The following table shows what quantity is in each stack register after the indicated  
calendar or financial function key is pressed. The symbols x, y, z, and t represent  
the number that was in the corresponding register (X, Y, Z, or T, respectively) at  
the time the function key was pressed.  
n, ¼, $,  
P, M, l,  
Register  
D
Ò
Ï
!
L
T
t
t
t
x
z
y
y
x (number of  
payments)  
Z
z
INT365  
Y
X
z
DYS30-day  
–PV  
x
PMTPRIN  
n, i, PV, PMT,  
FV, NPV, IRR  
DATE  
DYSactual  
INT360  
PMTINT  
Register  
V, Ý, #  
E
S
T
y (settlement date)  
z
y
Z
x (maturity date)  
y (settlement date)  
x (number of year)  
RDV (remaining  
depreciable value)  
Y
X
INT  
x (maturity date)  
PRICE  
YTM  
DEP  
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234 Appendix A: RPN and the Stack  
The LAST X Register and the  
Key  
The number in the displayed X-register is copied into the LAST X register  
whenever any of the following function keys is pressed:  
+
q
-
>
§
¿
_
b
¡
z
r
^
à
y
B
Q
T
R
Ñ
e
Z
D
Ò
Pressing gF lifts the stack (unless \, O, _ or ^ was the last key  
pressed, as described on page 230), then copies the number from the LAST X  
register into the displayed X-register. The number remains also in the LAST X  
register.  
Chain Calculations in RPN Mode  
The automatic stack lift and stack drop make it possible to do chain calculations  
without the necessity for keying in parentheses or storing intermediate results, as  
are required on some other calculators. An intermediate result in the displayed  
X-register is automatically copied into the Y-register when a number is keyed in  
after a function key is pressed. Therefore, when a two-number function key is  
*
then pressed, that function is performed using the number keyed into the displayed  
X-register and the intermediate result in the Y-register. The number then in the  
Y-register, if remaining as an intermediate result from an earlier calculation, can  
then be used with the intermediate result in the X-register for another calculation.  
The diagram on page 229 illustrates how the automatic stack lift and stack drop  
make chain calculations quick and error-free.  
Except for \, O, _, ^. For more information, refer to Stack Lift, page 230.  
*
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Appendix A: RPN and the Stack 235  
Virtually every chain calculation you are likely to encounter can be done using  
only the four stack registers. However, to avoid having to store an intermediate  
result in a storage register, you should begin every chain calculation at the  
innermost number or pair of parentheses and then work outward — just as you  
would if you were doing the calculation manually (that is, using pencil and paper).  
For example, consider the calculation of  
3 [4 + 5 (6 + 7)]  
If this calculation were done from left to right — as were the (simpler) examples  
under Chain Calculations on page 23 and page 25 — you would have to enter  
five numbers into the calculator before doing the first operation possible (6 + 7).  
But since the stack holds only four numbers, this calculation cannot be done  
left-to-right. However, it can easily be done if you begin with the calculation in the  
innermost pair of parentheses — again, (6 + 7).  
Keystrokes  
Display  
(RPN mode)  
13.00  
65.00  
69.00  
6\7+  
5§  
Intermediate result of (6+7).  
Intermediate result of 5 (6+7).  
4+  
Intermediate result of [4 + 5(6 +  
7)].  
207.00  
3§  
Final result: 3 [4 + 5 (6 + 7)].  
Arithmetic Calculations with Constants  
Because the number in the T-register remains there when the stack drops, this  
number can be used as a constant in arithmetic operations. To place the constant  
into the T-register, key it into the display (that is, into the X-register), then press  
\ three times. This also places the constant in the Y and Z-registers. Each time  
an arithmetic operation is then performed — using the constant in the Y-register  
and a number keyed into the displayed X-register — the constant will be  
“dropped” back into the Y-register.  
Example: The annual sales of solar engineering hardware your firm — currently  
$84,000 — are projected to double each year for the next 3 years. Calculate the  
annual sales for each of those years.  
Keystrokes  
Display  
(RPN mode)  
2\\  
\
2.00  
Enters constant into Y, Z, and  
T-registers.  
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236 Appendix A: RPN and the Stack  
Keystrokes  
Display  
(RPN mode)  
84,000.  
84000  
Enters base amount into displayed  
X-register.  
§
§
§
168,000.00  
336,000.00  
672,000.00  
Annual sales after first year.  
Annual sales after second year.  
Annual sales after third year.  
In the example above, the constant was repeatedly multiplied by the result of the  
previous operation, which was already in the displayed X-register. In another class  
of calculations with constants, the constant is multiplied by (or added to, etc.) a  
new number keyed into the displayed X-register. For these calculations, you must  
press O before keying in a new number after having pressed an operator key. If  
this were not done, the stack would lift when you keyed in a new number after  
pressing the operator key, and the Y-register would no longer contain the constant.  
(Recall — from page 230 — that the stack does not lift when a number is keyed  
into the displayed X-register after O is pressed.)  
Example: At Permex Pipes a certain pipe fitting is packaged in quantities of 15,  
75, and 250. If the cost per fitting is $4.38, calculate the cost of each package.  
*
Keystrokes  
Display  
(RPN mode)  
4.38\\  
\
4.38  
15.  
Enters constant into Y-, Z-, and  
T-registers.  
15  
Enters first quantity into displayed  
X-register.  
§
65.70  
75.  
Cost of a package of 15.  
O75  
Clears display and enters second  
quantity into displayed X-register.  
§
328.50  
250.  
Cost of a package of 75.  
O250  
Clears display and enters third  
quantity into displayed X-register.  
§
1,095.00  
Cost of a package of 250.  
You may want to compare this method of arithmetic calculations with constants to the method  
*
using F described on page 91.  
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Appendix B  
Algebraic Mode (ALG)  
Although most of this material is included at the appropriate places throughout this  
manual, it is collected here for easy reference.  
To select algebraic mode, press f[. When the calculator is in algebraic mode,  
the ALG status indicator is lit.  
Note: In ALG mode, it is a good idea to begin calculations by pressing  
OO. This will ensure that there are no pending arithmetic calculations  
that might interfere with the solution of a new problem. The reason this key is  
pressed twice is that pressing it the first time clears the display and X-register  
only, allowing you to correct an erroneous entry by keying in a correct  
number. The second press of O will clear any pending operations as well.  
Pressing the } key is another way to ensure that there are no pending  
operations before beginning a new calculation.  
Simple Arithmetic Calculations in ALG Mode  
To calculate 21.1 + 23.8:  
Keystrokes  
Display  
(ALG mode)  
OO  
0.00  
Clears any pending operations.  
21.10  
21.1+  
Enters first number and prepares to  
add.  
23.8  
23.8  
Enters the second number.  
}
44.90  
}
completes the calculation.  
Once a calculation has been completed:  
z
pressing another digit key starts a new calculation, or  
pressing an operator key continues the calculation.  
z
Keystrokes  
(ALG mode)  
Display  
OO  
0.00  
Clears any pending operations.  
77.35  
77.35-  
Enters first number and prepares to  
subtract.  
237  
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238 Appendix B: Algebraic Mode (ALG)  
Keystrokes  
Display  
(ALG mode)  
–13.54  
96.75  
}
90.89}  
completes the calculation.  
New calculation:  
Calculates 96.75 ÷ 3.5  
65gr§12}  
65 ×12  
z3.5}  
27.64  
You can also do long calculations without pressing } after each intermediate  
calculation: just press it at the end. The operators perform from left to right, in the  
order you enter them.  
Keying in Negative Numbers (  
)
The Þ key changes the sign of a number.  
z
To key in a negative number, type that number and then press Þ.  
To change the sign of an already displayed number, press Þ.  
z
Keystrokes  
(ALG mode)  
Display  
OO  
75Þ  
0.00  
Clears any pending operations.  
Changes the sign of 75  
Multiplies –75 by 7.1  
–75.  
§7.1}  
–532.50  
Chain Calculations in ALG Mode  
To do a chain calculation, you don’t need to press } after each operation, but  
only at the very end.  
750x12  
360  
For instance, to calculate  
you can enter either:  
z
z
750 § 12 } z 360 } or  
750 § 12 z 360 }  
In the second case, the z key acts like the } key by displaying the result of 750  
× 12.  
456 75 68  
×
Here’s a longer chain calculation:  
18.5  
1.9  
This calculation can be written as: 456 – 75 ÷ 18.5 × 68 ÷ 1.9. Watch what  
happens in the display as you key it in:  
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Appendix B: Algebraic Mode (ALG) 239  
Keystrokes  
(ALG mode)  
Display  
OO  
456-75z  
18.5§  
68z  
0.00  
Clears any pending operations.  
381.00  
20.59  
1,400.43  
737.07  
1.9}  
The  
Key in ALG Mode  
LAST X in ALG mode is not used in this book. It is the one function that is quite  
different in ALG and RPN modes. Refer to page 234 for the list of 23 different key  
presses that cause the displayed X-register to be copied into the LAST X register in  
RPN mode. In ALG mode, those key presses do not cause a refresh of the LAST X  
register. Instead, the displayed number is copied into the LAST X register when a  
new calculation commences either with digit entry (i.e., when one of the digits  
0-9, the decimal point, or Æ is pressed) or with gF itself, but not when a  
number is recalled using :.  
When gF is actually executed in ALG mode, it simply swaps the value in the  
X-register with the value in LAST X. Therefore, in ALG mode, it never lifts the stack  
and in general, it changes the value in LAST X. However, in RPN mode,  
gF always lifts the stack and leaves the value in LAST X unchanged.  
In general, LAST X in ALG mode is only useful in programs, where it can often be  
used instead of a numbered storage register, as it persists unchanged at least until  
digit entry or gF. There is an example of its use in the Combinations program  
in the hp 12c platinum Solutions Handbook.  
The History Stack in ALG Mode  
In ALG mode, the stack holds a “history” of 4 completed results. These results may  
be rearranged using d and ~ in the same way as described on page 230, for  
RPN mode.  
,
,
,
Note that once a two-numbered function (such as + - § z or q) has had  
the second argument entered, the two arguments cannot then be swapped using  
~ because when the second argument is entered it replaces the first, which is  
removed from the stack. So, if you wish to do 25.83 - 144.25, but then realize  
you meant to do 144.25 - 25.83, the way to correct this is to proceed and do  
. All ~ will do at this point is replace the 144.25 with whatever was  
displayed before the 25.83 was entered, and the first argument remains  
unchanged.  
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240 Appendix B: Algebraic Mode (ALG)  
The stack diagrams showing the output for the Calendar and Financial functions on  
page 233 are the same for ALG as RPN mode. To add INT and PRICE after  
executing the bond E function, press +~}. In this case, ~ is used to  
enter the second argument for the + operation. After executing +~}, the  
total price (INT + PRICE) will be displayed. LAST X will be unchanged, but the  
original PRICE will be found in the Y-register. One can also do +d} to get the  
total price, with the only difference being that the original PRICE would then be in  
the T-register.  
Parentheses Calculations  
In ALG mode, parentheses can be used in calculations to change the order in  
which operations are evaluated. When there are pending open parentheses, the ( )  
status indicator will be shown in the display. As open parentheses are closed, the  
expression contained within the parentheses is evaluated. The final result of a  
calculation will be displayed when you press the ³ key, and then any pending  
parentheses will be closed. You can’t use more than 13 pending (opened)  
parentheses at the same time.  
8
(5 1)  
Keying 8 ÷ 5 – 1 will calculate 8 ÷ 5 first and then the result (1.6) will have 1  
subtracted from it (resulting in 0.6).  
Keystrokes  
Display  
(ALG mode)  
OO  
0.00  
5.00  
4.00  
2.00  
Clears any pending operations.  
No calculation is done.  
Calculates 5 1.  
8
8zgØ5-  
1gÙ  
³
Calculates  
.
(5 1)  
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Appendix B: Algebraic Mode (ALG) 241  
Percentage Functions  
In most cases, b divides a number by 100.  
The one exception is when a plus or minus sign precedes the number.  
For instance, 25 b results in 0.25.  
To find 25% of 200, press: 200 § 25 b}. (Result is 50.)  
You can also calculate a net amount all in one calculation:  
For instance, to decrease 200 by 25%, just enter 200-25b}. (Result is 150.)  
Example: You borrow $1,250 from a relative, and agree to repay the loan in a  
?
year with 7% simple interest. How much money will you owe  
Keystrokes  
Display  
(ALG mode)  
OO  
0.00  
Clears any pending operations.  
Interest on the loan is $87.50.  
87.50  
1250+7b  
}
1,337.50  
You owe this amount at the end of  
one year.  
Percent Difference  
To find the percent difference between two numbers:  
1. Key in the base number.  
2. Press } to separate the other number from the base number.  
3. Key in the other number.  
4. Press à.  
Example: Yesterday your stock fell from 35.5 to 31.25 per share. What is the  
?
percent change  
Keystrokes  
(ALG mode)  
Display  
OO  
0.00  
Clears any pending operations.  
35.50  
35.5}  
Keys in the base number and  
separates it from the other number.  
31.25  
31.25  
Keys in the other number.  
Nearly a 12% decrease.  
à
-11.97  
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242 Appendix B: Algebraic Mode (ALG)  
Percent of Total  
To calculate what percentage one number is of another:  
1. Calculate the total amount by adding all individual amounts.  
2. Key in the number whose percentage equivalent you wish to find.  
3. Press Z.  
Example: Last month, your company posted sales of $3.92 million in the U.S.,  
$2.36 million in Europe, and $1.67 million in the rest of the world. What  
?
percentage of the total sales occurred in Europe  
Keystrokes  
Display  
(ALG mode)  
OO  
3.92+  
2.36+  
1.67}  
0.00  
3.92  
6.28  
7.95  
Clears any pending operations.  
Keys in the first number.  
Adds the second number.  
Adds the third number to get the  
total.  
Keys in 2.36 to find out what  
percentage it is of the number in  
the display.  
2.36  
2.36  
Europe had nearly 30% of the total  
sales.  
Z
29.69  
The Power Function  
Pressing q calculates a power of a number, that is, yx. Like the arithmetic function  
+, q requires two numbers:  
1. Key in the base number (which is designated by the y on the key).  
2. Press q and key in the exponent (which is designated by the x on the key)  
3. Press } to calculate the power.  
Don’t forget to press OO if you are unsure if there are any pending  
operations.  
Keystrokes  
To Calculate  
Display  
(ALG mode)  
21.4  
2q1.4}  
2.64  
0.38  
–8.00  
1.26  
2–1.4  
(–2)3  
2q1.4Þ}  
2Þq3}  
2q3y}  
or 21/3  
3
2
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Appendix C  
More About L  
Given a sequence of positive and negative cash flows, we hope that there is  
enough information to determine whether an IRR answer exists, and what that  
answer is. For the vast majority of cases, your hp 12c platinum will find the unique  
IRR answer if it exists. But the IRR computation is so complex that if the cash flow  
sequence does not meet certain criteria, then sometimes the calculator is unable to  
determine whether or not an answer or answers exist.  
Let’s look at all of the possible outcomes of IRR as calculated by your hp 12c  
platinum:  
Case 1: A positive answer. If a positive answer is displayed, it is the only such  
answer. One or more negative answers may also exist.  
Case 2: A negative answer. If a negative answer is displayed, there may be  
additional negative answers, and there may be a single positive answer. If  
additional answers (negative or positive) exist, they can be calculated using the  
procedure described below.  
Case 3: The calculator displays Error 3. This indicates that the computation is  
very complex, possibly involving multiple answers, and cannot be continued until  
you give the calculator an estimate of IRR. The procedure for doing so is described  
below.  
Case 4: The calculator displays Error 7. This indicates that there is no answer to  
the computation of IRR with the cash flow amounts you have entered. This situation  
is probably the result of a mistake in entering the magnitudes or signs of the cash  
flows or the number of times a cash flow amount occurs consecutively. Refer to  
Reviewing Cash Flow Entries (page 79) and Changing Cash Flow Entries (page  
80) to check and correct the entries. Error 7 will result if there is not at least one  
positive cash flow and at least one negative cash flow.  
Although the calculator will eventually reach one of the above outcomes, it may  
take a long time to get there. You may wish to terminate the IRR iterative process,  
by pressing any key, to see what interest rate the calculator has computed at that  
point. If you stop the calculation, you may continue searching for IRR as described  
below.  
243  
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244 Appendix C: More About L  
Searching for IRR. You can continue searching for IRR solutions, even after an  
Error 3 indication, as follows:  
1. Make a guess for the interest rate and key it in.  
2. Press:gt.  
Your guess will aid the calculator in its search, and if it finds an IRR answer near  
your guess, that answer will be displayed. Since the calculator cannot tell you the  
number of solutions that exist when there is more than one mathematically correct  
answer, you can continue to make guesses, pressing :gt after each one,  
to search for IRR solutions.  
You can hasten this process by using the l function to help you make a good  
guess. Remember that a correct IRR solution will make the calculated NPV very  
small. So continue to guess interest rates and solve for NPV until the answer you  
obtain is reasonably close to zero. Then press :gt to calculate the IRR  
answer near your guess.  
?
How would this work in case 2 above The calculator displays a negative answer  
and you wish to check for a unique positive IRR. Key in successively larger guesses  
for i (starting from 0) and solve for NPV until you reach a sign change in your NPV  
outcomes. Then press :gt to find an IRR solution near the last interest rate  
obtained using the l key.  
If you stop the IRR iterative process, you can test the interest obtained using l,  
and then restart the process by pressing :gt.  
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Appendix D  
Error Conditions  
Some calculator operations cannot be performed under certain conditions (for  
example, z when x = 0). If you attempt such an operation under these conditions,  
the calculator will display the word Error followed by a digit, 0 through 9. Listed  
below are operations that cannot be performed under the conditions specified. The  
symbols x and y represent the number in the X- and Y-registers, respectively, when  
the operation key is pressed.  
Error 0: Mathematics  
Operation  
Condition  
z
y
r
°
q
x = 0  
x = 0  
x < 0  
x 0  
y = 0 and x 0  
y < 0 and x is noninteger.  
à
y = 0  
Z
y = 0  
?z(0 through 4)  
x = 0  
e
x is noninteger  
x < 0  
245  
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246 Appendix D: Error Conditions  
Error 1: Storage Register Overflow  
Operation  
Condition  
?+(0 through 4)  
?-(0 through 4)  
(0 through 4)  
?z(0 through 4)  
A
Magnitude of result is greater than  
9.999999999×1099.  
Error 2: Statistics  
Operation  
Condition  
Ö
v
n (number in R1) = 0  
Σx = 0  
n = 0  
n = 1  
nΣx2 – (Σx)2< 0  
nΣy2 – (Σy)2< 0  
R
Q
n = 0  
nΣx2 – (Σx)2 = 0  
n = 0  
nΣy2 – (Σy)2 = 0  
R~  
Q~  
[nΣx2 – (Σx)2][nΣy2 – (Σy)2] 0  
Error 3: IRR  
Refer to Appendix C.  
Error 4: Memory  
z
z
z
z
Attempting to enter more than 400 program lines.  
Attempting to i to a program line that does not exist.  
Attempting storage register arithmetic in R5 through R9 or R.0 through R.9.  
Too many open parentheses.  
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Appendix D: Error Conditions 247  
Error 5: Compound Interest  
Operation  
Condition  
n
i = 0 and PMT = 0  
PMT is between FV × d and –PV × d, inclusive,  
i
(
)
100  
where d =  
, where S=0 for END  
S
100  
(1+ i ×  
)
mode and 1 for BEG mode.  
i –100  
¼
n=0  
n 1010 or n < 0  
i –100  
Cash flows all have same sign.  
$
i –100  
P
n = 0  
i –100  
M
i –100  
!
x 0  
x is noninteger.  
l
i –100  
V
Ý
#
n 0  
n > 1010  
x 0  
x is noninteger  
E
S
PMT < 0  
PMT < 0  
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248 Appendix D: Error Conditions  
Error 6: Storage Registers  
Operation  
Condition  
?
:
Storage register specified does not exist or has  
been converted to program lines.  
K
a
n specifies a storage register that does not exist  
or has been converted to program lines.  
l
L
n > 80  
n < 0  
n is noninteger  
a
x > 99  
x < 0  
x is noninteger  
Attempted to input Nj for CF0  
Error 7: IRR  
Refer to Appendix C.  
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Appendix D: Error Conditions 249  
Error 8: Calendar  
Operation  
Condition  
Ò
D
Improper date format or illegal date.  
D
Attempting to add days beyond calculator’s date  
capacity.  
E
S
Improper date format or illegal date.  
More than 500 years between settlement  
(purchase) date and maturity (redemption) date.  
Maturity date earlier than settlement date.  
Maturity date has no corresponding coupon date  
(6 months earlier).  
*
Error 9: Service  
Refer to Appendix F.  
Pr Error  
z
Continuous Memory has been reset. (Refer to Continuous Memory, page  
86.)  
z
You have reset the calculator using the reset hole (see page 261).  
This is the case for the 31st of March, May, August, October, and December, plus August 29  
*
(except in a leap year) and 30. For example, there is no September 31, so March 31 has no  
corresponding coupon date 6 months earlier.  
To correct this problem for all maturity dates except August 29 and 30, add one day to both  
the settlement date and the maturity date in your calculations. For instance, if a bond were  
purchased on June 1, 2004 (the settlement date) with a maturity date of December 31, 2005,  
you should change the dates to June 2, 2004 and January 1, 2006 for your calculations.  
For August 29 and 30, there is no calculator solution that gives the correct answer.  
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Appendix E  
Formulas Used  
Percentage  
Base(y)×Rate(x)  
% =  
100  
NewAmount(x) Base(y)  
% =100  
Base(y)  
Amount(x)  
Total(y)  
%T =100  
Interest  
n
i
= number of compounding periods.  
= periodic interest rate, expressed as a decimal.  
PV = present value.  
FV = future value or balance.  
PMT = periodic payment.  
S
= payment mode factor (0 or 1) indicating treatment of PMT.  
0 corresponds to End, 1 to Begin.  
I
= interest amount.  
INTG (n) = integer portion of n.  
FRAC (n) = fractional portion of n.  
Simple Interest  
n
360  
n
365  
I360  
I365  
=
× PV × i  
=
× PV × i  
250  
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Appendix E: Formulas Used 251  
Compound Interest  
Without an odd period:  
n  
1(1+ i)  
0 = PV + (1+ iS) PMT ⋅  
+ FV(1+ i)n  
i
With simple interest used for an odd period:  
INTG(n)  
1(1+ i)  
0 = PV[1+ iFRAC(n)]+ (1+ iS)PMT  
+
i
FV(1+ i)INTG(n)  
With compound interest used for an odd period:  
INTG(n)  
1(1+ i)  
0 = PV(1+ i)FRAC(n) + (1+ iS)PMT  
+
i
FV(1+ i)INTG(n)  
Amortization  
n
= number of payment periods to be amortized.  
INTj = amount of PMT applied to interest in period j.  
PRNj = amount of PMT applied to principal in period j.  
PVj = present value (balance) of loan after payment in period j.  
j
= period number.  
INT1 = {0 if n = 0 and payment mode is set to Begin.  
|PV0 × i|RND (sign of PMT)  
PRN1 = PMT INT1  
PV1 = PV0 + PRN1  
INTj = |PVj –1 × i|RND × (sign of PMT) for j > 1.  
PRNj = PMT INTj  
PVj = PVj –1 + PRNj  
n
INT = INT = INT + INT + ... + INT  
j
1
n
2
j=1  
n
PRN = PRN = PRN + PRN + ... + PRN  
j
1
n
2
j=1  
PV = PV + PRN  
n
0
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252 Appendix E: Formulas Used  
Discounted Cash Flow Analysis  
Net Present Value  
NPV = net present value of a discounted cash flow.  
= cash flow at period j.  
CFj  
CF1  
CF2  
CFn  
(1+ i)n  
NPV = CF0 +  
+
+ ... +  
(1+ i)1 (1+ )2  
i
Internal Rate of Return  
= number of cash flows  
n
CFj = cash flow at period j.  
IRR = Internal Rate of Return  
nj  
nq  
k
1(1+ IRR)  
q<j  
0 = CF ⋅  
(1+ IRR)  
+ CF  
0
j
IRR  
j=1  
Calendar  
Actual Day Basis  
DYS = f(DT2) – f(DT1)  
where  
f(DT) = 365 (yyyy) + 31 (mm – 1) + dd + INTG (z/4) – x  
and  
for mm 2  
x = 0  
z = (yyyy) – 1  
for mm > 2  
x = INTG (0.4mm + 2.3)  
z = (yyyy)  
INTG = Integer portion.  
Note: Additional tests are performed in order to ensure that the century (but  
not millennium) years are not considered leap years.  
30/360 Day Basis  
DAYS = f(DT2) – f(DT1)  
f(DT) = 360 (yyyy) + 30mm + z  
for f(DT1)  
if dd1 = 31 then z = 30  
if dd1 31 then z = dd1  
for f(DT2)  
if dd2 = 31 and dd1 = 30 or 31 then z = 30  
if dd2 = 31 and dd1 < 30 then z = dd2  
if dd2 < 31 then z = dd2  
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Appendix E: Formulas Used 253  
Bonds  
Reference:  
Jan Mayle, TIPS Inc., Standard Securities Calculation Methods, Volume 1, Third  
Edition, Securities Industry Association Inc., New York, 1993.  
DIM = days between issue date and maturity date.  
DSM = days between settlement date and maturity date.  
DCS = days between beginning of current coupon period and  
settlement date.  
E
= number of days in coupon period where settlement occurs.  
DSC = E DCS = days from settlement date to next 6–month coupon  
date.  
N
= number of semiannual coupons payable between settlement  
date and maturity date.  
CPN = annual coupon rate (as a percentage).  
YIELD = annual yield (as a percentage).  
PRICE = dollar price per $100 par value.  
RDV = redemption value.  
For semiannual coupon with 6 months or less to maturity:  
CPN  
100(RDV +  
)
DCS CPN  
2
PRICE =  
×
DSM YIELD  
E
2
100 + (  
×
)
E
2
For semiannual coupon with more than 6 months to maturity:  
RDV  
PRICE =  
DSC  
E
N1+  
YIELD  
1+  
200  
CPN  
N
CPN DCS  
2
+
×
DSC  
E
2
E
K 1+  
K=1  
YIELD  
1+  
200  
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254 Appendix E: Formulas Used  
Black-Scholes Formula for Valuing European Options  
P = current asset price.  
r% = risk-free rate (continuous, per time unit).  
s% = volatility (continuous, per time unit).  
T = term of option (same time unit as r% and s%).  
X = exercise price of option.  
N(z) = probability that a unit normal random variable is less than z.  
Call Value = P × N(d1) – Q × N(d2)  
Put Value = Call Value + Q – P  
where :  
d1 = LN(P/Q)/v + v/2, d2-= d1 – v  
Q = Xe(T×r%/100), v=s%/100×  
T
Depreciation  
L
= asset’s useful life expectancy.  
SBV = starting book value.  
SAL = salvage value.  
FACT = declining-balance factor expressed as a percentage.  
j
= period number.  
DPNj = depreciation expense during period j.  
RDVj = remaining depreciable value at end of period j  
= RDVj–1 DPNj where RDV0 = SBV SAL  
RBVj = remaining book value = RBVj–1 DPNj where RBV0 = SBV  
Y1 = number of months in partial first year.  
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Appendix E: Formulas Used 255  
Straight-Line Depreciation  
Keyboard function:  
SBV SAL  
for j = 1, 2, …, L  
DPNJ =  
L
Program for partial first year:  
SBV SAL Y1  
DPN1 =  
L
12  
SBV SAL  
for j = 2, 3, …, L  
DPNJ =  
L
DPNL + 1 = RDVL  
Sum-of-the-Years-Digits Depreciation  
(W +1)(W + 2F)  
SOYDk =  
2
where W = integer part of k  
F = fractional part of k.  
(i.e., for k = 12.25 years, W = 12 and F = 0.25).  
Keyboard function:  
(L j +1)  
SOYDL  
DPNJ =  
(SBV SAL)  
Program for partial year:  
Y
12  
L
1
DPN =  
(SBV SAL)  
1
SOYD  
LADJ j + 2  
SOYDLADJ  
DPNj =  
(SBV D1 SAL)  
for j 1  
Y
12  
1
LADJ = L −  
where  
Declining-Balance Depreciation  
Keyboard function:  
FACT  
100L  
DPNj = RBVj1  
for j = 1, 2, …, L  
Program for partial first year:  
Y1  
FACT  
DPN1 = SBV ⋅  
100L 12  
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256 Appendix E: Formulas Used  
FACT  
100L  
DPNj = RBVj1  
for j 1  
Modified Internal Rate of Return  
n
= number of compounding periods.  
NFVP = Net future value of the positive cash flows.  
NPVN = Net present value of the negative cash flows.  
1
n
NFVP  
NPVN  
MIRR =100  
1  
Advance Payments  
A
= number of payments made in advance.  
PV FV(1+ i)n  
PMT =  
(nA)  
1(1+ i)  
+ A  
i
Interest Rate Conversions  
C
= number of compounding periods per year.  
EFF = the effective annual interest rate as a decimal.  
NOM = the nominal annual interest rate as a decimal.  
Finite Compounding  
C
NOM  
C
EFF = 1+  
1  
Continuous Compounding  
EFF = (eNOM 1)  
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Appendix E: Formulas Used 257  
Statistics  
Mean  
x
n
y
n
x =  
y =  
Weighted Mean  
wx  
xw  
=
w
Linear Estimation  
n = number of data pairs  
ˆ
y = A + Bx  
y A  
B
ˆ
x =  
x ⋅  
n
x
n
y
xy −  
B =  
where  
2
(
)
x2 −  
A = y Bx  
x y  
n
∑ ∑  
xy −  
r =  
2
2
(
x
n
)
(
y
n
)
x2  
y2  
∑  
Standard Deviation  
2
2
n x2  
(
y
)
(
x
)
n y2  
sx =  
sy =  
n(n 1)  
n(n 1)  
Factorial  
0! = 1  
For n > 1 where n is an integer:  
n
n!=  
i
i=1  
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258 Appendix E: Formulas Used  
The Rent or Buy Decision  
Market Value = PRICE(1 + I)n  
where:  
I
= appreciation per year (as decimal)  
= number of years  
n
Net Cash Proceeds on Resale = Market Value – Mortgage Balance – Commission  
The interest rate is obtained by solving the financial (compound interest) equation  
for i using:  
n
= number of years house is owned  
PV = down payment + closing costs  
PMT  
= mortgage payment + taxes + maintenance rent – (% tax)  
(interest + taxes)  
FV = net cash proceeds on resale  
Annual interest rate = 12 × i  
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Appendix F  
Battery, Warranty, and  
Service Information  
Battery  
The hp 12c platinum is shipped with one 3 Volt CR2032 Lithium battery. Battery  
life depends on how the calculator is used. If the calculator is being used to  
perform operations other than running programs, it uses much less power.  
Low-Power Indication  
A battery symbol (  
) shown in the upper-left corner of the display when the  
calculator is on signifies that the available battery power is running low. When the  
battery symbol begins flashing, replace the battery as soon as possible to avoid  
losing data.  
Use only a fresh battery. Do not use rechargeable batteries.  
There is the danger of explosion if the battery is incorrectly  
replaced. Replace only with the same or equivalent type  
recommended by the manufacturer. Dispose of used batteries  
according to the manufacturer’s instructions. Do not mutilate,  
puncture, or dispose of batteries in fire. The batteries can burst or  
explode, releasing hazardous chemicals. Replacement battery is a  
Lithium 3V Coin Type CR2032.  
Warning  
259  
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260 Appendix F: Battery, Warranty, and Service Information  
Installing a New Battery  
The contents of the calculator’s Continuous Memory are preserved for a short time  
while the battery is out of the calculator (provided that you turn off the calculator  
before removing the battery). This allows you ample time to replace the battery  
without losing data or programs. If the battery is left out of the calculator for an  
extended period, the contents of Continuous Memory may be lost.  
To install a new battery, use the following procedure:  
1. With the calculator turned off, slide the battery cover off.  
2. Remove the old battery.  
3. Insert a new battery, with positive polarity facing outward.  
4. Replace the battery cover.  
Note: Be careful not to press any keys while the battery is out of the calculator. If  
you do so, the contents of Continuous Memory may be lost and keyboard control  
may be lost (that is, the calculator may not respond to keystrokes).  
5. Replace the battery compartment cover and press ; to turn on the power.  
If for any reason Continuous Memory has been reset (that is, if its contents  
have been lost), the display will show Pr Error. Pressing any key will clear  
this message.  
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Appendix F: Battery, Warranty, and Service Information 261  
Verifying Proper Operation (Self-Tests)  
If it appears that the calculator will not turn on or otherwise is not operating  
properly, use one of the following procedures.  
For a calculator that does not respond to keystrokes:  
1. Insert a thin, pointed object all the way into the reset hole near the battery  
compartment and then remove it.  
2. The display will show Pr Error. Pressing any key will clear this message  
from the display.  
3. If the calculator still does not respond to keystrokes, remove and reinsert the  
battery. Make sure that the battery is properly positioned in the battery  
compartment.  
4. If the calculator does not turn on, install a fresh battery. If there is still no  
response, the calculator requires service.  
For a calculator that does respond to keystrokes:  
1. With the calculator off, hold down the ; key and press §.  
2. Release the ; key, then release the § key. This initiates a complete test of  
the calculator’s electronic circuitry. If everything is working correctly, within  
about 25 seconds (during which the word running flashes) the display  
should show –8,8,8,8,8,8,8,8,8,8, and all of the status indicators (except  
the  
9, goes blank, or otherwise does not show the proper result, the calculator  
requires service.  
battery power indicator) should turn on.* If the display shows Error  
The status indicators turned on at the end of this test include some that normally are not  
displayed on the hp 12c platinum.  
*
If the calculator displays Error 9 as a result of the ;/µ test or the ;/+ test but you  
wish to continue using your calculator, you should reset Continuous Memory as described on  
page 86.  
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262 Appendix F: Battery, Warranty, and Service Information  
Note: Tests of the calculator’s electronics are also performed if the = key  
or the z key is held down when ; is released. These tests are included  
*
in the calculator to be used in verifying that it. is operating properly during  
manufacturing and service.  
If you had suspected that the calculator was not working properly but the proper  
display was obtained in step 2, it is likely that you made an error in operating the  
calculator. We suggest you reread the section in this handbook applicable to your  
calculation — including, if appropriate, Appendix A. If you still experience  
difficulty, write or telephone Hewlett-Packard at an address or phone number listed  
under Service (Page 264).  
The ;/= combination initiates a test that is similar to that described above, but continues  
*
indefinitely. The test can be terminated by pressing any key, which will halt the test within 25  
seconds. The ;/z combination initiates a test of the keyboard and the display. When the  
; key is released, certain segments in the display will be lit. To run the test, the keys are  
pressed in order from left to right along each row, from the top row to the bottom row. As  
each key is pressed, different segments in the display are lit. If the calculator is operating  
properly and all the keys are pressed in the proper order, the calculator will display 12 after  
the last key is pressed. (The \ key should be pressed both with the third-row keys and with  
the fourth-row keys.) If the calculator is not working properly, or if a key is pressed out of  
order, the calculator will display Error 9. Note that if this error display results from an  
incorrect key being pressed, this does not indicate that your calculator requires service. This  
test can be terminated by pressing any key out of order (which will, of course, result in the  
Error 9 display). Both the Error 9 display and the 12 display can be cleared by pressing  
any key.  
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Appendix F: Battery, Warranty, and Service Information 263  
Warranty  
hp 12c platinum Financial Calculator; Warranty period: 12 months  
1. HP warrants to you, the end-user customer, that HP hardware, accessories  
and supplies will be free from defects in materials and workmanship after the  
date of purchase, for the period specified above. If HP receives notice of  
such defects during the warranty period, HP will, at its option, either repair  
or replace products which prove to be defective. Replacement products may  
be either new or like-new.  
2. HP warrants to you that HP software will not fail to execute its programming  
instructions after the date of purchase, for the period specified above, due to  
defects in material and workmanship when properly installed and used. If HP  
receives notice of such defects during the warranty period, HP will replace  
software media which does not execute its programming instructions due to  
such defects.  
3. HP does not warrant that the operation of HP products will be uninterrupted  
or error free. If HP is unable, within a reasonable time, to repair or replace  
any product to a condition as warranted, you will be entitled to a refund of  
the purchase price upon prompt return of the product.  
4. HP products may contain remanufactured parts equivalent to new in  
performance or may have been subject to incidental use.  
5. Warranty does not apply to defects resulting from (a) improper or  
inadequate maintenance or calibration, (b) software, interfacing, parts or  
supplies not supplied by HP, (c) unauthorized modification or misuse, (d)  
operation outside of the published environmental specifications for the  
product, or (e) improper site preparation or maintenance.  
6. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER  
WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY  
IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY,  
SATISFACTORY QUALITY, OR FITNESS FOR A PARTICULAR PURPOSE IS  
LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH  
ABOVE. Some countries, states or provinces do not allow limitations on the  
duration of an implied warranty, so the above limitation or exclusion might  
not apply to you. This warranty gives you specific legal rights and you might  
also have other rights that vary from country to country, state to state, or  
province to province.  
7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS  
WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES.  
EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS  
BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL,  
CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR OTHER  
DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR OTHERWISE.  
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264 Appendix F: Battery, Warranty, and Service Information  
Some countries, States or provinces do not allow the exclusion or limitation  
of incidental or consequential damages, so the above limitation or exclusion  
may not apply to you.  
8. The only warranties for HP products and services are set forth in the express  
warranty statements accompanying such products and services. Nothing  
herein should be construed as constituting an additional warranty. HP shall  
not be liable for technical and editorial errors or omissions contained herein.  
FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE  
WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE  
EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY  
AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS  
APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU.  
Service  
Europe  
Country :  
Telephone numbers  
Austria  
Belgium  
+43-1-3602771203  
+32-2-7126219  
Denmark  
Eastern Europe countries  
Finland  
+45-8-2332844  
+420-5-41422523  
+35-89640009  
France  
Germany  
Greece  
Holland  
Italy  
Norway  
Portugal  
Spain  
+33-1-49939006  
+49-69-95307103  
+420-5-41422523  
+31-2-06545301  
+39-02-75419782  
+47-63849309  
+351-229570200  
+34-915-642095  
+46-851992065  
Sweden  
Switzerland  
+41-1-4395358 (German)  
+41-22-8278780 (French)  
+39-02-75419782 (Italian)  
+420-5-41422523  
+44-207-4580161  
+420-5-41422523  
+27-11-2376200  
+32-2-7126219  
Turkey  
UK  
Czech Republic  
South Africa  
Luxembourg  
Other European countries +420-5-41422523  
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Appendix F: Battery, Warranty, and Service Information 265  
Asia Pacific  
L.America  
Country :  
Telephone numbers  
Australia  
Singapore  
+61-3-9841-5211  
+61-3-9841-5211  
Country :  
Telephone numbers  
Argentina  
Brazil  
0-810-555-5520  
Sao Paulo 3747-7799; ROTC  
0-800-157751  
Mexico  
Mx City 5258-9922; ROTC  
01-800-472-6684  
0800-4746-8368  
800-360999  
Venezuela  
Chile  
Columbia  
Peru  
9-800-114726  
0-800-10111  
Central America &  
Caribbean  
Guatemala  
Puerto Rico  
Costa Rica  
1-800-711-2884  
1-800-999-5105  
1-877-232-0589  
0-800-011-0524  
N.America  
Country :  
Telephone numbers  
USA  
Canada  
1800-HP INVENT  
(905)206-4663 or  
800-HP INVENT  
ROTC = Rest of the country  
Please logon to http://www.hp.com for the latest service and support information.  
Regulatory Information  
This section contains information that shows how the hp 12c platinum financial  
calculator complies with regulations in certain regions. Any modifications to the  
calculator not expressly approved by Hewlett-Packard could void the authority to  
operate the 12c platinum in these regions.  
USA  
This calculator generates, uses, and can radiate radio frequency energy and may  
interfere with radio and television reception. The calculator complies with the limits  
for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are  
designed to provide reasonable protection against harmful interference in a  
residential installation.  
However, there is no guarantee that interference will not occur in a particular  
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266 Appendix F: Battery, Warranty, and Service Information  
installation. In the unlikely event that there is interference to radio or television  
reception(which can be determined by turning the calculator off and on), the user  
is encouraged to try to correct the interference by one or more of the following  
measures:  
z
Reorient or relocate the receiving antenna.  
z
Relocate the calculator, with respect to the receiver.  
Canada  
This Class B digital apparatus complies with Canadian ICES-003.  
Cet appareil numerique de la classe B est conforme a la norme NMB-003 du  
Canada.  
Japan  
この装置は、情報処理装置等電波障害自主規制協議会  
の基準  
(VCCI)  
に基づく第二情報技術装置です。この装置は、家庭環境で使用することを目的とし  
ていますが、この装置がラジオやテレビジョン受信機に近接して使用されると、受  
信障害を引き起こすことがあります。  
取扱説明書に従って正しい取り扱いをしてください。  
Temperature Specifications  
z
z
Operating: 0º to 55º C (32º to 131º F)  
Storage: –40º to 65º C (–40º to 149º F)  
Noise Declaration  
In the operator position under normal operation (per ISO 7779): LpA < 70dB.  
Disposal of Waste Equipment by Users in Private  
Household in the European Union  
This symbol on the product or on its packaging indicates that  
this product must not be disposed of with your other household  
waste. Instead, it is your responsibility to dispose of your waste  
equipment by handing it over to a designated collection point  
for the recycling of waste electrical and electronic equipment.  
The separate collection and recycling of your waste equipment  
at the time of disposal will help to conserve natural resources  
ensure that it is recycled in a manner that protects human health and the  
environment. For more information about where you can drop off your waste  
equipment for recycling, please contact your local city office, your household  
waste disposal service or the shop where you purchased the product.  
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Appendix G  
United Kingdom Calculations  
The calculations for most financial problems in the United Kingdom are identical to  
the calculations for those problems in the United States — which are described  
earlier in this handbook. Certain problems, however, require different calculation  
methods in the United Kingdom than in the United States, even though the  
terminology describing the problems may be similar. Therefore, it is recommended  
that you ascertain the usual practice in the United Kingdom for the financial  
problem you are solving.  
The remainder of this appendix describes three types of financial calculations for  
which the conventional practice differs significantly between the United Kingdom  
and the United States.  
Mortgages  
The amount of the repayments on home loans and mortgages offered by banks in  
the United Kingdom can usually be calculated as described under Calculating the  
Payment Amount, page 58. Building Societies in the United Kingdom, however,  
calculate the amount of these repayments differently. In general, the repayment  
amount of a Building Society mortgage is calculated as follows: first, the annual  
repayment amount is calculated using the annual interest rate; second, the periodic  
repayment amount is calculated by dividing the annual repayment amount by the  
number of repayment periods in one year.  
Furthermore, the calculations used by Building Societies are rounded; therefore, to  
match their scale repayment figures you would have to round your calculations  
accordingly.  
267  
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268 Appendix G: United Kingdom Calculations  
Annual Percentage Rate (APR) Calculations  
In the United Kingdom, the calculation of the Annual Percentage Rate of Charge  
(APR) in accordance with the United Kingdom Consumer Credit Act (1974) differs  
from the calculation of the APR in the United States. Unlike the practice in the  
United States, where the APR can be calculated by multiplying the periodic interest  
rate by the number of periods per year, in the United Kingdom the APR is  
calculated by converting the periodic interest rate to the “effective annual rate,”  
then rounding the result to one decimal place. With the periodic interest rate in the  
display and in the i register and the payment mode set to End, the effective annual  
rate can be calculated by pressing ÞP, then keying in the number of  
compounding periods per year and pressing w0$M. Pressing f1 will  
then display the rounded APR.  
Bond Calculations  
Solutions for the price and yield to maturity of United Kingdom bonds are not  
included in this handbook. Actual practice differs according to the type of bond;  
variations such as cumulative and ex-dividend pricing, simple or compound interest  
discounting, etc., may be encountered.  
Application Notes covering such situations may be available in the United  
Kingdom; check with your local authorized Hewlett-Packard dealer.  
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Function Key Index  
É Enter exponent.  
After pressing, next  
numbers keyed in are  
exponents of 10  
CLEAR H Clears  
contents of stack (X,Y,Z  
and T), all storage  
registers, statistical  
registers, and financial  
registers (page 28).  
Leaves program memory  
untouched; not  
General  
; Power on /off key  
(page 16).  
(page 18).  
f Shift key. Selects  
alternate function in gold  
above the function keys  
(page 16). Also used in  
display formatting  
0
9
digits. Used for  
keying in numbers  
(page 21) and display  
programmable.  
formatting (page 87)  
.
(page 87).  
Percentage  
. Decimal point  
g Shift key. Selects  
(page 17). Also used  
for display formatting  
(page 87).  
b Computes x% of y  
and retains the y-value in  
the Y-register (page 31).  
alternate function in blue  
on the slanted face of the  
function keys (page 16).  
O Clears contents of  
displayed X-register to  
zero (page 19).  
à Computes percent of  
change between number  
in Y-register and number  
in displayed X-register  
(page 33).  
fCLEARX after f,  
g, ?, : or i,  
cancels that key  
Arithmetic  
(page 19).  
+-§z} Arithm  
etic operators  
(page 21).  
fCLEARX also  
Z Computes percent  
that x is of number in  
Y-register (page 35).  
displays mantissa of  
number in the displayed  
X-register (page 89).  
Storage Registers  
Calendar  
Ú Backspacing. Deletes  
last character or a  
number. (page 18).  
? Store. Followed  
by number key,  
Ô Sets date format to  
day-month-year  
(page 38); not  
programmable.  
decimal point and  
number key, or top row  
financial key, stores  
displayed number in  
storage register  
ß Undo. Recovers the  
last operation.  
(page 19).  
Õ Sets date format to  
month-day-year  
(page 37); not  
programmable.  
specified (page 27).  
Also used to perform  
storage register  
Digit Entry  
\ Enters a copy of  
number in displayed  
X-register into Y-register.  
Used to separate numbers  
(pages 21 and 229).  
arithmetic (page 29).  
D Changes a date in  
the Y-register by the  
number of days in the  
X-register and displays  
day of week (page 38).  
: Recall. Followed  
by number key,  
decimal point and  
number key, or top-row  
financial key, recalls  
value from storage  
register specified into  
the displayed X-register  
(page 27).  
Þ Changes sign of  
number or exponent of  
10 in X-register  
Ò Computes the  
number of days between  
two dates in the Y and  
X-registers (page 40).  
(page 17).  
269  
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270 Function Key Index  
Financial  
M Stores or computes  
future value (final cash  
flow) of a financial  
V Calculates  
depreciation using  
straight-line method.  
(page 83).  
CLEAR G Clears  
contents of financial  
registers (page 42).  
problem (page 41).  
! Amortizes x  
number of periods  
using values stored in  
PMT, i, PV, and the  
display. Updates  
values in PV and n  
(page 69).  
E Calculates bond  
price, given desired  
yield to maturity  
(page 82).  
× Sets payment  
mode to Begin for  
compound interest  
calculations involving  
payments (page 46).  
S Calculates yield to  
maturity, given bond  
price (page 83).  
 Sets payment  
mode to End for  
compound interest  
calculations involving  
payments (page 46).  
l Calculates the net  
present value of up to  
80 uneven cash flows  
and initial investment  
using values stored  
with J, K, and  
a (page 73).  
a Stores the number  
(from 1 to 99) of times  
each cash flow occurs  
as Nj. Assumes 1  
unless otherwise  
specified (page 75).  
Ï Calculates simple  
interest (page 42).  
w Stores or computes  
number of periods in  
financial problem  
(page 41).  
Ý Calculates  
L Calculates the  
internal rate of return  
(yield) for up to 80  
uneven cash flows and  
initial investment using  
values stored with J,  
K, and a  
depreciation using  
sum-of-the-years-digits  
method (page 83).  
A Multiplies a  
# Calculates  
number in displayed  
X-register by 12 and  
stores the resulting  
value in the n-register  
(page 49).  
depreciation using  
declining-balance  
method (page 83).  
(page 78).  
J Initial cash flow.  
Stores contents of  
Statistics  
¼ Stores or computes  
interest rate per  
compounding period  
(page 41).  
CLEAR² Clears  
statistical storage  
registers R1 through R6  
and stack registers  
(page 93).  
displayed X-register in  
R0, initializes n to zero,  
sets N0 to 1. Used at  
the beginning of a  
discounted cash flow  
problem (page 73).  
C Divides number in  
displayed X-register by  
12 and stores the  
resulting value in the  
i-register (page 49).  
_ Accumulates  
statistics using numbers  
from X- and Y-registers  
in storage registers R1  
through R6 (page 93).  
K Cash flow j.  
Stores the contents of  
X-register in Rj ,  
increments n by 1, and  
sets Nj to 1. Used for  
all cash flows except  
the initial cash flow in  
a discounted cash flow  
problem (page 73).  
$ Stores or computes  
the present value (that  
is, the initial cash flow)  
of a financial problem  
(page 41).  
^ Cancels effect of  
numbers from X- and  
Y-registers in storage  
registers R1 through R6  
(page 94).  
P Stores or  
computes payment  
amount (page 41).  
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Function Key Index 271  
Number Alteration  
Ö Computes mean  
(average) of x-values and  
y-values using  
Modes  
] sets calculator to  
RPN mode (page 19).  
B Rounds mantissa of  
10-digit number in  
X-register to match the  
display (page 100).  
accumulated statistics  
(page 94).  
[ sets calculator to  
algebraic (ALG) mode  
(page 19).  
Computes weighted  
average of y-(item) and  
x-(weight) values using  
accumulated statistics  
(page 99).  
Ñ Leaves only the  
integer portion of  
number in displayed  
X-register by truncating  
fractional portion  
(page 101).  
Mathematics  
r Computes square root  
of number in displayed  
X-register (page 100).  
v Computes sample  
standard deviations of x-  
and y-values using  
accumulated statistics  
(page 96).  
T Leaves only the  
fractional portion of  
number in displayed  
X-register by truncating  
integer portion  
q Raises number in  
Y-register to power of  
number in X-register  
(page 102).  
R Linear estimate  
y Computes reciprocal  
of number in displayed  
X-register (page 100).  
(X-register), correlation  
coefficient (Y-register).  
Fits a line to a set of (x,y)  
data pairs entered using  
_, then extrapolates this  
line to estimate a y-value  
for a given x-value. Also  
computes strength of  
(page 101).  
Stack Rearrangement  
Ø Ù Opens and  
closes parenthesis in  
ALG mode.  
e Computes factorial  
[n•(n–1)... 3•2•1] of  
number in displayed  
X-register (page 100).  
(page 239)  
~ Exchanges contents  
of X and Y-registers of  
stack (pages 90 and  
230).  
> Natural antilogarithm.  
Raises e (approximately  
2.718281828) to power  
of number in displayed  
X-register (page 100).  
linear relationship (r)  
among that set of (x, y)  
data pairs (page 97).  
Q Linear estimate  
d RolIs down contents  
of stack for viewing in  
displayed X-register  
(page 230).  
(X-register), correlation  
coefficient (Y-register).  
Fits a line to a set of (x,  
y) data pairs entered  
using _, then  
¿ Computes natural  
logarithm (base e) of  
number in displayed  
X-register (page 100).  
F Recalls number  
displayed before the  
previous operation back  
into the displayed  
X-register (pages 91  
and 234).  
extra-polates this line to  
estimate an x-value for a  
given y-value. Also  
computes strength of  
linear relationship (r)  
among that set of (x,y)  
data pairs (page 97).  
¡ Computes square of  
the number displayed in  
the X-register  
(page 100).  
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Programming Key Index  
s Program/Run. Toggles into and out of Program mode. Automatically sets  
program to line 000 when returning to Run mode (page 86).  
N Memory map. Describes the current allocation of memory; the number of lines  
allotted to program memory and the number of available data registers (page  
93).  
Program Mode  
Run Mode  
In Program mode, function  
keys are recorded in  
program memory. Display  
shows program memory  
line number and the  
keycode (keyboard row  
and location in row) of the  
function key.  
In Run mode, function keys may be executed  
as part of a recorded program or  
individually by pressing from the keyboard.  
Active Keys:  
Pressed from  
keyboard:  
Executed as a  
recorded program  
instruction  
In Program mode only the  
following keys are active;  
they cannot be recorded in  
program memory.  
CLEARÎ  
Resets calculator (in  
Run mode) so  
CLEARÎ  
Clear program. Clears  
program memory to all  
i000 instructions and  
resets calculator so  
operations begin at  
line 000 of program  
memory. Does not  
erase program  
operations begin at line 000  
of program memory. Resets  
N to P008 r20  
memory.  
(page 113)  
272  
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Programming Key Index 273  
Run Mode  
Program Mode  
Active Keys:  
Pressed from  
keyboard:  
Executed as a  
recorded program  
instruction:  
t Run/Stop. Begins  
execution of a stored  
program. Stops  
t Run/Stop. Stops  
program execution  
(page 122).  
execution if program is  
running (page 106).  
i Go to. Followed by a  
decimal point and a  
i Go to. Followed by  
a three-digit number,  
positions calculator to  
that line in program  
memory. No instructions  
are executed  
i Go to. Followed by  
a three-digit number,  
causes calculator to  
branch to the specified  
line number next, and  
resumes program  
three-digit number,  
positions calculator to that  
line in program memory.  
No instructions are  
executed (page 114)  
(page 125).  
execution from there  
(page 125).  
Ç Single step. Displays  
line number and contents  
of next program memory  
line. If held down,  
displays line number and  
contents of all program  
memory lines, one at a  
time (page 109).  
Ç Single step.  
Displays line number  
and keycode of current  
program memory line  
when pressed; executes  
instruction, displays  
result, and moves to  
next line when released  
(page 114).  
u Pause. Stops  
program execution for  
about 1 second and  
displays contents of  
X-register, then resumes  
program execution  
(page 117).  
Ü Back step. Displays  
line number and contents  
of previous program  
Ü Back step. Displays  
line number and  
om Conditional.  
o tests number in  
X-register against that in  
Y-register. m tests  
number in X-register  
against zero. If true,  
calculator continues  
execution at next  
program memory line.  
If false, calculator skips  
next line before  
resuming execution  
(page 129)  
memory line. When back  
stepped from line 000,  
goes to end of program  
memory as defined by  
gN. If held down,  
displays line number and  
contents of all program  
memory lines, one at a  
time (page 113).  
keycode of previous  
program memory line  
when pressed; displays  
original contents of  
X-register when  
released. No  
instructions are  
executed (page 116).  
Any key. Pressing any  
key on the keyboard  
stops execution of a  
program (page 124)  
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Subject Index  
Bonds, 82–83, 217–25, 253, 268  
Bonds, 30/360 day basis, 217–21  
Bonds, annual coupon, 222  
Bonds, corporate, 82  
A
, 13, 69, 230  
Adding instructions, 140–48  
Adjusting the Display Contrast, 16  
Advance payments, 202, 209  
Algebraic mode, 20, 237  
Amortization, 48, 69–71, 251  
Annual interest rate, 49  
Annual Percentage Rate, 65–68,  
156–59, 268  
Bonds, municipal, 82  
Bonds, U.S. Treasury, 82  
Branching, 125–38, 144  
Branching, adding instructions by,  
144–48  
Branching, conditional, 129–30  
Branching, simple, 125  
Annuities, 45  
Annuities, deferred, 169–70  
Annuity due, 47–48  
C
, 74, 76  
Appreciation, 48  
, 73, 74, 76, 79  
APR. See Annual Percentage Rate  
Arithmetic calculations with constants,  
91, 235  
Arithmetic calculations, chain,  
23–25  
Arithmetic calculations, simple, 21,  
22  
Arithmetic operations and the stack,  
231  
, 17, 21, 42, 73, 230  
, 19, 35, 230, 234, 236  
C status indicator, 65  
Calendar functions, 37–40, 252  
Calendar functions and the stack,  
233  
Cash flow diagram, 44–48  
Cash flow sign convention, 42, 46  
Cash flows, changing, 80  
Cash flows, reviewing, 79  
Arithmetic, storage register, 29  
Average. See Mean  
Cash flows, storing for  
, 73, 80  
and  
B
Chain calculations, 23–25, 26, 234,  
238  
Clearing display, 19  
Clearing financial registers, 19  
Clearing operations, 17, 19  
Clearing prefix keys, 17  
Clearing program memory, 19, 105  
Clearing statistics registers, 19, 93  
Clearing storage registers, 19, 29,  
86  
, 46  
, 109, 116, 139  
, 18  
Backstep, 109  
Balloon payments, 50, 52  
Battery, 259  
Battery power, low, 13, 16, 259  
Battery, installing, 260  
BEGIN status indicator, 47  
Black-Scholes formula for valuing  
European options, 194, 254  
Clearing X-register, 19  
Compound growth, 47, 49  
274  
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Subject Index 275  
Compound interest, 49–68, 251  
Compound interest calculation, 12  
Compounding periods, 44, 49  
Conditional branching, 129–30  
Conditional test instructions, 129  
Constants, arithmetic calculations  
with, 235  
Display format, mantissa, 89  
Display format, standard, 88  
Display formats, number, 87  
Display, scientific notation, 88  
Displaying numbers, 41  
Displays, special, 90  
Constants, arithmetic calculations  
with, 91  
Continuous compounding, 216, 256  
Continuous memory, 86  
Continuous memory, resetting of, 42,  
47, 86, 88, 112  
Continuous rate, 216  
E
, 18, 21, 65, 230  
, 46  
, 21, 31, 36, 93, 99, 102,  
129, 229, 234  
, 100, 231  
, 20, 22, 26, 237  
Editing a program, 139  
Effective interest rate, converting,  
215  
D
, 37–40  
, 84, 230  
, 65, 230  
Effective rate, 216  
Entry errors, 92  
, 38  
Error conditions, 90  
Error, Pr, 90  
Errors, 90  
Errors, in digit entry, 92  
Excess depreciation, 191  
Exponent, 18, 102  
Exponential, 100  
D.MY status indicator, 38  
Data storage registers, 27–30  
Date format, 37, 86  
Dates, days between, 40  
Dates, future or past, 38  
Days, between dates, 40  
Decimal places, rounding, 87  
Decimal point, changing, 17  
Declining-balance depreciation, 176  
Deferred annuities, 169–70  
Depreciation, 84, 171–91, 254–56  
Depreciation, declining-balance,  
176  
Depreciation, excess, 191  
Depreciation, partial year, 171–91  
Depreciation, sum-of-the-years-digits,  
180  
Depreciation, with crossover,  
184–91  
F
, 16, 21, 69, 88, 108, 230  
, 19, 42  
, 101, 231  
, 41, 61  
Factorial, 100  
Financial registers, 41  
Financial registers, clearing, 42  
Fractional, 101  
Future value, 46  
Future value, calculating, 61  
FV, 46  
Digit entry, recovering from errors in,  
92  
Digit entry, termination of, 21, 229  
Discounted cashflow analysis, 72  
Display, 87  
G
, 16, 21, 108, 112, 230  
, 17, 21, 108, 114, 125, 130,  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 275 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
276 Subject Index  
143, 230  
, 114, 139  
000, 112–13  
Memory, program, 112  
Modes  
alegebraic, 20  
RPN, 20  
Modified internal rate of return, 192  
Mortgage, price of, 159  
Mortgage, yield of, 161  
Multiple programs, 149  
I
, 13, 41, 42  
, 42, 230  
, 13, 72, 73, 78, 243  
, 101, 231  
N
Indicators, status, 87  
Instructions in program lines, 108  
Interest rate, annual, 55  
Interest rate, periodic, 55  
Interest, simple, 42  
, 41, 49  
, 100, 231  
, 75, 79, 80  
, 72, 73  
Internal rate of return, 72  
Internal rate of return, calculating,  
78  
Internal rate of return, modified, 192  
Interrupting a program, 117  
IRR, 72, 192  
Negative numbers, 17, 238  
Net amount, 33  
Net present value, 72  
Net present value, calculating, 73  
Nominal interest rate, converting,  
213  
NPV, 72  
Number display formats, 87  
Numbers, keying in, 17  
Numbers, large, 18  
Numbers, negative, 17  
Numbers, recalling, 27  
Numbers, storing, 27  
K
Keyboard, 16  
L
, 91, 101, 234  
, 100, 231  
LAST X register, 86  
Leasing, 202  
Linear estimation, 97  
Logarithm, 100  
Looping, 125  
Low-power indicator, 16  
O
, 16, 260  
Odd-period calculations, 63  
Odd-period mode, 45  
One-number functions, 100  
One-variable statistics, 93  
Overflow, 90  
M
, 37  
, 113  
P
, 104, 106, 109, 124  
, 41, 59  
, 17, 89  
, 19, 104, 112  
, 82, 230  
, 117, 118  
Mantissa, 18, 89  
Mantissa Display Format, 89  
Mean, 94  
Mean, weighted, 99  
memory, 27  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 276 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
Subject Index 277  
, 41, 42, 55  
Registers, financial, 41  
Parentheses Calculations, 26, 240  
Partial-year depreciation, 171  
Payment, 45, 209  
Registers, statistics, 93  
Renting versus Buying, 163  
Residual, 209  
Payment amount, calculating, 59  
Payment mode, 46  
Round, 100  
Rounding, 87  
RPN mode, 20, 23, 228  
Running message, 13, 78  
Payments, advance, 202, 209  
Payments, number of, 49  
Percent difference, 34, 241  
Percent of total, 35, 242  
Percentages, 31, 32, 241  
PMT, 45  
Populations, 96  
Power function, 102, 242  
Pr error, 90  
S
, 96, 230  
, 84, 230  
, 84, 230  
, 17, 21, 27, 29, 65, 108, 230  
, 109, 114, 133, 139  
Samples, 96  
Prefix key, 16  
Present value, 45  
Savings, 213  
Present value, calculating, 56  
PRGM status indicator, 104, 106  
Program branching, 125  
Program editing, 139  
Program lines, displaying, 109  
Program looping, 125  
Program memory, 108, 112  
Program mode, 104  
Program, creating, 104  
Program, interrupting, 117  
Program, running, 106, 153  
Program, running one line at a time,  
112  
Scientific notation, 18, 88  
Simple branching, 125  
Simple interest, 42  
Square Root, 100  
Stack, 228  
Standard deviation, 96  
Statistics, 93  
Status indicators, 87  
Storage register arithmetic, 29  
Storage registers, clearing, 29  
Storing numbers, 41  
Storing programs, 149  
Straight-line depreciation, 171  
Sum-of-the-years-digits depreciation,  
180  
Program, stopping, 117, 122  
Program, storing, 149  
Programming, 104  
Programs, multiple, 149  
PV, 45  
T
Two-variable statistics, 93  
R
U
, 42, 69, 230  
, 106, 117, 122  
, 17, 21, 27, 41, 108, 230  
, 19, 42  
, 20  
Underflow, 90  
W
, 88, 100, 231  
Reciprocal, 100  
registers, 27  
Weighted mean, 99  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 277 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  
278 Subject Index  
X
Y
, 40, 42, 69, 82, 90, 94, 96,  
125, 129, 230  
, 100, 231  
, 13, 82, 83  
, 97, 230  
, 102, 231  
, 230  
, 94, 230  
, 97, 230  
Yield, 206, 212  
, 99, 125, 129  
File name: hp 12c pt_user's guide_English_HDPMF123E27 Page: 278 of 275  
Printed Date: 2005/8/1 Dimension: 14.8 cm x 21 cm  

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