HP (Hewlett Packard) F1902 90001 User Manual
hp 10BII financial calculator  
user’s guide  
Edition 1  
HP part number F1902-90001  
Notice  
REGISTER YOUR PRODUCT AT: www.register.hp.com  
THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE  
PROVIDED “AS IS” AND ARE SUBJECT TO CHANGE WITHOUT  
NOTICE.  
HEWLETT-PACKARD  
COMPANY  
MAKES  
NO  
WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL,  
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES  
OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS  
FOR A PARTICULAR PURPOSE.  
HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY  
ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES  
IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR  
USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.  
© Copyright 1988, 1989, 2001, 2004 Hewlett-Packard Development  
Company, L.P. Reproduction, adaptation, or translation of this manual is  
prohibited without prior written permission of Hewlett-Packard Company,  
except as allowed under the copyright laws.  
Hewlett-Packard Company  
4995 Murphy Canyon Rd,  
Suite 301  
San Diego,CA 92123  
Printing History  
Edition 1  
May 2003  
Welcome to the HP 10BII  
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Welcome to the HP 10BII  
3
Features  
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4
Welcome to the HP 10BII  
Contents  
11  
11  
12  
13  
14  
15  
16  
17  
18  
19  
21  
At a Glance...  
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1
23  
23  
23  
23  
25  
25  
25  
25  
26  
27  
27  
28  
28  
28  
29  
30  
30  
31  
31  
32  
32  
Getting Started  
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Contents  
5
2
3
4
33  
33  
33  
34  
34  
35  
35  
35  
36  
Business Percentages  
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37  
37  
37  
39  
40  
41  
42  
43  
43  
Number Storage and Arithmetic  
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45  
45  
46  
47  
47  
47  
48  
49  
49  
49  
51  
Picturing Financial Problems  
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6
Contents  
5
53  
53  
54  
55  
55  
60  
63  
67  
72  
72  
73  
Time Value of Money Calculations  
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6
7
75  
75  
77  
77  
78  
79  
80  
83  
84  
Cash Flow Calculations  
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85  
85  
86  
86  
86  
87  
87  
87  
87  
88  
90  
93  
Statistical Calculations  
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Contents  
7
8
95  
95  
Additional Examples  
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95  
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96  
97  
98  
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98  
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98  
99  
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101  
103  
104  
105  
106  
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108 6DYLQJV  
108  
110  
112  
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113  
115  
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117 Assistance, Batteries, and Service  
117 $QVZHUVꢀWRꢀ&RPPRQꢀ4XHVWLRQV  
118 (QYLURQPHQWDOꢀ/LPLWV  
119 3RZHUꢀDQGꢀ%DWWHULHV  
119  
119  
119  
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122 /LPLWHGꢀ2QHꢆ<HDUꢀ:DUUDQW\  
122  
122  
123  
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8
Contents  
123 ,IꢀWKHꢀ&DOFXODWRUꢀ5HTXLUHVꢀ6HUYLFH  
123  
124  
124  
124  
125  
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125 5HJXODWRU\ꢀ,QIRUPDWLRQ  
126 (QGꢆXVHUꢀWHUPVꢀDQGꢀFRQGLWLRQV  
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129 More About Calculations  
129 ,55ꢄ<5ꢀ&DOFXODWLRQV  
129  
130  
130  
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131 (IIHFWꢀRIꢀ8VLQJꢀΣ²ꢀWRꢀ&RUUHFWꢀ'DWD  
131 5DQJHꢀRIꢀ1XPEHUV  
132 (TXDWLRQV  
132  
132  
132  
133  
134  
135  
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137 Messages  
139 Index  
Contents  
9
At a Glance...  
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Basics—At a Glance...  
Keys:  
Display:  
0.00  
Description:  
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[orange label]  
0.00  
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DQQXQFLDWRUꢀꢂSHIFTꢃꢁ  
0.00  
12_  
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PHPRU\ꢁ  
0.00  
0.00  
0.00  
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7XUQVꢀFDOFXODWRUꢀRIIꢁ  
At a Glance... 11  
Percentages—At a Glance...  
3HUFHQWꢁ  
&RVWꢁ  
3ULFHꢁ  
0DUJLQꢁ  
0DUNXSꢁ  
$GGꢀꢄꢅꢆꢀWRꢀꢇꢄꢈꢁꢅꢉꢁ  
Keys:  
Display:  
17.50  
Description:  
(QWHUVꢀQXPEHUꢁ  
$GGVꢀꢄꢅꢆꢁ  
20.13  
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15.00  
(QWHUVꢀFRVWꢁ  
22.00  
(QWHUVꢀSULFHꢁ  
31.82  
&DOFXODWHVꢀPDUJLQꢁ  
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20.00  
(QWHUVꢀFRVWꢁ  
33.00  
(QWHUVꢀPDUNXSꢁ  
26.60  
&DOFXODWHVꢀSULFHꢁ  
12 At a Glance...  
Memory Keys—At a Glance…  
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5HFDOOVꢀDꢀYDOXHꢀIURPꢀDꢀQXPEHUHGꢀUHJLVWHUꢁ  
0XOWLSO\ꢀꢄꢈꢌꢀꢊꢊꢌꢀDQGꢀꢊꢅꢀE\ꢀꢈꢌꢀVWRULQJꢀ´ïꢀꢈµꢀDVꢀDꢀFRQVWDQWꢀRSHUDWLRQꢁ  
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7.00  
6WRUHVꢀ´ïꢀꢈµꢀDVꢀDꢀ  
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119.00  
154.00  
175.00  
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0XOWLSOLHVꢀꢊꢊꢀïꢀꢈꢁ  
0XOWLSOLHVꢀꢊꢅꢀïꢀꢈꢁ  
6WRUHꢀꢅꢄꢍꢀLQꢀUHJLVWHUꢀꢊꢌꢀWKHQꢀUHFDOOꢀLWꢁ  
519.00  
0.00  
6WRUHVꢀLQꢀUHJLVWHUꢀꢊꢁ  
&OHDUVꢀGLVSOD\ꢁ  
519.00  
5HFDOOVꢀUHJLVWHUꢀꢊꢁ  
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Time Value of Money (TVM)—At a Glance…  
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$ꢀQHJDWLYHꢀVLJQꢀLQꢀWKHꢀGLVSOD\ꢀUHSUHVHQWVꢀPRQH\ꢀSDLGꢀRXWꢎꢀ  
PRQH\ꢀUHFHLYHGꢀLVꢀSRVLWLYHꢁ  
1XPEHUꢀRIꢀSD\PHQWVꢁ  
,QWHUHVWꢀSHUꢀ\HDUꢁ  
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6HWꢀWRꢀ(QGꢀPRGHꢁꢀ3UHVVꢀ  
ꢀLIꢀBEGIN DQQXQFLDWRUꢀLVꢀGLVSOD\HGꢁ  
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12.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢁ  
360.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
SD\PHQWVꢁ  
10.00  
(QWHUVꢀLQWHUHVWꢀSHUꢀ  
\HDUꢁ  
14,000.00  
0.00  
(QWHUVꢀSUHVHQWꢀYDOXHꢁ  
(QWHUVꢀIXWXUHꢀYDOXHꢁ  
–122.86  
&DOFXODWHVꢀSD\PHQWꢀLIꢀ  
SDLGꢀDWꢀHQGꢀRIꢀSHULRGꢁ  
14 At a Glance...  
TVM What if…—At a Glance…  
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8VLQJꢀWKHꢀYDOXHVꢀ\RXꢀMXVWꢀHQWHUHGꢀꢂSDJH ꢄꢏꢃꢌꢀKRZꢀPXFKꢀFDQꢀ  
\RXꢀERUURZꢀLIꢀ\RXꢀZDQWꢀDꢀSD\PHQWꢀRIꢀꢇꢄꢉꢉꢁꢉꢉ"  
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–100.00  
(QWHUVꢀQHZꢀSD\PHQWꢀ  
DPRXQWꢁꢀꢂ0RQH\ꢀSDLGꢀ  
RXWꢀLVꢀQHJDWLYHꢁꢃ  
11,395.08  
&DOFXODWHVꢀDPRXQWꢀ\RXꢀ  
FDQꢀERUURZꢁ  
+RZꢀPXFKꢀFDQꢀ\RXꢀERUURZꢀDWꢀDꢀꢍꢁꢅꢆꢀLQWHUHVWꢀUDWH"  
9.50  
(QWHUVꢀQHZꢀLQWHUHVWꢀ  
UDWHꢁ  
11,892.67  
&DOFXODWHVꢀQHZꢀSUHVHQWꢀ  
YDOXHꢀIRUꢀꢇꢄꢉꢉꢁꢉꢉꢀ  
SD\PHQWꢀDQGꢀꢍꢁꢅꢆꢀ  
LQWHUHVWꢁ  
10.00  
5HHQWHUVꢀRULJLQDOꢀ  
LQWHUHVWꢀUDWHꢁ  
14,000.00  
–122.86  
5HHQWHUVꢀRULJLQDOꢀ  
SUHVHQWꢀYDOXHꢁ  
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SD\PHQWꢁ  
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Amortization—At a Glance…  
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7KHQꢀSUHVVꢀ WRꢀFRQWLQXDOO\ꢀF\FOHꢀWKURXJKꢀWKHꢀSULQFLSDOꢌꢀ  
LQWHUHVWꢌꢀDQGꢀEDODQFHꢀYDOXHVꢀꢂLQGLFDWHGꢀE\ꢀWKHꢀPRINꢌꢀINTꢌꢀ  
DQGꢀBALꢀDQQXQFLDWRUVꢀUHVSHFWLYHO\ꢃꢁ  
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VLQJOHꢀSD\PHQWꢀDQGꢀWKHQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢁ  
$PRUWL]HꢀWKHꢀꢊꢉ ꢀSD\PHQWꢀRIꢀWKHꢀORDQꢁ  
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20.00  
(QWHUVꢀSHULRGꢀWRꢀ  
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20 – 20  
'LVSOD\VꢀSHULRGꢀWRꢀ  
DPRUWL]Hꢁ  
–7.25  
'LVSOD\VꢀSULQFLSDOꢁ  
–115.61  
'LVSOD\VꢀLQWHUHVWꢁꢀ  
ꢂ0RQH\ꢀSDLGꢀRXWꢀLVꢀ  
QHJDWLYHꢁꢃ  
13,865.83  
'LVSOD\VꢀEDODQFHꢁ  
$PRUWL]HꢀWKHꢀꢄ ꢀWKURXJKꢀꢄꢊ ꢀORDQꢀSD\PHQWVꢁ  
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(QWHUVꢀUDQJHꢀRIꢀSHULRGVꢀ  
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1 – 12  
'LVSOD\VꢀUDQJHꢀRIꢀ  
SHULRGVꢀꢂSD\PHQWVꢃꢁ  
–77.82  
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–1,396.50  
'LVSOD\VꢀLQWHUHVWꢁꢀ  
ꢂ0RQH\ꢀSDLGꢀRXWꢀLVꢀ  
QHJDWLYHꢁꢃ  
13,922.18  
'LVSOD\VꢀEDODQFHꢁ  
16 At a Glance...  
Interest Rate Conversion—At a Glance…  
7RꢀFRQYHUWꢀEHWZHHQꢀQRPLQDOꢀDQGꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHVꢌꢀ  
HQWHUꢀWKHꢀNQRZQꢀUDWHꢀDQGꢀWKHꢀQXPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢌꢀ  
WKHQꢀVROYHꢀIRUꢀWKHꢀXQNQRZQꢀUDWHꢁ  
1RPLQDOꢀLQWHUHVWꢀSHUFHQWꢁ  
(IIHFWLYHꢀLQWHUHVWꢀSHUFHQWꢁ  
3HULRGVꢀSHUꢀ\HDUꢁ  
)LQGꢀWKHꢀDQQXDOꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHꢀRIꢀꢄꢉꢆꢀQRPLQDOꢀLQWHUHVWꢀ  
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10.00  
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(QWHUVꢀQRPLQDOꢀUDWHꢁ  
12.00  
(QWHUVꢀSD\PHQWVꢀSHUꢀ  
\HDUꢁ  
10.47  
&DOFXODWHVꢀDQQXDOꢀ  
HIIHFWLYHꢀLQWHUHVWꢁ  
At a Glance... 17  
IRR/YR and NPV—At a Glance…  
1XPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢀꢂGHIDXOWꢀLVꢀꢄꢊꢃꢁ  
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1XPEHUꢀRIꢀFRQVHFXWLYHꢀWLPHVꢀFDVKꢀIORZꢀ´MµꢀRFFXUVꢁ  
,QWHUQDOꢀUDWHꢀRIꢀUHWXUQꢀSHUꢀ\HDUꢁ  
1HWꢀSUHVHQWꢀYDOXHꢁ  
,Iꢀ\RXꢀKDYHꢀDQꢀLQLWLDOꢀFDVKꢀRXWIORZꢀRIꢀꢇꢏꢉꢌꢉꢉꢉꢌꢀIROORZHGꢀE\ꢀPRQWKO\ꢀFDVKꢀ  
LQIORZVꢀRIꢀꢇꢏꢌꢈꢉꢉꢌꢀꢇꢈꢌꢉꢉꢉꢌꢀꢇꢈꢌꢉꢉꢉꢌꢀDQGꢀꢇꢊꢋꢌꢉꢉꢉꢌꢀZKDWꢀLVꢀWKHꢀ,55ꢀ<5"ꢀ  
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12.00  
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(QWHUVꢀLQLWLDOꢀRXWIORZꢁ  
(QWHUVꢀILUVWꢀFDVKꢀIORZꢁ  
(QWHUVꢀVHFRQGꢀFDVKꢀIORZꢁ  
(QWHUVꢀQXPEHUꢀRIꢀFRQVHFꢒ  
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4,700.00  
7,000.00  
2.00  
23,000.00  
15.96  
(QWHUVꢀWKLUGꢀFDVKꢀIORZꢁ  
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1.33  
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PRQWKꢁ  
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622.85  
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18 At a Glance...  
Statistics—At a Glance…  
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3RSXODWLRQꢀVWDQGDUGꢀGHYLDWLRQVꢀRIꢀ[ꢀDQGꢀ\ꢁ  
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8VLQJꢀWKHꢀIROORZLQJꢀGDWDꢌꢀILQGꢀWKHꢀPHDQVꢀRIꢀ[ꢀDQGꢀ\ꢌꢀWKHꢀVDPSOHꢀVWDQGDUGꢀ  
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y-data  
2
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6
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90  
160  
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(QWHUVꢀILUVWꢀ[ꢅ\ꢀSDLUꢁ  
(QWHUVꢀVHFRQGꢀ[ꢅ\ꢀSDLUꢁ  
(QWHUVꢀWKLUGꢀ[ꢅ\ꢀSDLUꢁ  
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'LVSOD\VꢀPHDQꢀRIꢀ\ꢁ  
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100.00  
2.00  
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3.00  
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1,420.00  
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SURGXFWVꢀRIꢀ[ꢒꢀDQGꢀ  
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20 At a Glance...  
Keyboard Map  
1. Time value of money (page 53)  
2. Separate two numbers (page 28)  
3. Percent (page 33)  
13. n through Σxy: statistical  
summation registers (page 88)  
14. 3-key memory (page 39)  
15. Backspace (page 25)  
4. Constant (page 37)  
16. Accumulate statistical data  
(page 86)  
5. Store and recall (page 40)  
6. Change sign (page 24)  
7. Statistics key (page 27)  
8. Shift key (page 27)  
17. Cash flows (page 75)  
18. Business functions: margin,  
markup, cost, price (page 35)  
9. Clear display, cancel operation  
(page 25)  
19. Interest conversion (page 72)  
20. Amortization (page 67)  
10. Clear all memory (page 25)  
11. On (page 87)  
21. Annunciator lines (page 26)  
12. Statistical functions (page 87)  
At a Glance... 21  
1
Getting Started  
Power On and Off  
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Simple Arithmetic Calculations  
Arithmetic Operators. 7KHꢀIROORZLQJꢀH[DPSOHVꢀGHPRQVWUDWHꢀXVLQJꢀWKHꢀ  
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1: Getting Started 23  
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87.18  
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240.92  
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40.57  
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13.00  
$GGVꢀꢈꢀꢉꢀꢊꢄ  
39.00  
0XOWLSOLHVꢀꢁꢋꢀïꢀꢋꢄ  
Negative Numbers. (QWHUꢀWKHꢀQXPEHUꢀDQGꢀSUHVVꢀ ꢀWRꢀFKDQJHꢀWKHꢀVLJQꢄꢀ  
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Keys:  
Display:  
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Description:  
&KDQJHVꢀWKHꢀVLJQꢀRIꢀꢌꢍꢄ  
&DOFXODWHVꢀUHVXOWꢄ  
–25.00  
24 1: Getting Started  
Understanding the Display and Keyboard  
Cursor  
7KHꢀFXUVRUꢀꢅꢀBꢀꢆꢀLVꢀYLVLEOHꢀZKHQꢀ\RXꢀDUHꢀHQWHULQJꢀDꢀQXPEHUꢄ  
Clearing the Calculator  
:KHQꢀWKHꢀFXUVRUꢀLVꢀRQꢃꢀ ꢀHUDVHVꢀWKHꢀODVWꢀGLJLWꢀ\RXꢀHQWHUHGꢄꢀ  
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FDOFXODWLRQꢄ  
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]HURꢄꢀ2WKHUZLVHꢃꢀ ꢀFOHDUVꢀWKHꢀGLVSOD\ꢀRIꢀLWVꢀFXUUHQWꢀ  
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Clearing Messages.:KHQꢀWKHꢀ+3ꢀꢁꢂ%,,ꢀLVꢀGLVSOD\LQJꢀDQꢀHUURUꢀPHVVDJHꢃꢀ  
ꢀRUꢀ ꢀFOHDUVꢀWKHꢀPHVVDJHꢀDQGꢀUHVWRUHVꢀWKHꢀRULJLQDOꢀFRQWHQWVꢀRIꢀWKHꢀ  
GLVSOD\ꢄꢀ6HHꢀ´0HVVDJHVµꢀRQꢀSDJH ꢁꢋꢌꢀIRUꢀDꢀFRPSOHWHꢀOLVWꢀRIꢀ  
PHVVDJHVꢀDQGꢀPHDQLQJVꢄꢀ  
Clearing Memory  
Keys  
Description  
&OHDUVꢀDOOꢀPHPRU\ꢄꢀ'RHVꢀQRWꢀUHVHWꢀPRGHVꢄꢑ  
&OHDUVꢀVWDWLVWLFDOꢀPHPRU\ꢄ  
7RꢀFOHDUꢀDOOꢀPHPRU\ꢀDQGꢀUHVHWꢀFDOFXODWRUꢀPRGHVꢃꢀSUHVVꢀDQGꢀKROGꢀGRZQꢀ ꢃꢀ  
WKHQꢀSUHVVꢀDQGꢀKROGꢀGRZQꢀERWKꢀ ꢀDQGꢀ ꢄꢀ:KHQꢀ\RXꢀUHOHDVHꢀDOOꢀWKUHHꢃꢀDOOꢀ  
PHPRU\ꢀLVꢀFOHDUHGꢄꢀ7KHꢀAll ClearꢀPHVVDJHꢀLVꢀGLVSOD\HGꢄꢀ  
1: Getting Started 25  
Annunciators  
$QQXQFLDWRUVꢀDUHꢀV\PEROVꢀLQꢀWKHꢀGLVSOD\ꢀWKDWꢀLQGLFDWHꢀWKHꢀVWDWXVꢀRIꢀWKHꢀ  
FDOFXODWRUꢄ  
Annunciator  
Status  
SHIFT  
7KHꢀVKLIWꢀNH\ꢀꢅ ꢆꢀKDVꢀEHHQꢀSUHVVHGꢄꢀ:KHQꢀDQRWKHUꢀ  
NH\ꢀLVꢀSUHVVHGꢃꢀWKHꢀIXQFWLRQꢀODEHOHGꢀLQꢀRUDQJHꢀRQꢀWKHꢀ  
NH\ꢀLVꢀH[HFXWHGꢄ  
STATS  
7KHꢀVWDWLVWLFVꢀNH\ꢀꢅ ꢆꢀLVꢀDFWLYHꢄꢀ:KHQꢀDQRWKHUꢀNH\ꢀLVꢀ  
SUHVVHGꢃꢀWKHꢀIXQFWLRQꢀODEHOHGꢀLQꢀPDXYHꢀDERYHꢀWKHꢀ  
NH\ꢀLVꢀH[HFXWHGꢄ  
PEND  
$QꢀRSHUDWLRQꢀLVꢀZDLWLQJꢀIRUꢀDQRWKHUꢀRSHUDQGꢄ  
BEGIN  
%HJLQꢀPRGHꢀLVꢀDFWLYHꢀꢅSDJH ꢍꢍꢆꢒꢀWKDWꢀLVꢃꢀSD\ꢇ  
PHQWVꢀDUHꢀDWꢀWKHꢀEHJLQQLQJꢀRIꢀDꢀSHULRGꢄ  
INPUT  
7KHꢀ ꢀNH\ꢀKDVꢀEHHQꢀSUHVVHGꢀDQGꢀDꢀQXPEHUꢀVWRUHGꢄ  
%DWWHU\ꢀSRZHUꢀLVꢀORZꢀꢅSDJH ꢁꢁꢊꢆꢄ  
AMORT  
BAL  
7KHꢀDPRUWL]DWLRQꢀDQQXQFLDWRUꢀLVꢀOLWꢃꢀWRJHWKHUꢀZLWKꢀ  
RQHꢀRIꢀWKHꢀIROORZLQJꢀIRXUꢀDQQXQFLDWRUVꢓꢄ  
7KHꢀEDODQFHꢀRIꢀDQꢀDPRUWL]DWLRQꢀLVꢀGLVSOD\HGꢀ  
ꢅSDJH ꢏꢐꢆꢄ  
INT  
7KHꢀLQWHUHVWꢀRIꢀDQꢀDPRUWL]DWLRQꢀLVꢀGLVSOD\HGꢀ  
ꢅSDJH ꢏꢊꢆꢄ  
PRIN  
PER  
7KHꢀSULQFLSDOꢀRIꢀDQꢀDPRUWL]DWLRQꢀLVꢀGLVSOD\HGꢀ  
ꢅSDJH ꢏꢐꢆꢄ  
$ꢀUDQJHꢀRIꢀSHULRGVꢀIRUꢀDQꢀDPRUWL]DWLRQꢀLVꢀXVHGꢀ  
ꢅSDJH ꢏꢐꢆꢄ  
C-FLOW  
CF  
7KHꢀFDVKꢀIORZꢀDQQXQFLDWRUꢀLVꢀOLWꢃꢀWRJHWKHUꢀZLWKꢀRQHꢀ  
RIꢀWKHꢀIROORZLQJꢀꢎꢀDQQXQFLDWRUVꢓ  
7KHꢀFDVKꢀIORZꢀQXPEHUꢀDSSHDUVꢀEULHIO\ꢃꢀWKHQꢀWKHꢀ  
FDVKꢀIORZꢀLVꢀVKRZQꢄ  
N
7KHꢀFDVKꢀIORZꢀQXPEHUꢀDSSHDUVꢀEULHIO\ꢃꢀWKHQꢀWKHꢀ  
QXPEHUꢀRIꢀWLPHVꢀWKHꢀFDVKꢀIORZꢀLVꢀUHSHDWHGꢀLVꢀVKRZQꢄ  
ERROR  
TVM  
7KHꢀHUURUꢀDQQXQFLDWRUꢀLVꢀOLWꢃꢀWRJHWKHUꢀZLWKꢀRQHꢀRIꢀ  
WKHꢀIROORZLQJꢀIRXUꢀDQQXQFLDWRUVꢓ  
7KHUHꢀLVꢀDꢀ790ꢀHUURUꢀꢅVXFKꢀDVꢀVROYLQJꢀIRUꢀ3ꢔ<5ꢆꢄ  
26 1: Getting Started  
Annunciator  
FULL  
Status (Continued)  
0RUHꢀWKDQꢀꢁꢍꢀFDVKꢀIORZVꢀKDYHꢀEHHQꢀHQWHUHGꢃꢀRUꢀ  
PRUHꢀWKDQꢀꢍꢀXQVROYHGꢀEUDFNHWVꢀXVHGꢄ  
STAT  
FUNC  
,QFRUUHFWꢀGDWDꢀXVHGꢀLQꢀDꢀVWDWLVWLFVꢀFDOFXODWLRQꢀRUꢃꢀ  
ZKHQꢀERROR LVꢀQRWꢀOLWꢃꢀDꢀVWDWLVWLFDOꢀFDOFXODWLRQꢀKDVꢀ  
EHHQꢀSHUIRUPHGꢄ  
$ꢀPDWKꢀHUURUꢀKDVꢀRFFXUUHGꢀꢅIRUꢀH[DPSOHꢃꢀGLYLVLRQꢀE\ꢀ  
]HURꢆꢄ  
STAT  
$ꢀVWDWLVWLFDOꢀFDOFXODWLRQꢀKDVꢀEHHQꢀSHUIRUPHGꢄ  
Shift Key  
0RVWꢀRIꢀWKHꢀ+3ꢀꢁꢂ%,,ꢀNH\VꢀKDYHꢀDꢀVHFRQGꢀRUꢀ´VKLIWHGµꢀ  
IXQFWLRQꢀSULQWHGꢀLQꢀRUDQJHꢀRQꢀWKHꢀNH\ꢄꢀ7KHꢀRUDQJHꢀVKLIWꢀ  
NH\ꢀꢅ ꢆꢀLVꢀXVHGꢀWRꢀDFFHVVꢀWKHVHꢀIXQFWLRQVꢄ  
:KHQꢀ\RXꢀSUHVVꢀ ꢃꢀWKHꢀVKLIWꢀDQQXQFLDWRUꢀꢅSHIFTꢆꢀLVꢀ  
GLVSOD\HGꢀWRꢀLQGLFDWHꢀWKDWꢀWKHꢀVKLIWHGꢀIXQFWLRQVꢀDUHꢀDFWLYHꢄꢀ  
7RꢀWXUQꢀWKHꢀSHIFTꢀDQQXQFLDWRUꢀRIIꢃꢀSUHVVꢀ ꢀDJDLQꢄ  
)RUꢀH[DPSOHꢃꢀSUHVVꢀ ꢀIROORZHGꢀE\ꢀ ꢀꢅDOVRꢀVKRZQꢀDVꢀ  
QXPEHUꢀLQꢀWKHꢀGLVSOD\ꢀE\ꢀLWVHOIꢄ  
ꢆꢀWRꢀPXOWLSO\ꢀDꢀ  
Statistics Key  
7KHꢀVWDWLVWLFVꢀNH\ꢀꢅ ꢃꢀFRORUHGꢀPDXYHꢆꢀLVꢀXVHGꢀWRꢀDFFHVVꢀ  
VXPPDU\ꢀVWDWLVWLFVꢀIURPꢀWKHꢀVWDWLVWLFVꢀPHPRU\ꢀUHJLVWHUVꢄ  
:KHQꢀ\RXꢀSUHVVꢀ ꢃꢀWKHꢀVWDWLVWLFVꢀDQQXQFLDWRUꢀꢅSTATSꢆꢀLVꢀ  
GLVSOD\HGꢄꢀ7KLVꢀLQGLFDWHVꢀWKDWꢀ\RXꢀFDQꢀUHFDOOꢀRQHꢀRIꢀVL[ꢀ  
VXPPDU\ꢀVWDWLVWLFVꢀZLWKꢀWKHꢀQH[WꢀNH\VWURNHꢀꢅVHHꢀ  
SDJH ꢐꢐꢆꢄꢀ7RꢀWXUQꢀWKHꢀSTATS DQQXQFLDWRUꢀRIIꢃꢀSUHVVꢀ  
DJDLQꢄ  
)RUꢀH[DPSOHꢃꢀSUHVVꢀ ꢀIROORZHGꢀE\ꢀ ꢀWRꢀUHFDOOꢀWKHꢀVXPꢀRIꢀWKHꢀ[ꢀ  
YDOXHVꢀHQWHUHGꢄ  
1: Getting Started 27  
INPUT Key  
7KHꢀ ꢀNH\ꢀLVꢀXVHGꢀWRꢀVHSDUDWHꢀWZRꢀQXPEHUVꢀZKHQꢀXVLQJꢀ  
WZRꢇQXPEHUꢀIXQFWLRQVꢀRUꢀWZRꢇYDULDEOHꢀVWDWLVWLFVꢄꢀ7KHꢀ  
NH\ꢀFDQꢀDOVRꢀEHꢀXVHGꢀWRꢀHYDOXDWHꢀDQ\ꢀSHQGLQJꢀDULWKPHWLFꢀ  
ꢀ
RSHUDWLRQVꢃꢀLQꢀZKLFKꢀFDVHꢀWKHꢀUHVXOWꢀLVꢀWKHꢀVDPHꢀDVꢀSUHVVLQJꢀ  
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SWAP Key  
3UHVVLQJꢀ  
ꢀH[FKDQJHVꢀWKHꢀIROORZLQJꢓ  
7KHꢀODVWꢀWZRꢀQXPEHUVꢀWKDWꢀ\RXꢀHQWHUHGꢒꢀIRUꢀLQVWDQFHꢃꢀ  
WRꢀFKDQJHꢀWKHꢀRUGHUꢀRIꢀGLYLVLRQꢀRUꢀVXEWUDFWLRQꢄ  
7KHꢀUHVXOWVꢀRIꢀIXQFWLRQVꢀWKDWꢀUHWXUQꢀWZRꢀYDOXHVꢄ  
7KHꢀ[ꢇꢀDQGꢀ\ꢇYDOXHVꢀZKHQꢀXVLQJꢀVWDWLVWLFVꢄ  
Math Functions  
One-Number Functions. 0DWKꢀIXQFWLRQVꢀLQYROYLQJꢀRQHꢀ  
QXPEHUꢀXVHꢀWKHꢀQXPEHUꢀLQꢀWKHꢀGLVSOD\ꢄ  
Keys:  
Display:  
9.45  
Description:  
&DOFXODWHVꢀVTXDUHꢀURRWꢄ  
ꢁꢔꢎꢄꢋꢏꢀLVꢀFDOFXODWHGꢀILUVWꢄ  
0.42  
3.99  
$GGVꢀꢋꢄꢍꢌꢀDQGꢀꢁꢔꢎꢄꢋꢏ  
28 1: Getting Started  
Two-Number Functions. :KHQꢀDꢀIXQFWLRQꢀUHTXLUHVꢀWZRꢀ  
QXPEHUVꢃꢀWKHꢀQXPEHUVꢀDUHꢀHQWHUHGꢀOLNHꢀWKLVꢓꢀQXPEHUꢀꢁ  
ꢀ
QXPEHUꢂꢀIROORZHGꢀE\ꢀWKHꢀRSHUDWLRQꢄꢀ3UHVVLQJꢀ ꢀHYDOXDWHVꢀ  
WKHꢀFXUUHQWꢀH[SUHVVLRQꢀDQGꢀGLVSOD\VꢀWKHꢀINPUTꢀ  
DQQXQFLDWRUꢄꢀ)RUꢀH[DPSOHꢃꢀWKHꢀIROORZLQJꢀNH\VWURNHVꢀ  
FDOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀꢁꢌꢀDQGꢀꢎꢊꢄ  
Keys:  
Display:  
Description:  
17.00  
(QWHUVꢀQXPEHUꢀꢃꢀGLVSOD\Vꢀ  
WKHꢀINPUTꢀDQQXQFLDWRUꢄ  
29_  
(QWHUVꢀQXPEHUꢂꢄ  
70.59  
&DOFXODWHVꢀWKHꢀSHUFHQWꢀ  
FKDQJHꢄ  
Display Format of Numbers  
:KHQꢀ\RXꢀWXUQꢀRQꢀWKHꢀ+3ꢀꢁꢂ%,,ꢀIRUꢀWKHꢀILUVWꢀWLPHꢃꢀ  
QXPEHUVꢀDUHꢀGLVSOD\HGꢀZLWKꢀWZRꢀGHFLPDOꢀSODFHVꢀDQGꢀDꢀ  
SHULRGꢀDVꢀWKHꢀGHFLPDOꢀSRLQWꢄꢀ7KHꢀGLVSOD\ꢀIRUPDWꢀFRQWUROVꢀ  
KRZꢀPDQ\ꢀGLJLWVꢀDSSHDUꢀLQꢀWKHꢀGLVSOD\ꢄ  
,IꢀWKHꢀUHVXOWꢀRIꢀDꢀFDOFXODWLRQꢀLVꢀDꢀQXPEHUꢀFRQWDLQLQJꢀPRUHꢀ  
VLJQLILFDQWꢀGLJLWVꢀWKDQꢀFDQꢀEHꢀGLVSOD\HGꢀLQꢀWKHꢀFXUUHQWꢀ  
GLVSOD\ꢀIRUPDWꢃꢀWKHꢀQXPEHUꢀLVꢀURXQGHGꢀWRꢀILWꢀWKHꢀFXUUHQWꢀGLVSOD\ꢀVHWWLQJꢄ  
5HJDUGOHVVꢀRIꢀWKHꢀFXUUHQWꢀGLVSOD\ꢀIRUPDWꢃꢀHDFKꢀQXPEHUꢀLVꢀVWRUHGꢀLQWHUQDOO\ꢀ  
DVꢀDꢀVLJQHGꢃꢀꢁꢎꢇGLJLWꢀQXPEHUꢀZLWKꢀDꢀVLJQHGꢃꢀWKUHHꢇGLJLWꢀH[SRQHQWꢄ  
1: Getting Started 29  
Specifying Displayed Decimal Places  
7RꢀVSHFLI\ꢀWKHꢀQXPEHUꢀRIꢀGLVSOD\HGꢀGHFLPDOꢀSODFHVꢓ  
ꢀꢁ 3UHVVꢀ  
ꢄ
ꢂꢁ (QWHUꢀWKHꢀQXPEHUꢀRIꢀGLJLWVꢀꢅꢂꢀWKURXJKꢀꢊꢆꢀWKDWꢀ\RXꢀZLVKꢀWRꢀDSSHDUꢀ  
DIWHUꢀWKHꢀGHFLPDOꢀSRLQWꢄ  
Keys:  
Display:  
0.00  
Description:  
&OHDUVꢀGLVSOD\ꢄ  
0.000  
'LVSOD\VꢀWKUHHꢀGHFLPDOꢀ  
SODFHVꢄ  
5.727  
5.727360000  
'LVSOD\VꢀQLQHꢀGHFLPDOꢀ  
SODFHVꢄ  
5.73  
5HVWRUHVꢀWZRꢀGHFLPDOꢀ  
SODFHVꢀDQGꢀURXQGVꢀ  
QXPEHUꢀLQꢀGLVSOD\ꢄ  
:KHQꢀDꢀQXPEHUꢀLVꢀWRRꢀODUJHꢀRUꢀWRRꢀVPDOOꢀWRꢀEHꢀGLVSOD\HGꢀLQꢀ',63ꢀIRUPDWꢃꢀ  
LWꢀDXWRPDWLFDOO\ꢀGLVSOD\VꢀLQꢀVFLHQWLILFꢀQRWDWLRQꢄ  
Scientific Notation  
6FLHQWLILFꢀQRWDWLRQꢀLVꢀXVHGꢀWRꢀUHSUHVHQWꢀQXPEHUVꢀWKDWꢀDUHꢀ  
WRRꢀODUJHꢀRUꢀWRRꢀVPDOOꢀWRꢀILWꢀLQꢀWKHꢀGLVSOD\ꢄꢀ)RUꢀH[DPSOHꢃꢀLIꢀ  
\RXꢀHQWHUꢀWKHꢀQXPEHUꢀꢁꢂꢃꢂꢂꢂꢃꢂꢂꢂꢀ ꢀꢁꢂꢃꢂꢂꢂꢃꢂꢂꢂꢀ ꢃꢀWKHꢀ  
UHVXOWꢀLVꢀꢁꢄꢂꢂ(ꢁꢈꢃꢀZKLFKꢀPHDQVꢀ´RQHꢀWLPHVꢀWHQꢀWRꢀWKHꢀ  
IRXUWHHQWKꢀSRZHUµꢀRUꢀ´ꢁꢄꢂꢂꢀZLWKꢀWKHꢀGHFLPDOꢀSRLQWꢀPRYHGꢀ  
IRXUWHHQꢀSODFHVꢀWRꢀWKHꢀULJKWꢄµꢀ<RXꢀFDQꢀHQWHUꢀWKLVꢀQXPEHUꢀ  
E\ꢀSUHVVLQJꢀꢁ  
ꢁꢈꢄꢀ7KHꢀ(ꢀVWDQGVꢀIRUꢀ´H[SRQHQWꢀRIꢀWHQꢄµ  
([SRQHQWVꢀFDQꢀDOVRꢀEHꢀQHJDWLYHꢀIRUꢀYHU\ꢀVPDOOꢀQXPEHUVꢄꢀ7KHꢀQXPEHUꢀ  
ꢂꢄꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢂꢈꢀLVꢀGLVSOD\HGꢀDVꢀꢈꢄꢂꢂ(²ꢁꢎꢃꢀZKLFKꢀPHDQVꢀ´IRXUꢀWLPHVꢀWHQꢀ  
WRꢀWKHꢀQHJDWLYHꢀWZHOIWKꢀSRZHUµꢀRUꢀ´ꢈꢄꢂꢀZLWKꢀWKHꢀGHFLPDOꢀSRLQWꢀPRYHGꢀꢁꢎꢀ  
SODFHVꢀWRꢀWKHꢀOHIWꢄµꢀ<RXꢀFDQꢀHQWHUꢀWKLVꢀQXPEHUꢀE\ꢀSUHVVLQJꢀ  
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30 1: Getting Started  
Displaying the Full Precision of Numbers  
7RꢀVHWꢀ\RXUꢀFDOFXODWRUꢀWRꢀGLVSOD\ꢀQXPEHUVꢀDVꢀSUHFLVHO\ꢀDVꢀ  
SRVVLEOHꢃꢀSUHVVꢀ ꢀꢅWUDLOLQJꢀ]HURVꢀDUHꢀQRWꢀGLVSOD\HGꢄꢆꢀ  
7RꢀWHPSRUDULO\ꢀYLHZꢀDOOꢀꢁꢎꢀGLJLWVꢀRIꢀWKHꢀQXPEHUꢀLQꢀ  
WKHꢀGLVSOD\ꢀꢅUHJDUGOHVVꢀRIꢀWKHꢀFXUUHQWꢀGLVSOD\ꢀIRUPDWꢀ  
VHWWLQJꢆꢃꢀSUHVVꢀ  
ꢀDQGꢀKROGꢀ ꢄꢀ7KHꢀQXPEHUꢀLVꢀ  
GLVSOD\HGꢀDVꢀORQJꢀDVꢀ\RXꢀFRQWLQXHꢀKROGLQJꢀ ꢄꢀ7KHꢀ  
GHFLPDOꢀSRLQWꢀLVꢀQRWꢀVKRZQꢄ  
6WDUWꢀZLWKꢀWZRꢀGHFLPDOꢀSODFHVꢀꢅ  
ꢎꢆꢄ  
Keys:  
Display:  
Description:  
1.43  
'LYLGHVꢄ  
142857142857  
'LVSOD\VꢀDOOꢀꢁꢎꢀGLJLWVꢄ  
Interchanging the Period and Comma  
7RꢀVZLWFKꢀEHWZHHQꢀWKHꢀSHULRGꢀDQGꢀFRPPDꢀꢅ8QLWHGꢀ6WDWHVꢀ  
DQGꢀ,QWHUQDWLRQDOꢀGLVSOD\ꢆꢀXVHGꢀDVꢀWKHꢀGHFLPDOꢀSRLQWꢀDQGꢀ  
GLJLWꢀVHSDUDWRUꢃꢀSUHVVꢀ  
ꢄ
)RUꢀH[DPSOHꢃꢀRQHꢀPLOOLRQꢀFDQꢀEHꢀGLVSOD\HGꢀDVꢀꢁꢃꢂꢂꢂꢃꢂꢂꢂꢄꢂꢂꢀ  
RUꢀꢁꢄꢂꢂꢂꢄꢂꢂꢂꢃꢂꢂꢄ  
1: Getting Started 31  
Rounding Numbers  
7KHꢀFDOFXODWRUꢀVWRUHVꢀDQGꢀFDOFXODWHVꢀXVLQJꢀꢁꢎꢇGLJLWꢀ  
QXPEHUVꢄꢀ:KHQꢀꢁꢎꢀGLJLWꢀDFFXUDF\ꢀLVꢀQRWꢀGHVLUDEOHꢃꢀXVHꢀ  
ꢀWRꢀURXQGꢀWKHꢀQXPEHUꢀWRꢀWKHꢀGLVSOD\HGꢀIRUPDWꢀ  
EHIRUHꢀXVLQJꢀLWꢀLQꢀDꢀFDOFXODWLRQꢄꢀ5RXQGLQJꢀQXPEHUVꢀ  
LVꢀXVHIXOꢀZKHQꢀ\RXꢀZDQWꢀWKHꢀDFWXDOꢀꢅGROODUVꢀDQGꢀ  
FHQWVꢆꢀPRQWKO\ꢀSD\PHQWꢄ  
Keys:  
Display:  
Description:  
9.87654321_  
(QWHUVꢀDꢀQXPEHUꢀZLWKꢀ  
PRUHꢀWKDQꢀWZRꢀQRQꢇ  
]HURꢀGHFLPDOꢀSODFHVꢄ  
9.88  
'LVSOD\VꢀWZRꢀGHFLPDOꢀ  
SODFHVꢄ  
987654321000  
'LVSOD\VꢀDOOꢀGLJLWVꢀZLWKꢇ  
RXWꢀWKHꢀGHFLPDOꢀZKLOHꢀ  
\RXꢀSUHVVꢀ ꢄ  
9.88  
5RXQGVꢀWRꢀWZRꢀGHFLPDOꢀ  
SODFHVꢀꢅVSHFLILHGꢀE\ꢀ  
SUHVVLQJꢀ  
ꢆꢄ  
988000000000  
6KRZVꢀURXQGHGꢃꢀVWRUHGꢀ  
QXPEHUꢄ  
Messages  
7KHꢀ+3ꢀꢁꢂ%,,ꢀGLVSOD\VꢀPHVVDJHVꢀDERXWꢀWKHꢀVWDWXVꢀRIꢀWKHꢀFDOFXODWRUꢀRUꢀ  
LQIRUPVꢀ\RXꢀWKDWꢀ\RXꢀKDYHꢀDWWHPSWHGꢀDQꢀLQFRUUHFWꢀRSHUDWLRQꢄꢀ7RꢀFOHDUꢀDꢀ  
PHVVDJHꢀIURPꢀWKHꢀGLVSOD\ꢃꢀSUHVVꢀ ꢀRUꢀ ꢄꢀ6HHꢀ´0HVVDJHVµꢀRQꢀ  
SDJH ꢁꢋꢌꢀIRUꢀDꢀOLVWꢀRIꢀPHDQLQJVꢄ  
32 1: Getting Started  
2
Business Percentages  
<RXꢀFDQꢀXVHꢀWKHꢀ+3ꢀꢁꢂ%,,ꢀWRꢀFDOFXODWHꢀVLPSOHꢀSHUFHQWꢃꢀSHUFHQWꢀFKDQJHꢃꢀ  
FRVWꢃꢀSULFHꢃꢀPDUJLQꢃꢀDQGꢀPDUNXSꢄ  
Percent Key  
7KHꢀ ꢀNH\ꢀKDVꢀWZRꢀIXQFWLRQVꢅꢀILQGLQJꢀDꢀSHUFHQWꢀDQGꢀ  
DGGLQJꢀRUꢀVXEWUDFWLQJꢀDꢀSHUFHQWꢄ  
Finding a Percent  
7KHꢀ ꢀNH\ꢀGLYLGHVꢀDꢀQXPEHUꢀE\ꢀꢁꢂꢂꢀXQOHVVꢀLWꢀLVꢀSUHFHGHGꢀE\ꢀDQꢀDGGLWLRQꢀ  
RUꢀVXEWUDFWLRQꢀVLJQꢄ  
Example. )LQGꢀꢆꢇꢈꢀRIꢀꢆꢂꢂꢄ  
Keys:  
Display:  
200.00  
0.25  
Description:  
(QWHUVꢀꢆꢂꢂꢄ  
&RQYHUWVꢀꢆꢇꢈꢀWRꢀDꢀGHFLPDOꢄ  
0XOWLSOLHVꢀꢆꢂꢂꢀE\ꢀꢆꢇꢈꢄ  
50.00  
2: Business Percentages 33  
Adding or Subtracting a Percent  
<RXꢀFDQꢀDGGꢀRUꢀVXEWUDFWꢀDꢀSHUFHQWꢀLQꢀRQHꢀFDOFXODWLRQꢄ  
Example. 'HFUHDVHꢀꢆꢂꢂꢀE\ꢀꢆꢇꢈꢄ  
Keys:  
Display:  
200.00  
50.00  
Description:  
(QWHUVꢀꢆꢂꢂꢄ  
0XOWLSOLHVꢀꢆꢂꢂꢀE\ꢀꢂꢄꢆꢇꢄ  
6XEWUDFWVꢀꢇꢂꢀIURPꢀꢆꢂꢂꢄ  
150.00  
Example. <RXꢀERUURZꢀꢉꢁꢃꢆꢇꢂꢀIURPꢀDꢀUHODWLYHꢃꢀDQGꢀ\RXꢀDJUHHꢀWRꢀUHSD\ꢀWKHꢀ  
ORDQꢀLQꢀDꢀ\HDUꢀZLWKꢀꢊꢈꢀVLPSOHꢀLQWHUHVWꢄꢀ+RZꢀPXFKꢀPRQH\ꢀZLOOꢀ\RXꢀRZH"  
Keys:  
Display:  
87.50  
Description:  
&DOFXODWHVꢀORDQꢀLQWHUHVWꢄ  
1,337.50  
$GGVꢀꢉꢐꢊꢄꢇꢂꢀDQGꢀ  
ꢉꢁꢃꢆꢇꢂꢄꢂꢂꢀWRꢀVKRZꢀ  
UHSD\PHQWꢀDPRXQWꢄ  
Percent Change  
&DOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀWZRꢀQXPEHUVꢀꢋQ DQGꢀ  
Q ꢃꢀH[SUHVVHGꢀDVꢀDꢀSHUFHQWꢀRIꢀQ ꢌꢀE\ꢀHQWHULQJꢀQ ꢀQ ꢃꢀWKHQꢀ  
SUHVVꢀ  
ꢄ
Example. &DOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀꢆꢍꢁꢄꢊꢀDQGꢀ  
ꢎꢁꢏꢄꢐꢄ  
Keys:  
Display:  
Description:  
291.70  
(QWHUVꢀQ ꢄ  
8.60  
&DOFXODWHVꢀSHUFHQWꢀ  
FKDQJHꢄ  
Example. &DOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀꢋꢁꢆꢀïꢀꢇꢌꢀDQGꢀꢋꢏꢇꢀꢑꢀꢁꢐꢌꢄ  
Keys:  
Display:  
Description:  
60.00  
&DOFXODWHVꢀDQGꢀHQWHUVꢀQ ꢄ  
38.33  
&DOFXODWHVꢀSHUFHQWꢀ  
FKDQJHꢄ  
34 2: Business Percentages  
Margin and Markup Calculations  
7KHꢀ+3ꢀꢁꢂ%,,ꢀFDQꢀFDOFXODWHꢀFRVWꢃꢀVHOOLQJꢀSULFHꢃꢀPDUJLQꢃꢀRUꢀPDUNXSꢄ  
Application  
0DUJLQ  
Keys  
Description  
0DUJLQꢀLVꢀPDUNXSꢀH[SUHVVHGꢀDVꢀ  
DꢀSHUFHQWꢀRIꢀSULFHꢄ  
0DUNXSꢀFDOFXODWLRQVꢀDUHꢀ  
H[SUHVVHGꢀDVꢀDꢀSHUFHQWꢀRIꢀFRVWꢄ  
,
,
,
0DUNXS  
,
7RꢀVHHꢀDQ\ꢀYDOXHꢀXVHGꢀE\ꢀWKHꢀ0DUJLQꢀDQGꢀ0DUNXSꢀDSSOLFDWLRQꢃꢀSUHVVꢀ  
DQGꢀWKHQꢀWKHꢀNH\ꢀ\RXꢀZLVKꢀWRꢀVHHꢄꢀ)RUꢀH[DPSOHꢃꢀWRꢀVHHꢀWKHꢀYDOXHꢀVWRUHGꢀDVꢀ  
ꢃꢀSUHVVꢀ ꢄꢀ0DUJLQꢀDQGꢀ0DUNXSꢀVKDUHꢀWKHꢀVDPHꢀVWRUDJHꢀUHJLVWHUꢄꢀ  
ꢀ
)RUꢀH[DPSOHꢃꢀLIꢀ\RXꢀVWRUHꢀꢆꢂꢀLQꢀ ꢃꢀWKHQꢀSUHVVꢀ  
GLVSOD\HGꢄꢀ  
ꢃꢀ\RXꢀZLOOꢀVHHꢀꢆꢂꢄꢂꢂꢀ  
Margin Calculations  
Example. .LORZDWWꢀ(OHFWURQLFVꢀSXUFKDVHVꢀWHOHYLVLRQVꢀIRUꢀꢉꢆꢇꢇꢄꢀ7KHꢀ  
WHOHYLVLRQVꢀDUHꢀVROGꢀIRUꢀꢉꢎꢂꢂꢄꢀ:KDWꢀLVꢀWKHꢀPDUJLQ"  
Keys:  
Display:  
255.00  
Description:  
6WRUHVꢀFRVWꢀLQꢀ&67ꢄ  
300.00  
6WRUHVꢀVHOOLQJꢀSULFHꢀLQꢀ  
35&ꢄ  
15.00  
&DOFXODWHVꢀPDUJLQꢄ  
Markup on Cost Calculations  
Example. 7KHꢀVWDQGDUGꢀPDUNXSꢀRQꢀFRVWXPHꢀMHZHOU\ꢀDWꢀ.OHLQHU·Vꢀ  
.RVPHWLTXHꢀLVꢀꢏꢂꢈꢄꢀ7KH\ꢀMXVWꢀUHFHLYHGꢀDꢀVKLSPHQWꢀRIꢀFKRNHUVꢀFRVWLQJꢀ  
ꢉꢁꢍꢄꢂꢂꢀHDFKꢄꢀ:KDWꢀLVꢀWKHꢀUHWDLOꢀSULFHꢀSHUꢀFKRNHU"  
Keys:  
Display:  
19.00  
Description:  
6WRUHVꢀFRVWꢄ  
60.00  
6WRUHVꢀPDUNXSꢄ  
&DOFXODWHVꢀUHWDLOꢀSULFHꢄ  
30.40  
2: Business Percentages 35  
Using Margin and Markup Together  
Example.$ꢀIRRGꢀFRRSHUDWLYHꢀEX\VꢀFDVHVꢀRIꢀFDQQHGꢀVRXSꢀZLWKꢀDQꢀLQYRLFHꢀ  
FRVWꢀRIꢀꢉꢍꢄꢏꢂꢀSHUꢀFDVHꢄꢀ,IꢀWKHꢀFRꢒRSꢀURXWLQHO\ꢀXVHVꢀDꢀꢁꢇꢈꢀPDUNXSꢃꢀIRUꢀZKDWꢀ  
SULFHꢀVKRXOGꢀLWꢀVHOOꢀDꢀFDVHꢀRIꢀVRXS"ꢀ:KDWꢀLVꢀWKHꢀPDUJLQ"  
Keys:  
Display:  
9.60  
Description:  
6WRUHVꢀLQYRLFHꢀFRVWꢄ  
6WRUHVꢀPDUNXSꢄ  
15.00  
11.04  
&DOFXODWHVꢀWKHꢀSULFHꢀRQꢀ  
DꢀFDVHꢀRIꢀVRXSꢄ  
13.04  
&DOFXODWHVꢀPDUJLQꢄ  
36 2: Business Percentages  
3
Number Storage and Arithmetic  
Using Stored Numbers in Calculations  
<RXꢀFDQꢀVWRUHꢀQXPEHUVꢁꢀIRUꢀUHXVHꢁꢀLQꢀVHYHUDOꢀGLIIHUHQWꢀZD\Vꢂ  
8VHꢀ ꢀꢃ&RQVWDQWꢄꢀWRꢀVWRUHꢀDꢀQXPEHUꢀDQGꢀLWVꢀRSHUDWRUꢀIRUꢀUHSHWLWLYHꢀ  
RSHUDWLRQVꢅ  
8VHꢀꢆꢀ.H\ꢀ0HPRU\ꢀꢃ ꢁꢀ ꢁꢀDQGꢀ ꢄꢀWRꢀVWRUHꢁꢀUHFDOOꢁꢀDQGꢀVXPꢀ  
QXPEHUVꢀZLWKꢀDꢀVLQJOHꢀNH\VWURNHꢅ  
8VHꢀ  
UHJLVWHUVꢅ  
ꢀDQGꢀ ꢀWRꢀVWRUHꢀWRꢁꢀDQGꢀUHFDOOꢀIURPꢁꢀWKHꢀꢇꢈꢀQXPEHUHGꢀ  
Using Constants  
8VHꢀ ꢀWRꢀVWRUHꢀDꢀQXPEHUꢀDQGꢀDULWKPHWLFꢀRSHUDWRUꢀIRUꢀ  
UHSHWLWLYHꢀFDOFXODWLRQVꢅꢀ2QFHꢀWKHꢀFRQVWDQWꢀRSHUDWLRQꢀLVꢀ  
VWRUHGꢁꢀHQWHUꢀDꢀQXPEHUꢀDQGꢀSUHVVꢀ ꢅꢀ7KHꢀVWRUHGꢀRSHUDWLRQꢀ  
LVꢀSHUIRUPHGꢀRQꢀWKHꢀQXPEHUꢀLQꢀWKHꢀGLVSOD\ꢅ  
3: Number Storage and Arithmetic 37  
Keys  
Operation  
6WRUHVꢀ´ꢊꢀQXPEHUµꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´²ꢀQXPEHUµꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´ïꢀQXPEHUµꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´¸ꢀQXPEHUµꢀDVꢀFRQVWDQWꢅ  
QXPEHU  
QXPEHU  
QXPEHU  
QXPEHU  
[ꢀYDOXH  
6WRUHVꢀ´\  
µꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´ꢊꢀQXPEHUꢀꢎµꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´²ꢀQXPEHUꢀꢎµꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´ïꢀQXPEHUꢀꢎµꢀDVꢀFRQVWDQWꢅ  
6WRUHVꢀ´¸ꢀQXPEHUꢀꢎµꢀDVꢀFRQVWDQWꢅ  
QXPEHU  
QXPEHU  
QXPEHU  
QXPEHU  
Example. &DOFXODWHꢀꢉꢀꢊꢀꢋꢁꢀꢌꢀꢊꢀꢋꢁꢀDQGꢀꢍꢀꢊꢀꢋꢅ  
Keys:  
Display:  
Description:  
2.00  
6WRUHVꢀ´ꢊꢀꢋµꢀDVꢀ  
FRQVWDQWꢅ  
7.00  
8.00  
9.00  
$GGVꢀꢉꢀꢊꢀꢋꢅ  
$GGVꢀꢌꢀꢊꢀꢋꢅ  
$GGVꢀꢍꢀꢊꢀꢋꢅ  
Example. &DOFXODWHꢀꢇꢈꢀꢊꢀꢇꢈꢎꢁꢀꢇꢇꢀꢊꢀꢇꢈꢎꢁꢀDQGꢀꢋꢉꢀꢊꢀꢇꢈꢎꢅ  
Keys:  
Display:  
Description:  
1.00  
6WRUHVꢀ´ꢊꢀꢇꢈꢎµꢀDVꢀ  
FRQVWDQWꢅ  
11.00  
12.10  
27.50  
$GGVꢀꢇꢈꢎꢀWRꢀꢇꢈꢅ  
$GGVꢀꢇꢈꢎꢀWRꢀꢇꢇꢅ  
$GGVꢀꢇꢈꢎꢀWRꢀꢋꢉꢅ  
Example. &DOFXODWHꢀꢋ ꢀDQGꢀꢏ ꢅ  
Keys: Display:  
Description:  
3.00  
6WRUHVꢀ´\ µꢀDVꢀFRQꢐ  
VWDQWꢅ  
8.00  
&DOFXODWHVꢀꢋ ꢅ  
38 3: Number Storage and Arithmetic  
64.00  
&DOFXODWHVꢀꢏ ꢅ  
Using the M Register  
7KHꢀ ꢁꢀ ꢁꢀDQGꢀ NH\VꢀSHUIRUPꢀPHPRU\ꢀRSHUDWLRQVꢀRQꢀ  
DꢀVLQJOHꢀVWRUDJHꢀUHJLVWHUꢁꢀFDOOHGꢀWKHꢀ0ꢀUHJLVWHUꢅꢀ,QꢀPRVWꢀ  
FDVHVꢁꢀLWꢀLVꢀXQQHFHVVDU\ꢀWRꢀFOHDUꢀWKHꢀ0ꢀUHJLVWHUꢁꢀVLQFHꢀ  
UHSODFHVꢀWKHꢀSUHYLRXVꢀFRQWHQWVꢅꢀ+RZHYHUꢁꢀ\RXꢀFDQꢀFOHDUꢀ  
WKHꢀ0ꢀUHJLVWHUꢀE\ꢀSUHVVLQJꢀ  
ꢅꢀ7RꢀDGGꢀDꢀVHULHVꢀRIꢀ  
WRꢀVWRUHꢀWKHꢀILUVWꢀ  
QXPEHUVꢀWRꢀWKHꢀ0ꢀUHJLVWHUꢁꢀXVHꢀ  
QXPEHUꢀDQGꢀ ꢀWRꢀDGGꢀVXEVHTXHQWꢀQXPEHUVꢅꢀ7RꢀVXEWUDFWꢀ  
WKHꢀGLVSOD\HGꢀQXPEHUꢀIURPꢀWKHꢀQXPEHUꢀLQꢀWKHꢀ0ꢀUHJLVWHUꢁꢀSUHVVꢀ  
IROORZHGꢀE\ꢀ  
ꢀ
ꢅ
Keys  
Description  
6WRUHVꢀGLVSOD\HGꢀQXPEHUꢀLQꢀWKHꢀ0ꢀUHJLVWHUꢅ  
5HFDOOVꢀQXPEHUꢀIURPꢀWKHꢀ0ꢀUHJLVWHUꢅ  
$GGVꢀGLVSOD\HGꢀQXPEHUꢀWRꢀWKHꢀ0ꢀUHJLVWHUꢅ  
Example.8VHꢀWKHꢀ0ꢀUHJLVWHUꢀWRꢀDGGꢀꢇꢍꢁꢀꢇꢏꢅꢋꢉꢁꢀDQGꢀꢇꢌꢅꢑꢉꢅꢀ7KHQꢀVXEWUDFWꢀ  
ꢏꢅꢌꢉꢀDQGꢀUHFDOOꢀWKHꢀUHVXOWꢅ  
Keys:  
Display:  
17.00  
Description:  
6WRUHVꢀꢇꢍꢀLQꢀ0ꢀUHJLVWHUꢅ  
14.25  
$GGVꢀꢇꢏꢅꢋꢉꢀWRꢀ0ꢀ  
UHJLVWHUꢅ  
16.95  
–4.65  
43.55  
$GGVꢀꢇꢌꢅꢑꢉꢀWRꢀ0ꢀ  
UHJLVWHUꢅ  
$GGVꢀ²ꢏꢅꢌꢉꢀWRꢀ0ꢀ  
UHJLVWHUꢅ  
5HFDOOVꢀFRQWHQWVꢀRIꢀWKHꢀ  
0ꢀUHJLVWHUꢅ  
3: Number Storage and Arithmetic 39  
Using Numbered Registers  
7KHꢀ  
ꢀDQGꢀ ꢀNH\VꢀDFFHVVꢀWKHꢀꢇꢈꢀXVHUꢀUHJLVWHUVꢅꢀ7KHꢀ  
ꢀNH\ꢀLVꢀXVHGꢀWRꢀFRS\ꢀWKHꢀGLVSOD\HGꢀQXPEHUꢀWRꢀDꢀ  
GHVLJQDWHGꢀUHJLVWHUꢅꢀ7KHꢀ ꢀNH\ꢀLVꢀXVHGꢀWRꢀFRS\ꢀDꢀQXPEHUꢀ  
IURPꢀDꢀUHJLVWHUꢀWRꢀWKHꢀGLVSOD\ꢅ  
7RꢀVWRUHꢀRUꢀUHFDOOꢀDꢀQXPEHUꢀLQꢀWZRꢀVWHSVꢂ  
ꢀꢁ 3UHVVꢀ ꢀRUꢀ ꢅꢀꢃ7RꢀFDQFHOꢀWKLVꢀVWHSꢁꢀSUHVVꢀ ꢀRUꢀ ꢅꢄ  
ꢂꢁ (QWHUꢀWKHꢀUHJLVWHUꢀQXPEHUꢀꢃꢈꢀWKURXJKꢀꢑꢄꢅ  
,QꢀWKHꢀIROORZLQJꢀH[DPSOHꢁꢀWZRꢀVWRUDJHꢀUHJLVWHUVꢀDUHꢀXVHGꢅꢀ&DOFXODWHꢀWKHꢀ  
IROORZLQJꢂ  
475.6  
------------  
560.1 + 475.6  
--------------------------------  
ꢀDQGꢀ  
39.15  
39.15  
Keys:  
Display:  
Description:  
475.60  
6WRUHVꢀꢏꢍꢉꢅꢌꢈꢀꢃGLVꢐ  
SOD\HGꢀQXPEHUꢄꢀLQꢀ5 ꢅ  
39.15  
12.15  
6WRUHVꢀꢆꢑꢅꢇꢉꢀLQꢀ5 ꢅ  
&RPSOHWHVꢀILUVWꢀ  
FDOFXODWLRQꢅ  
475.60  
39.15  
26.45  
5HFDOOVꢀ5 ꢅ  
5HFDOOVꢀ5 ꢅ  
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WKLUGꢄꢀIRXUWKꢄꢀDQGꢀILIWKꢀPRQWKVꢃꢀ7KHꢀLQWHUPHGLDWHꢀUHVXOWVꢀLQꢀWKLVꢀ  
LOOXVWUDWLRQꢀDUHꢀURXQGHGꢀWRꢀGROODUVꢀDQGꢀFHQWVꢃ  
7KHꢀZRUGꢀFRPSRXQGꢀLQꢀFRPSRXQGꢀLQWHUHVWꢀFRPHVꢀIURPꢀWKHꢀLGHDꢀWKDWꢀ  
LQWHUHVWꢀSUHYLRXVO\ꢀHDUQHGꢀRUꢀRZHGꢀLVꢀDGGHGꢀWRꢀWKHꢀSULQFLSDOꢃꢀ7KXVꢄꢀLWꢀFDQꢀ  
HDUQꢀPRUHꢀLQWHUHVWꢃꢀ7KHꢀILQDQFLDOꢀFDOFXODWLRQꢀFDSDELOLWLHVꢀRIꢀWKHꢀ+3ꢀꢁꢂ%,,ꢀ  
DUHꢀEDVHGꢀRQꢀFRPSRXQGꢀLQWHUHVWꢃ  
48 4: Picturing Financial Problems  
Interest Rates  
:KHQꢀ\RXꢀDSSURDFKꢀDꢀILQDQFLDOꢀSUREOHPꢄꢀLWꢀLVꢀLPSRUWDQWꢀWRꢀUHFRJQL]HꢀWKDWꢀ  
WKHꢀLQWHUHVWꢀUDWHꢀRUꢀUDWHꢀRIꢀUHWXUQꢀFDQꢀEHꢀGHVFULEHGꢀLQꢀDWꢀOHDVWꢀWKUHHꢀ  
GLIIHUHQWꢀZD\Vꢌ  
$VꢀDꢀSHULRGLFꢀUDWHꢃꢀ7KLVꢀLVꢀWKHꢀUDWHꢀWKDWꢀLVꢀDSSOLHGꢀWRꢀ\RXUꢀPRQH\ꢀIURPꢀ  
SHULRGꢀWRꢀSHULRGꢃ  
$VꢀDQꢀDQQXDOꢀQRPLQDOꢀUDWHꢃꢀ7KLVꢀLVꢀWKHꢀSHULRGLFꢀUDWHꢀPXOWLSOLHGꢀE\ꢀWKHꢀ  
QXPEHUꢀRIꢀSHULRGVꢀLQꢀDꢀ\HDUꢃ  
$VꢀDQꢀDQQXDOꢀHIIHFWLYHꢀUDWHꢃꢀ7KLVꢀLVꢀDQꢀDQQXDOꢀUDWHꢀWKDWꢀFRQVLGHUVꢀ  
FRPSRXQGLQJꢃ  
,QꢀWKHꢀSUHYLRXVꢀH[DPSOHꢀRIꢀDꢀꢇꢁꢄꢂꢂꢂꢃꢂꢂꢀVDYLQJVꢀDFFRXQWꢄꢀWKHꢀSHULRGLFꢀUDWHꢀ  
LVꢀóꢎꢀꢅSHUꢀPRQWKꢆꢄꢀTXRWHGꢀDVꢀDQꢀDQQXDOꢀQRPLQDOꢀUDWHꢀRIꢀꢊꢎꢀꢅóꢀïꢀꢁꢋꢆꢃꢀ  
7KLVꢀVDPHꢀSHULRGLFꢀUDWHꢀFRXOGꢀEHꢀTXRWHGꢀDVꢀDQꢀDQQXDOꢀHIIHFWLYHꢀUDWHꢄꢀZKLFKꢀ  
FRQVLGHUVꢀFRPSRXQGLQJꢃꢀ7KHꢀEDODQFHꢀDIWHUꢀꢁꢋꢀPRQWKVꢀRIꢀFRPSRXQGLQJꢀLVꢀ  
ꢇꢁꢄꢂꢊꢁꢃꢊꢐꢄꢀZKLFKꢀPHDQVꢀWKHꢀDQQXDOꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHꢀLVꢀꢊꢃꢁꢊꢐꢎꢃ  
([DPSOHVꢀRIꢀFRQYHUWLQJꢀEHWZHHQꢀQRPLQDOꢀDQGꢀDQQXDOꢀHIIHFWLYHꢀUDWHVꢀDUHꢀ  
RQꢀSDJHVꢀꢈꢋꢀWKURXJKꢀꢈꢑꢃ  
Two Types of Financial Problems  
7KHꢀILQDQFLDOꢀSUREOHPVꢀLQꢀWKLVꢀPDQXDOꢀXVHꢀFRPSRXQGꢀLQWHUHVWꢀXQOHVVꢀ  
VSHFLILFDOO\ꢀVWDWHGꢀDVꢀVLPSOHꢀLQWHUHVWꢀFDOFXODWLRQVꢃꢀ)LQDQFLDOꢀSUREOHPVꢀDUHꢀ  
GLYLGHGꢀLQWRꢀWZRꢀJURXSVꢌꢀ790ꢀSUREOHPVꢀDQGꢀFDVKꢀIORZꢀSUREOHPVꢃ  
Recognizing a TVM Problem  
,IꢀXQLIRUPꢀFDVKꢀIORZVꢀRFFXUꢀEHWZHHQꢀWKHꢀILUVWꢀDQGꢀODVWꢀSHULRGVꢀRQꢀWKHꢀ  
FDVKꢀIORZꢀGLDJUDPꢄꢀWKHꢀILQDQFLDOꢀSUREOHPꢀLVꢀDꢀ790ꢀꢅWLPHꢀYDOXHꢀRIꢀPRQH\ꢆꢀ  
SUREOHPꢃꢀ7KHUHꢀDUHꢀILYHꢀPDLQꢀNH\VꢀXVHGꢀWRꢀVROYHꢀDꢀ790ꢀSUREOHPꢃ  
1XPEHUꢀRIꢀSHULRGVꢀRUꢀSD\PHQWVꢃ  
$QQXDOꢀSHUFHQWDJHꢀLQWHUHVWꢀUDWHꢀꢅXVXDOO\ꢀWKHꢀDQQXDOꢀQRPLQDOꢀUDWHꢆꢃ  
3UHVHQWꢀYDOXHꢀꢅWKHꢀFDVKꢀIORZꢀDWꢀWKHꢀEHJLQQLQJꢀRIꢀWKHꢀWLPHꢀOLQHꢆꢃ  
3HULRGLFꢀSD\PHQWꢃ  
)XWXUHꢀYDOXHꢀꢅWKHꢀFDVKꢀIORZꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀFDVKꢀIORZꢀGLDJUDPꢄꢀ  
LQꢀDGGLWLRQꢀWRꢀDQ\ꢀUHJXODUꢀSHULRGLFꢀSD\PHQWꢆꢃ  
4: Picturing Financial Problems 49  
<RXꢀFDQꢀFDOFXODWHꢀDQ\ꢀYDOXHꢀDIWHUꢀHQWHULQJꢀWKHꢀRWKHUꢀIRXUꢃꢀ&DVKꢀIORZꢀ  
GLDJUDPVꢀIRUꢀORDQVꢄꢀPRUWJDJHVꢄꢀOHDVHVꢄꢀVDYLQJVꢀDFFRXQWVꢄꢀRUꢀDQ\ꢀFRQWUDFWꢀ  
ZLWKꢀUHJXODUꢀFDVKꢀIORZVꢀRIꢀWKHꢀVDPHꢀDPRXQWꢀDUHꢀQRUPDOO\ꢀWUHDWHGꢀDVꢀ790ꢀ  
SUREOHPVꢃꢀ)RUꢀH[DPSOHꢄꢀIROORZLQJꢀLVꢀDꢀFDVKꢀIORZꢀGLDJUDPꢄꢀIURPꢀWKHꢀ  
ERUURZHU·VꢀSHUVSHFWLYHꢄꢀIRUꢀDꢀꢑꢂꢍ\HDUꢄꢀꢇꢁꢉꢂꢄꢂꢂꢂꢃꢂꢂꢀPRUWJDJHꢄꢀZLWKꢀDꢀ  
SD\PHQWꢀRIꢀꢇꢁꢄꢂꢒꢁꢃꢒꢂꢄꢀDWꢀꢈꢃꢉꢎꢀDQQXDOꢀLQWHUHVWꢄꢀZLWKꢀDꢀꢇꢁꢂꢄꢂꢂꢂꢀEDOORRQꢀ  
SD\PHQWꢃ  
2QHꢀRIꢀWKHꢀYDOXHVꢀIRUꢀ39ꢄꢀ307ꢄꢀ)9 FDQꢀEHꢀ]HURꢃꢀ)RUꢀH[DPSOHꢄꢀIROORZLQJꢀ  
LVꢀDꢀFDVKꢀIORZꢀGLDJUDPꢀꢅIURPꢀWKHꢀVDYHU·VꢀSHUVSHFWLYHꢆꢀIRUꢀDꢀVDYLQJVꢀDFFRXQWꢀ  
ZLWKꢀDꢀVLQJOHꢀGHSRVLWꢀDQGꢀDꢀVLQJOHꢀZLWKGUDZDOꢀILYHꢀ\HDUVꢀODWHUꢃꢀ,QWHUHVWꢀ  
FRPSRXQGVꢀPRQWKO\ꢃꢀ,QꢀWKLVꢀH[DPSOHꢄꢀ307 LVꢀ]HURꢃ  
7LPHꢀYDOXHꢀRIꢀPRQH\ꢀFDOFXODWLRQVꢀDUHꢀGHVFULEHGꢀLQꢀWKHꢀQH[WꢀFKDSWHUꢃ  
50 4: Picturing Financial Problems  
Recognizing a Cash Flow Problem  
$ꢀILQDQFLDOꢀSUREOHPꢀWKDWꢀGRHVꢀQRWꢀKDYHꢀUHJXODUꢄꢀXQLIRUPꢀSD\PHQWVꢀ  
ꢅVRPHWLPHVꢀFDOOHGꢀXQHYHQꢀFDVKꢀIORZVꢆꢀLVꢀDꢀFDVKꢀIORZꢀSUREOHPꢀUDWKHUꢀWKDQꢀDꢀ  
790ꢀSUREOHPꢃ  
$ꢀFDVKꢀIORZꢀGLDJUDPꢀIRUꢀDQꢀLQYHVWPHQWꢀLQꢀDꢀPXWXDOꢀIXQGꢀIROORZVꢃꢀ7KLVꢀLVꢀ  
DQꢀH[DPSOHꢀRIꢀDꢀSUREOHPꢀWKDWꢀLVꢀVROYHGꢀXVLQJꢀHLWKHUꢀ  
9DOXHꢆꢀRUꢀ ꢀꢅ,QWHUQDOꢀ5DWHꢀRIꢀ5HWXUQꢀSHUꢀ<HDUꢆꢃ  
ꢀꢅ1HWꢀ3UHVHQWꢀ  
&DVKꢀIORZꢀSUREOHPVꢀDUHꢀGHVFULEHGꢀLQꢀFKDSWHUꢀꢊꢃ  
4: Picturing Financial Problems 51  
5
Time Value of Money Calculations  
Using the TVM Application  
7KHꢀWLPHꢀYDOXHꢀRIꢀPRQH\ꢀꢁ790ꢂꢀDSSOLFDWLRQꢀLVꢀXVHGꢀIRUꢀ  
FRPSRXQGꢀLQWHUHVWꢀFDOFXODWLRQVꢀWKDWꢀLQYROYHꢀUHJXODUꢃꢀ  
XQLIRUPꢀFDVKꢀIORZVꢀ²ꢀFDOOHGꢀSD\PHQWVꢄꢀ2QFHꢀWKHꢀYDOXHVꢀDUHꢀ  
HQWHUHGꢀ\RXꢀFDQꢀYDU\ꢀRQHꢀYDOXHꢀDWꢀDꢀWLPHꢃꢀZLWKRXWꢀHQWHULQJꢀ  
DOOꢀWKHꢀYDOXHVꢀDJDLQꢄ  
7RꢀXVHꢀ790ꢃꢀVHYHUDOꢀSUHUHTXLVLWHVꢀPXVWꢀEHꢀPHWꢅ  
7KHꢀDPRXQWꢀRIꢀHDFKꢀSD\PHQWꢀPXVWꢀEHꢀWKHꢀVDPHꢄꢀ,IꢀWKHꢀSD\PHQWꢀ  
DPRXQWVꢀYDU\ꢃꢀXVHꢀWKHꢀSURFHGXUHVꢀGHVFULEHGꢀLQꢀFKDSWHUꢀꢆꢃꢀ´&DVKꢀ  
)ORZꢀ&DOFXODWLRQVµꢄ  
3D\PHQWVꢀPXVWꢀRFFXUꢀDWꢀUHJXODUꢀLQWHUYDOVꢄ  
7KHꢀSD\PHQWꢀSHULRGꢀPXVWꢀFRLQFLGHꢀZLWKꢀWKHꢀLQWHUHVWꢀFRPSRXQGLQJꢀ  
SHULRGꢄꢀꢁ,IꢀLWꢀGRHVꢀQRWꢃꢀFRQYHUWꢀWKHꢀLQWHUHVWꢀUDWHꢀXVLQJꢀWKHꢀ  
ꢃꢀDQGꢀ ꢀNH\VꢀGHVFULEHGꢀRQꢀSDJH ꢇꢈꢄꢂ  
7KHUHꢀPXVWꢀEHꢀDWꢀOHDVWꢀRQHꢀSRVLWLYHꢀDQGꢀRQHꢀQHJDWLYHꢀFDVKꢀIORZꢄ  
ꢃꢀ  
5: Time Value of Money Calculations 53  
Key  
Stores or Calculates  
7KHꢀQXPEHUꢀRIꢀSD\PHQWVꢀRUꢀFRPSRXQGLQJꢀSHULRGVꢄ  
7KHꢀDQQXDOꢀQRPLQDOꢀLQWHUHVWꢀUDWHꢄ  
7KHꢀSUHVHQWꢀYDOXHꢀRIꢀIXWXUHꢀFDVKꢀIORZVꢄꢀ39ꢀLVꢀXVXꢉ  
DOO\ꢀDQꢀLQLWLDOꢀLQYHVWPHQWꢀRUꢀORDQꢀDPRXQWꢀDQGꢀDOZD\Vꢀ  
RFFXUVꢀDWꢀWKHꢀEHJLQQLQJꢀRIꢀWKHꢀILUVWꢀSHULRGꢄ  
7KHꢀDPRXQWꢀRIꢀSHULRGLFꢀSD\PHQWVꢄꢀ$OOꢀSD\PHQWVꢀ  
DUHꢀHTXDOꢃꢀDQGꢀQRQHꢀDUHꢀVNLSSHGꢊꢀSD\PHQWVꢀFDQꢀ  
RFFXUꢀDWꢀWKHꢀEHJLQQLQJꢀRUꢀHQGꢀRIꢀHDFKꢀSHULRGꢄ  
7KHꢀIXWXUHꢀYDOXHꢄꢀ)9ꢀLVꢀHLWKHUꢀDꢀILQDOꢀFDVKꢀIORZꢀRUꢀ  
FRPSRXQGHGꢀYDOXHꢀRIꢀDꢀVHULHVꢀRIꢀSUHYLRXVꢀFDVKꢀ  
IORZVꢄꢀ)9ꢀRFFXUVꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀODVWꢀSHULRGꢄ  
6WRUHVꢀWKHꢀQXPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢄꢀ7KHꢀGHIDXOWꢀ  
LVꢀꢋꢈꢄꢀ5HVHWꢀRQO\ꢀZKHQꢀ\RXꢀZLVKꢀWRꢀFKDQJHꢀLWꢄꢀꢁ7KLVꢀ  
NH\ꢀLVꢀORFDWHGꢀEHORZꢀWKHꢀ ꢀNH\ꢄꢂ  
2SWLRQDOꢀVKRUWFXWꢀIRUꢀVWRULQJꢀ1ꢅꢀ1XPEHUꢀLQꢀGLVSOD\ꢀ  
LVꢀPXOWLSOLHGꢀE\ꢀWKHꢀYDOXHꢀLQꢀ3ꢀ<5ꢀDQGꢀVWRUHVꢀUHVXOWꢀ  
LQꢀ1ꢄꢀꢁ7KLVꢀNH\ꢀLVꢀORFDWHGꢀEHORZꢀWKHꢀ ꢀNH\ꢄꢂ  
6ZLWFKHVꢀEHWZHHQꢀ%HJLQꢀDQGꢀ(QGꢀPRGHꢄꢀ,Qꢀ%HJLQꢀ  
PRGHꢃꢀWKHꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄꢀ  
&DOFXODWHVꢀDQꢀDPRUWL]DWLRQꢀWDEOHꢄꢀ  
7RꢀYHULI\ꢀYDOXHVꢃꢀSUHVVꢀ  
ꢃꢀ  
ꢃꢀ  
ꢃꢀ  
ꢃꢀDQGꢀ  
ꢄꢀ  
3UHVVLQJꢀ  
ꢀUHFDOOVꢀWKHꢀWRWDOꢀQXPEHUꢀRIꢀSD\PHQWVꢀLQꢀ\HDUVꢀDQGꢀ  
ꢀVKRZVꢀ\RXꢀWKHꢀQXPEHUꢀRIꢀSD\PHQWVꢀSHUꢀ\HDUꢄꢀ5HFDOOLQJꢀWKHVHꢀ  
QXPEHUVꢀGRHVꢀQRWꢀFKDQJHꢀWKHꢀFRQWHQWꢀRIꢀWKHꢀUHJLVWHUVꢄ  
Clearing TVM  
3UHVVꢀ  
ꢀWRꢀFOHDUꢀWKHꢀ790ꢀUHJLVWHUVꢄꢀ7KLVꢀVHWVꢀ1ꢃꢀ,ꢀ<5ꢃꢀ39ꢃꢀ307ꢃꢀDQGꢀ  
)9ꢀWRꢀ]HURꢀDQGꢀEULHIO\ꢀGLVSOD\VꢀWKHꢀFXUUHQWꢀYDOXHꢀLQꢀ3ꢀ<5ꢄ  
54 5: Time Value of Money Calculations  
Begin and End Modes  
%HIRUHꢀ\RXꢀVWDUWꢀDꢀ790ꢀFDOFXODWLRQꢃꢀLGHQWLI\ꢀZKHWKHUꢀWKHꢀ  
ILUVWꢀSHULRGLFꢀSD\PHQWꢀRFFXUVꢀDWꢀWKHꢀEHJLQQLQJꢀRUꢀHQGꢀRIꢀ  
WKHꢀILUVWꢀSHULRGꢄꢀ,IꢀWKHꢀILUVWꢀSD\PHQWꢀRFFXUVꢀDWꢀWKHꢀHQGꢀRIꢀ  
WKHꢀILUVWꢀSHULRGꢃꢀVHWꢀ\RXUꢀ+3ꢀꢋꢌ%,,ꢀWRꢀ(QGꢀPRGHꢊꢀLIꢀLWꢀ  
RFFXUVꢀDWꢀWKHꢀEHJLQQLQJꢀRIꢀWKHꢀILUVWꢀSHULRGꢃꢀVHWꢀ\RXUꢀ  
FDOFXODWRUꢀWRꢀ%HJLQꢀPRGHꢄ  
7RꢀVZLWFKꢀEHWZHHQꢀPRGHVꢃꢀSUHVVꢀ  
ꢄꢀ7KHꢀBEGINꢀDQQXQFLDWRUꢀLVꢀ  
GLVSOD\HGꢀZKHQꢀ\RXUꢀFDOFXODWRUꢀLVꢀLQꢀ%HJLQꢀPRGHꢄꢀ1RꢀDQQXQFLDWRUꢀLVꢀ  
GLVSOD\HGꢀZKHQꢀ\RXꢀDUHꢀLQꢀ(QGꢀPRGHꢄꢀ  
0RUWJDJHVꢀDQGꢀORDQVꢀW\SLFDOO\ꢀXVHꢀ(QGꢀPRGHꢄꢀ/HDVHVꢀDQGꢀVDYLQJVꢀSODQVꢀ  
W\SLFDOO\ꢀXVHꢀ%HJLQꢀPRGHꢄ  
Loan Calculations  
Example: A Car Loan. <RXꢀDUHꢀILQDQFLQJꢀDꢀQHZꢀFDUꢀZLWKꢀDꢀWKUHHꢀ\HDUꢀ  
ORDQꢀDWꢀꢋꢌꢄꢍꢎꢀDQQXDOꢀQRPLQDOꢀLQWHUHVWꢃꢀFRPSRXQGHGꢀPRQWKO\ꢄꢀ7KHꢀSULFHꢀ  
RIꢀWKHꢀFDUꢀLVꢀꢏꢋꢐꢃꢍꢌꢌꢄꢀ<RXUꢀGRZQꢀSD\PHQWꢀLVꢀꢏꢋꢃꢍꢌꢌꢄ  
Part 1. :KDWꢀDUHꢀ\RXUꢀPRQWKO\ꢀSD\PHQWVꢀDWꢀꢋꢌꢄꢍꢎꢀLQWHUHVW"ꢀꢁ$VVXPHꢀ  
\RXUꢀSD\PHQWVꢀVWDUWꢀRQHꢀPRQWKꢀDIWHUꢀWKHꢀSXUFKDVHꢀRUꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀ  
ILUVWꢀSHULRGꢄꢂ  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄꢀ  
5: Time Value of Money Calculations 55  
Keys:  
Display:  
12.00  
Description:  
6HWVꢀSHULRGVꢀSHUꢀ\HDUꢄ  
36.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
SHULRGVꢀLQꢀORDQꢄ  
10.50  
6WRUHVꢀDQQXDOꢀQRPLQDOꢀ  
LQWHUHVWꢀUDWHꢄ  
13,000.00  
0.00  
6WRUHVꢀDPRXQWꢀ  
ERUURZHGꢄ  
6WRUHVꢀWKHꢀDPRXQWꢀOHIWꢀ  
WRꢀSD\ꢀDIWHUꢀꢑꢀ\HDUVꢄ  
–422.53  
&DOFXODWHVꢀWKHꢀPRQWKO\ꢀ  
SD\PHQWꢄꢀ7KHꢀQHJDWLYHꢀ  
VLJQꢀLQGLFDWHVꢀPRQH\ꢀ  
SDLGꢀRXWꢄ  
Part 2. $WꢀDꢀSULFHꢀRIꢀꢏꢋꢐꢃꢍꢌꢌꢃꢀZKDWꢀLQWHUHVWꢀUDWHꢀLVꢀQHFHVVDU\ꢀWRꢀORZHUꢀ\RXUꢀ  
SD\PHQWꢀE\ꢀꢏꢍꢌꢄꢌꢌꢃꢀWRꢀꢏꢑꢇꢈꢄꢍꢑ"  
–372.53  
'HFUHDVHVꢀSD\PHQWꢀ  
IURPꢀꢏꢐꢈꢈꢄꢍꢑꢄ  
2.03  
&DOFXODWHVꢀDQQXDOꢀ  
LQWHUHVWꢀUDWHꢀIRUꢀWKHꢀ  
UHGXFHGꢀSD\PHQWꢄ  
Part 3. ,IꢀLQWHUHVWꢀLVꢀꢋꢌꢄꢍꢎꢃꢀZKDWꢀLVꢀWKHꢀPD[LPXPꢀ\RXꢀFDQꢀVSHQGꢀRQꢀWKHꢀ  
FDUꢀWRꢀORZHUꢀ\RXUꢀFDUꢀSD\PHQWꢀWRꢀꢏꢑꢇꢍꢄꢌꢌ"  
10.50  
6WRUHVꢀRULJLQDOꢀLQWHUHVWꢀ  
UDWHꢄ  
–375.00  
6WRUHVꢀGHVLUHGꢀ  
SD\PHQWꢄ  
11,537.59  
&DOFXODWHVꢀDPRXQWꢀRIꢀ  
PRQH\ꢀWRꢀILQDQFHꢄ  
13,037.59  
$GGVꢀWKHꢀGRZQꢀSD\ꢉ  
PHQWꢀWRꢀWKHꢀDPRXQWꢀ  
ILQDQFHGꢀIRUꢀWRWDOꢀSULFHꢀ  
RIꢀWKHꢀFDUꢄ  
56 5: Time Value of Money Calculations  
Example: A Home Mortgage. <RXꢀGHFLGHꢀWKDWꢀWKHꢀPD[LPXPꢀPRQWKO\ꢀ  
PRUWJDJHꢀSD\PHQWꢀ\RXꢀFDQꢀDIIRUGꢀLVꢀꢏꢒꢑꢌꢄꢌꢌꢄꢀ<RXꢀFDQꢀPDNHꢀDꢀꢏꢋꢈꢃꢌꢌꢌꢀ  
GRZQꢀSD\PHQWꢃꢀDQGꢀDQQXDOꢀLQWHUHVWꢀUDWHVꢀDUHꢀFXUUHQWO\ꢀꢇꢄꢍꢎꢄꢀ,Iꢀ\RXꢀREWDLQꢀ  
Dꢀꢑꢌꢀ\HDUꢀPRUWJDJHꢃꢀZKDWꢀLVꢀWKHꢀPD[LPXPꢀSXUFKDVHꢀSULFHꢀ\RXꢀFDQꢀDIIRUG"  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄ  
Keys:  
Display:  
Description:  
12.00  
6HWVꢀSHULRGVꢀSHUꢀ\HDUꢄ  
360.00  
6WRUHVꢀWKHꢀOHQJWKꢀRIꢀWKHꢀ  
PRUWJDJHꢀꢁꢑꢌꢀïꢀꢋꢈꢂꢄ  
0.00  
3D\VꢀPRUWJDJHꢀRIIꢀLQꢀ  
ꢑꢌꢀ\HDUVꢄ  
7.50  
6WRUHVꢀLQWHUHVWꢀUDWHꢄ  
–930.00  
6WRUHVꢀGHVLUHGꢀSD\ꢉ  
PHQWꢀꢁPRQH\ꢀSDLGꢀRXWꢀ  
LVꢀQHJDWLYHꢂꢄ  
133,006.39  
145,006.39  
&DOFXODWHVꢀWKHꢀORDQꢀ\RXꢀ  
FDQꢀDIIRUGꢀZLWKꢀDꢀꢏꢒꢑꢌꢀ  
SD\PHQWꢄ  
$GGVꢀꢏꢋꢈꢃꢌꢌꢌꢀGRZQꢀ  
SD\PHQWꢀIRUꢀWKHꢀWRWDOꢀ  
SXUFKDVHꢀSULFHꢄ  
5: Time Value of Money Calculations 57  
Example: A Mortgage With a Balloon Payment. <RX·YHꢀREWDLQHGꢀDꢀ  
ꢈꢍꢀ\HDUꢃꢀꢏꢋꢇꢈꢃꢍꢌꢌꢀPRUWJDJHꢀDWꢀꢓꢄꢓꢎꢀDQQXDOꢀLQWHUHVWꢄꢀ<RXꢀDQWLFLSDWHꢀWKDWꢀ  
\RXꢀZLOOꢀRZQꢀWKHꢀKRXVHꢀIRUꢀIRXUꢀ\HDUVꢀDQGꢀWKHQꢀVHOOꢀLWꢃꢀUHSD\LQJꢀWKHꢀORDQꢀ  
ZLWKꢀDꢀEDOORRQꢀSD\PHQWꢄꢀ:KDWꢀZLOOꢀ\RXUꢀEDOORRQꢀSD\PHQWꢀEH"  
6ROYHꢀWKLVꢀSUREOHPꢀXVLQJꢀWZRꢀVWHSVꢅ  
ꢀꢁ &DOFXODWHꢀWKHꢀORDQꢀSD\PHQWꢀXVLQJꢀDꢀꢈꢍꢀ\HDUꢀWHUPꢄ  
ꢂꢁ &DOFXODWHꢀWKHꢀUHPDLQLQJꢀEDODQFHꢀDIWHUꢀꢐꢀ\HDUVꢄ  
Step 1. )LUVWꢀFDOFXODWHꢀWKHꢀORDQꢀSD\PHQWꢀXVLQJꢀDꢀꢈꢍꢀ\HDUꢀWHUPꢄ  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄ  
Keys:  
Display:  
Description:  
12.00  
6HWVꢀSHULRGVꢀSHUꢀ\HDUꢄ  
300.00  
6WRUHVꢀOHQJWKꢀRIꢀ  
PRUWJDJHꢀꢁꢈꢍꢀïꢀꢋꢈꢀ ꢀ  
ꢑꢌꢌꢀPRQWKVꢂꢄ  
0.00  
6WRUHVꢀORDQꢀEDODQFHꢀ  
DIWHUꢀꢈꢍꢀ\HDUVꢄ  
172,500.00  
8.80  
6WRUHVꢀRULJLQDOꢀORDQꢀ  
EDODQFHꢄ  
6WRUHVꢀDQQXDOꢀLQWHUHVWꢀ  
UDWHꢄ  
–1,424.06  
&DOFXODWHVꢀPRQWKO\ꢀ  
SD\PHQWꢄ  
58 5: Time Value of Money Calculations  
Step 2. 6LQFHꢀWKHꢀSD\PHQWꢀLVꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀPRQWKꢃꢀWKHꢀSDVWꢀSD\PHQWꢀ  
DQGꢀWKHꢀEDOORRQꢀSD\PHQWꢀRFFXUꢀDWꢀWKHꢀVDPHꢀWLPHꢄꢀ7KHꢀILQDOꢀSD\PHQWꢀLVꢀWKHꢀ  
VXPꢀRIꢀ307ꢀDQGꢀ)9ꢄ  
7KHꢀYDOXHꢀLQꢀ307ꢀVKRXOGꢀDOZD\VꢀEHꢀURXQGHGꢀWRꢀWZRꢀ  
GHFLPDOꢀSODFHVꢀZKHQꢀFDOFXODWLQJꢀ)9ꢀRUꢀ39ꢀWRꢀDYRLGꢀVPDOOꢃꢀ  
DFFXPXODWLYHꢀGLVFUHSDQFLHVꢀEHWZHHQꢀQRQꢉURXQGHGꢀ  
QXPEHUVꢀDQGꢀDFWXDOꢀꢁGROODUVꢀDQGꢀFHQWVꢂꢀSD\PHQWVꢄꢀ,IꢀWKHꢀ  
GLVSOD\ꢀLVꢀQRWꢀVHWꢀWRꢀWZRꢀGHFLPDOꢀSODFHVꢃꢀSUHVVꢀ  
ꢈꢄꢀ  
Keys:  
Display:  
Description:  
–1,424.06  
5RXQGVꢀSD\PHQWꢀWRꢀ  
WZRꢀGHFLPDOꢀSODFHVꢃꢀ  
WKHQꢀVWRUHVꢄ  
48.00  
6WRUHVꢀꢐꢀ\HDUꢀWHUPꢀꢁꢋꢈꢀ  
ïꢀꢐꢂꢀWKDWꢀ\RXꢀH[SHFWꢀWRꢀ  
RZQꢀKRXVHꢄ  
–163,388.39  
–164,812.45  
&DOFXODWHVꢀORDQꢀEDOꢉ  
DQFHꢀDIWHUꢀꢐꢀ\HDUVꢄ  
&DOFXODWHVꢀWRWDOꢀꢐꢓ ꢀ  
SD\PHQWꢀꢁ307ꢀDQGꢀ  
)9ꢂꢀWRꢀSD\ꢀRIIꢀORDQꢀ  
ꢁPRQH\ꢀSDLGꢀRXWꢀLVꢀ  
QHJDWLYHꢂꢄ  
5: Time Value of Money Calculations 59  
Savings Calculations  
Example: A Savings Account. ,Iꢀ\RXꢀGHSRVLWꢀꢏꢈꢃꢌꢌꢌꢀLQꢀDꢀVDYLQJVꢀ  
DFFRXQWꢀWKDWꢀSD\VꢀꢇꢄꢈꢎꢀDQQXDOꢀLQWHUHVWꢀFRPSRXQGHGꢀDQQXDOO\ꢃꢀDQGꢀPDNHꢀ  
QRꢀRWKHUꢀGHSRVLWVꢀWRꢀWKHꢀDFFRXQWꢃꢀKRZꢀORQJꢀZLOOꢀLWꢀWDNHꢀIRUꢀWKHꢀDFFRXQWꢀWRꢀ  
JURZꢀWRꢀꢏꢑꢃꢌꢌꢌ"  
6LQFHꢀWKLVꢀDFFRXQWꢀKDVꢀQRꢀUHJXODUꢀSD\PHQWVꢀꢁ307ꢀ ꢀꢌꢂꢃꢀWKHꢀSD\PHQWꢀ  
PRGHꢀꢁ(QGꢀRUꢀ%HJLQꢂꢀLVꢀLUUHOHYDQWꢄ  
Keys:  
Display:  
0.00  
Description:  
&OHDUVꢀDOOꢀUHJLVWHUVꢄ  
1.00  
6HWVꢀ3ꢀ<5ꢀWRꢀꢋꢀVLQFHꢀLQWHUHVWꢀ  
LVꢀFRPSRXQGHGꢀDQQXDOO\ꢄ  
–2,000.00  
3,000.00  
6WRUHVꢀDPRXQWꢀSDLGꢀRXWꢀIRUꢀ  
ILUVWꢀGHSRVLWꢄ  
6WRUHVꢀWKHꢀDPRXQWꢀ\RXꢀZLVKꢀ  
WRꢀDFFXPXODWHꢄ  
7.20  
5.83  
6WRUHVꢀDQQXDOꢀLQWHUHVWꢀUDWHꢄ  
&DOFXODWHVꢀQXPEHUꢀRIꢀ\HDUVꢀLWꢀ  
WDNHVꢀWRꢀUHDFKꢀꢏꢑꢃꢌꢌꢌꢄ  
60 5: Time Value of Money Calculations  
6LQFHꢀWKHꢀFDOFXODWHGꢀYDOXHꢀRIꢀ1ꢀLVꢀEHWZHHQꢀꢍꢀDQGꢀꢆꢃꢀLWꢀZLOOꢀWDNHꢀVL[ꢀ\HDUVꢀRIꢀ  
DQQXDOꢀFRPSRXQGLQJꢀWRꢀDFKLHYHꢀDꢀEDODQFHꢀRIꢀDWꢀOHDVWꢀꢏꢑꢃꢌꢌꢌꢄꢀ&DOFXODWHꢀWKHꢀ  
DFWXDOꢀEDODQFHꢀDWꢀWKHꢀHQGꢀRIꢀVL[ꢀ\HDUVꢄ  
6.00  
6HWVꢀ ꢀWRꢀꢆꢀ\HDUVꢄ  
3,035.28  
&DOFXODWHVꢀDPRXQWꢀ\RXꢀ  
FDQꢀZLWKGUDZꢀDIWHUꢀꢆꢀ  
\HDUVꢄ  
Example: An Individual Retirement Account. <RXꢀRSHQHGꢀDQꢀ  
LQGLYLGXDOꢀUHWLUHPHQWꢀDFFRXQWꢀRQꢀ$SULOꢀꢋꢐꢃꢀꢋꢒꢒꢍꢃꢀZLWKꢀDꢀGHSRVLWꢀRIꢀꢏꢈꢃꢌꢌꢌꢄꢀ  
ꢏꢓꢌꢄꢌꢌꢀLVꢀGHGXFWHGꢀIURPꢀ\RXUꢀSD\FKHFNꢀDQGꢀ\RXꢀDUHꢀSDLGꢀWZLFHꢀDꢀPRQWKꢄꢀ  
7KHꢀDFFRXQWꢀSD\VꢀꢆꢄꢑꢎꢀDQQXDOꢀLQWHUHVWꢀFRPSRXQGHGꢀVHPLPRQWKO\ꢄꢀ+RZꢀ  
PXFKꢀZLOOꢀEHꢀLQꢀWKHꢀDFFRXQWꢀRQꢀ$SULOꢀꢋꢐꢃꢀꢈꢌꢋꢌ"  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄ  
5: Time Value of Money Calculations 61  
Keys:  
Display:  
Description:  
24.00  
6HWVꢀQXPEHUꢀRIꢀSHULRGVꢀ  
SHUꢀ\HDUꢄ  
–2,000.00  
–80.00  
6WRUHVꢀLQLWLDOꢀGHSRVLWꢄ  
6WRUHVꢀUHJXODUꢀ  
VHPLPRQWKO\ꢀGHSRVLWVꢄ  
6.30  
6WRUHVꢀLQWHUHVWꢀUDWHꢄ  
360.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
GHSRVLWVꢄ  
52,975.60  
&DOFXODWHVꢀEDODQFHꢄ  
Example: An Annuity Account. <RXꢀRSWꢀIRUꢀDQꢀHDUO\ꢀUHWLUHPHQWꢀDIWHUꢀDꢀ  
VXFFHVVIXOꢀEXVLQHVVꢀFDUHHUꢄꢀ<RXꢀKDYHꢀDFFXPXODWHGꢀDꢀVDYLQJVꢀRIꢀꢏꢐꢌꢌꢃꢌꢌꢌꢀ  
WKDWꢀHDUQVꢀDQꢀDYHUDJHꢀRIꢀꢇꢎꢀDQQXDOꢀLQWHUHVWꢃꢀFRPSRXQGHGꢀPRQWKO\ꢄꢀ:KDWꢀ  
DQQXLW\ꢀꢁUHSHWLWLYHꢃꢀXQLIRUPꢃꢀZLWKGUDZDOꢀRIꢀIXQGVꢂꢀZLOOꢀ\RXꢀUHFHLYHꢀDWꢀWKHꢀ  
EHJLQQLQJꢀRIꢀHDFKꢀPRQWKꢀLIꢀ\RXꢀZLVKꢀWKDWꢀVDYLQJVꢀDFFRXQWꢀWRꢀVXSSRUWꢀ\RXꢀ  
IRUꢀWKHꢀQH[Wꢀꢍꢌꢀ\HDUV"  
6HWꢀWRꢀ%HJLQꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢄ  
62 5: Time Value of Money Calculations  
Keys:  
Display:  
12.00  
Description:  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
–400,000.00  
6WRUHVꢀ\RXUꢀQHVWꢀHJJꢀDVꢀ  
DQꢀRXWJRLQJꢀGHSRVLWꢄ  
7.00  
6WRUHVꢀDQQXDOꢀLQWHUHVWꢀ  
UDWHꢀ\RXꢀH[SHFWꢀWRꢀHDUQꢄ  
600.00  
0.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
ZLWKGUDZDOVꢄ  
6WRUHVꢀEDODQFHꢀRIꢀ  
DFFRXQWꢀDIWHUꢀꢍꢌꢀ\HDUVꢄ  
2,392.80  
&DOFXODWHVꢀDPRXQWꢀWKDWꢀ  
\RXꢀFDQꢀZLWKGUDZꢀDWꢀ  
WKHꢀEHJLQQLQJꢀRIꢀHDFKꢀ  
PRQWKꢄ  
Lease Calculations  
$ꢀOHDVHꢀLVꢀDꢀORDQꢀRIꢀYDOXDEOHꢀSURSHUW\ꢀꢁOLNHꢀUHDOꢀHVWDWHꢃꢀDXWRPRELOHVꢃꢀRUꢀ  
HTXLSPHQWꢂꢀIRUꢀDꢀVSHFLILFꢀDPRXQWꢀRIꢀWLPHꢃꢀLQꢀH[FKDQJHꢀIRUꢀUHJXODUꢀ  
SD\PHQWVꢄꢀ6RPHꢀOHDVHVꢀDUHꢀZULWWHQꢀDVꢀSXUFKDVHꢀDJUHHPHQWVꢃꢀZLWKꢀDQꢀ  
RSWLRQꢀWRꢀEX\ꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀOHDVHꢀꢁVRPHWLPHVꢀIRUꢀDVꢀOLWWOHꢀDVꢀꢏꢋꢄꢌꢌꢂꢄꢀ  
7KHꢀGHILQHGꢀIXWXUHꢀYDOXHꢀꢁ)9ꢂꢀRIꢀWKHꢀSURSHUW\ꢀDWꢀWKHꢀHQGꢀRIꢀDꢀOHDVHꢀLVꢀ  
VRPHWLPHVꢀFDOOHGꢀWKHꢀ´UHVLGXDOꢀYDOXHµꢀRUꢀ´EX\ꢀRXWꢀYDOXHꢄµ  
$OOꢀILYHꢀ790ꢀDSSOLFDWLRQꢀNH\VꢀFDQꢀEHꢀXVHGꢀLQꢀOHDVHꢀFDOFXODWLRQVꢄꢀ7KHUHꢀDUHꢀ  
WZRꢀFRPPRQꢀOHDVHꢀFDOFXODWLRQVꢄ  
)LQGLQJꢀWKHꢀOHDVHꢀSD\PHQWꢀQHFHVVDU\ꢀWRꢀDFKLHYHꢀDꢀVSHFLILHGꢀ\LHOGꢄ  
)LQGLQJꢀWKHꢀSUHVHQWꢀYDOXHꢀꢁFDSLWDOL]HGꢀYDOXHꢂꢀRIꢀDꢀOHDVHꢄ  
7KHꢀILUVWꢀSD\PHQWꢀRQꢀDꢀOHDVHꢀXVXDOO\ꢀRFFXUVꢀDWꢀWKHꢀEHJLQQLQJꢀRIꢀWKHꢀILUVWꢀ  
SHULRGꢄꢀ7KXVꢃꢀPRVWꢀOHDVHꢀFDOFXODWLRQVꢀXVHꢀ%HJLQꢀPRGHꢄ  
Example: Calculating a Lease Payment. $ꢀFXVWRPHUꢀZLVKHVꢀWRꢀOHDVHꢀ  
DꢀꢏꢋꢑꢃꢍꢌꢌꢀFDUꢀIRUꢀWKUHHꢀ\HDUVꢄꢀ7KHꢀOHDVHꢀLQFOXGHVꢀDQꢀRSWLRQꢀWRꢀEX\ꢀWKHꢀFDUꢀ  
IRUꢀꢏꢇꢃꢍꢌꢌꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀOHDVHꢄꢀ7KHꢀILUVWꢀPRQWKO\ꢀSD\PHQWꢀLVꢀGXHꢀWKHꢀ  
GD\ꢀWKHꢀFXVWRPHUꢀGULYHVꢀWKHꢀFDUꢀRIIꢀWKHꢀORWꢄꢀ,Iꢀ\RXꢀZDQWꢀWRꢀ\LHOGꢀꢋꢌꢎꢀ  
DQQXDOO\ꢃꢀFRPSRXQGHGꢀPRQWKO\ꢃꢀZKDWꢀZLOOꢀWKHꢀSD\PHQWVꢀEH"ꢀ&DOFXODWHꢀWKHꢀ  
SD\PHQWVꢀIURPꢀ\RXUꢀꢁWKHꢀGHDOHU·VꢂꢀSRLQWꢀRIꢀYLHZꢄ  
5: Time Value of Money Calculations 63  
6HWꢀWRꢀ%HJLQꢀPRGHꢄꢀ3UHVVꢀ  
Keys:  
ꢀLIꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢄ  
Display:  
Description:  
12.00  
10.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
6WRUHVꢀGHVLUHGꢀDQQXDOꢀ  
\LHOGꢄ  
–13,500.00  
7,500.00  
6WRUHVꢀOHDVHꢀSULFHꢄ  
6WRUHVꢀUHVLGXDOꢀꢁEX\ꢀRXWꢀ  
YDOXHꢂꢄ  
36.00  
6WRUHVꢀOHQJWKꢀRIꢀOHDVHꢃꢀ  
LQꢀPRQWKVꢄ  
253.99  
&DOFXODWHVꢀPRQWKO\ꢀ  
OHDVHꢀSD\PHQWꢄ  
1RWLFHꢀWKDWꢀHYHQꢀLIꢀWKHꢀFXVWRPHUꢀFKRRVHVꢀQRWꢀWRꢀEX\ꢀWKHꢀFDUꢃꢀWKHꢀOHVVRUꢀ  
VWLOOꢀLQFOXGHVꢀDꢀFDVKꢀIORZꢀFRPLQJꢀLQꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀOHDVHꢀHTXDOꢀWRꢀWKHꢀ  
UHVLGXDOꢀYDOXHꢀRIꢀWKHꢀFDUꢄꢀ:KHWKHUꢀWKHꢀFXVWRPHUꢀEX\VꢀWKHꢀFDUꢀRUꢀLWꢀLVꢀVROGꢀ  
RQꢀWKHꢀRSHQꢀPDUNHWꢃꢀWKHꢀOHVVRUꢀH[SHFWVꢀWRꢀUHFRYHUꢀꢏꢇꢃꢍꢌꢌꢄ  
64 5: Time Value of Money Calculations  
Example: Lease With Advance Payments. <RXUꢀFRPSDQ\ꢃꢀ4XLFNꢉ.LWꢀ  
3ROHꢀ%DUQVꢃꢀSODQVꢀWRꢀOHDVHꢀDꢀIRUNOLIWꢀIRUꢀWKHꢀZDUHKRXVHꢄꢀ7KHꢀOHDVHꢀLVꢀZULWWHQꢀ  
IRUꢀDꢀWHUPꢀRIꢀꢐꢀ\HDUVꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢀRIꢀꢏꢈꢃꢐꢌꢌꢄꢀ3D\PHQWVꢀDUHꢀGXHꢀ  
DWꢀWKHꢀEHJLQQLQJꢀRIꢀWKHꢀPRQWKꢀZLWKꢀWKHꢀILUVWꢀDQGꢀODVWꢀSD\PHQWVꢀGXHꢀDWꢀWKHꢀ  
RQVHWꢀRIꢀWKHꢀOHDVHꢄꢀ<RXꢀKDYHꢀDQꢀRSWLRQꢀWRꢀEX\ꢀWKHꢀIRUNOLIWꢀIRUꢀꢏꢋꢍꢃꢌꢌꢌꢀDWꢀ  
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6HWꢀWRꢀ%HJLQꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢄ  
5: Time Value of Money Calculations 65  
Keys:  
Display:  
12.00  
Description:  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
47.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
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–2,400.00  
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SD\PHQWꢄ  
0.00  
6WRUHVꢀ)9ꢀIRUꢀVWHSꢀꢋꢄ  
9.00  
6WRUHVꢀLQWHUHVWꢀUDWHꢄ  
95,477.55  
&DOFXODWHVꢀSUHVHQWꢀ  
YDOXHꢀRIꢀꢐꢇꢀPRQWKO\ꢀ  
SD\PHQWVꢄ  
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97,877.55  
$GGVꢀDGGLWLRQDOꢀ  
DGYDQFHꢀSD\PHQWꢄ  
97,877.55  
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48.00  
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–15,000.00  
6WRUHVꢀYDOXHꢀWRꢀ  
GLVFRXQWꢄ  
10,479.21  
&DOFXODWHVꢀSUHVHQWꢀ  
YDOXHꢀRIꢀODVWꢀFDVKꢀIORZꢄ  
Step 4. $GGꢀWKHꢀUHVXOWVꢀRIꢀVWHSVꢀꢈꢀDQGꢀꢑꢄ  
Keys:  
Display:  
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108,356.77  
&DOFXODWHVꢀSUHVHQWꢀ  
ꢁFDSLWDOL]HGꢂꢀYDOXHꢀRIꢀ  
OHDVHꢄꢀꢁ5RXQGLQJꢀ  
GLVFUHSDQFLHVꢀDUHꢀ  
H[SODLQHGꢀRQꢀSDJH ꢍꢒꢄꢂ  
66 5: Time Value of Money Calculations  
Amortization  
$PRUWL]DWLRQꢀLVꢀWKHꢀSURFHVVꢀRIꢀGLYLGLQJꢀDꢀSD\PHQWꢀLQWRꢀWKHꢀ  
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DSSOLHVꢀWRꢀSULQFLSDOꢄꢀ3D\PHQWVꢀQHDUꢀWKHꢀEHJLQQLQJꢀRIꢀDꢀORDQꢀ  
FRQWULEXWHꢀPRUHꢀLQWHUHVWꢃꢀDQGꢀOHVVꢀSULQFLSDOꢃꢀWKDQꢀSD\PHQWVꢀ  
QHDUꢀWKHꢀHQGꢀRIꢀDꢀORDQꢄ  
7KHꢀ  
7KHꢀ  
ꢀNH\ꢀRQꢀWKHꢀ+3ꢀꢋꢌ%,,ꢀDOORZVꢀ\RXꢀWRꢀFDOFXODWHꢄ  
7KHꢀDPRXQWꢀDSSOLHGꢀWRꢀLQWHUHVWꢀLQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢄ  
7KHꢀDPRXQWꢀDSSOLHGꢀWRꢀSULQFLSDOꢀLQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢄ  
7KHꢀORDQꢁEDODQFHꢀDIWHUꢀDꢀVSHFLILHGꢀQXPEHUꢀRIꢀSD\PHQWVꢀDUHꢀPDGHꢄ  
ꢀIXQFWLRQꢀDVVXPHVꢀ\RXꢀKDYHꢀMXVWꢀFDOFXODWHGꢀDꢀSD\PHQWꢀRUꢀ\RXꢀ  
KDYHꢀVWRUHGꢀWKHꢀDSSURSULDWHꢀDPRUWL]DWLRQꢀYDOXHVꢀLQꢀ,ꢀ<5ꢃꢀ39ꢃꢀ)9ꢃꢀ307ꢃꢀ  
DQGꢀ3ꢀ<5ꢄ  
5: Time Value of Money Calculations 67  
$QQXDOꢀQRPLQDOꢀLQWHUHVWꢀUDWHꢄ  
6WDUWLQJꢀEDODQFHꢄ  
(QGLQJꢀEDODQFHꢄ  
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1XPEHUꢀRIꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
7KHꢀQXPEHUVꢀGLVSOD\HGꢀIRUꢀLQWHUHVWꢃꢀSULQFLSDOꢃꢀDQGꢀEDODQFHꢀDUHꢀURXQGHGꢀWRꢀ  
WKHꢀFXUUHQWꢀGLVSOD\ꢀVHWWLQJꢄꢀ  
To Amortize. 7RꢀDPRUWL]HꢀDꢀVLQJOHꢀSD\PHQWꢃꢀHQWHUꢀWKHꢀSHULRGꢀQXPEHUꢀ  
DQGꢀSUHVVꢀ  
ꢄꢀ7KHꢀ+3ꢀꢋꢌ%,,ꢀGLVSOD\VꢀWKHꢀDQQXQFLDWRUꢀPERꢀIROORZHGꢀ  
E\ꢀWKHꢀVWDUWLQJꢀDQGꢀHQGLQJꢀSD\PHQWVꢀWKDWꢀZLOOꢀEHꢀDPRUWL]HGꢄ  
3UHVVꢀ ꢀWRꢀVHHꢀLQWHUHVWꢀꢁINTꢂꢄꢀ3UHVVꢀ ꢀDJDLQꢀWRꢀVHHꢀWKHꢀSULQFLSDOꢀꢁPRINꢂꢀ  
DQGꢀDJDLQꢀWRꢀVHHꢀWKHꢀEDODQFHꢀꢁBALꢂꢄꢀ&RQWLQXHꢀSUHVVLQJꢀ ꢀWRꢀF\FOHꢀWKURXJKꢀ  
WKHꢀVDPHꢀYDOXHVꢀDJDLQꢄ  
7RꢀDPRUWL]HꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢃꢀHQWHUꢀVWDUWLQJꢁSHULRGꢁQXPEHUꢀ ꢀHQGLQJꢁ  
SHULRGꢁQXPEHUꢃꢀWKHQꢀSUHVVꢀ  
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DQGꢀEDODQFHꢄ  
3UHVVꢀ  
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LQFUHPHQWꢀIHDWXUHꢀVDYHVꢀ\RXꢀWKHꢀNH\VWURNHVꢀRIꢀHQWHULQJꢀWKHꢀQHZꢀVWDUWLQJꢀ  
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PRUWJDJHꢃꢀDWꢀꢇꢄꢇꢍꢎꢀDQQXDOꢀLQWHUHVWꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢄ  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄꢀ  
68 5: Time Value of Money Calculations  
Keys:  
Display:  
12.00  
Description:  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
360.00  
6WRUHVꢀWRWDOꢀQXPEHUꢀRIꢀ  
SD\PHQWVꢄ  
7.75  
6WRUHVꢀLQWHUHVWꢀSHUꢀ\HDUꢄ  
6WRUHVꢀSUHVHQWꢀYDOXHꢄ  
6WRUHVꢀIXWXUHꢀYDOXHꢄ  
180,000.00  
0.00  
–1,289.54  
&DOFXODWHVꢀPRQWKO\ꢀ  
SD\PHQWꢄ  
,Iꢀ\RXꢀDOUHDG\ꢀNQRZꢀWKHꢀPRUWJDJHꢀSD\PHQWꢃꢀ\RXꢀFDQꢀHQWHUꢀDQGꢀVWRUHꢀLWꢀMXVWꢀ  
OLNHꢀ\RXꢀVWRUHꢀWKHꢀRWKHUꢀIRXUꢀYDOXHVꢄꢀ1H[WꢃꢀDPRUWL]HꢀWKHꢀILUVWꢀ\HDUꢄꢀ  
12_  
(QWHUVꢀVWDUWLQJꢀDQGꢀ  
HQGLQJꢀSHULRGVꢄ  
1– 12  
'LVSOD\VꢀWKHꢀ3(5ꢀ  
DQQXQFLDWRUꢀDQGꢀUDQJHꢄ  
–1,579.82  
'LVSOD\VꢀWKHꢀ35,1ꢀ  
DQQXQFLDWRUꢀDQGꢀWKHꢀ  
SULQFLSDOꢀSDLGꢀLQꢀWKHꢀ  
ILUVWꢀ\HDUꢄ  
–13,894.66  
'LVSOD\VꢀWKHꢀ,17ꢀ  
DQQXQFLDWRUꢀDQGꢀWKHꢀ  
LQWHUHVWꢀSDLGꢀLQꢀWKHꢀILUVWꢀ  
\HDUꢄ  
178,420.18  
'LVSOD\VꢀWKHꢀ%$/ꢀ  
DQQXQFLDWRUꢀDQGꢀWKHꢀ  
ORDQꢀEDODQFHꢀDIWHUꢀRQHꢀ  
\HDUꢄ  
7KHꢀDPRXQWꢀSDLGꢀWRZDUGꢀLQWHUHVWꢀDQGꢀSULQFLSDOꢀꢁꢋꢑꢃꢓꢒꢐꢄꢆꢇꢀꢔꢀꢋꢃꢍꢇꢒꢄꢓꢐꢀ ꢀ  
ꢋꢍꢃꢐꢇꢐꢄꢍꢋꢂꢀHTXDOVꢀWKHꢀWRWDOꢀRIꢀꢋꢈꢀPRQWKO\ꢀSD\PHQWVꢀꢁꢋꢈꢀïꢀꢋꢃꢈꢓꢒꢄꢍꢐꢀ ꢀ  
ꢋꢍꢃꢐꢇꢐꢄꢍꢋꢂꢄꢀ7KHꢀUHPDLQLQJꢀEDODQFHꢀHTXDOVꢀWKHꢀLQLWLDOꢀPRUWJDJHꢃꢀOHVVꢀWKHꢀ  
DPRXQWꢀDSSOLHGꢀWRZDUGꢀSULQFLSDOꢀꢁꢋꢓꢌꢃꢌꢌꢌꢀ²ꢀꢋꢃꢍꢇꢒꢄꢓꢐꢀ ꢀꢋꢇꢓꢃꢐꢈꢌꢄꢋꢆꢂꢄ  
5: Time Value of Money Calculations 69  
$PRUWL]HꢀWKHꢀVHFRQGꢀ\HDUꢅ  
13– 24  
'LVSOD\Vꢀ3(5ꢀDQGꢀWKHꢀ  
QH[WꢀUDQJHꢀRIꢀSHULRGVꢄ  
–1,706.69  
–13,767.79  
176,713.49  
'LVSOD\Vꢀ35,1ꢀDQGꢀWKHꢀ  
SULQFLSDOꢀSDLGꢀLQꢀWKHꢀ  
VHFRQGꢀ\HDUꢄ  
'LVSOD\Vꢀ,17ꢀDQGꢀWKHꢀ  
LQWHUHVWꢀSDLGꢀLQꢀWKHꢀVHFꢉ  
RQGꢀ\HDUꢄ  
'LVSOD\Vꢀ%$/ꢀDQGꢀWKHꢀ  
ORDQꢀEDODQFHꢀDIWHUꢀꢈꢐꢀ  
SD\PHQWVꢄ  
7KHꢀDPRXQWꢀSDLGꢀWRZDUGꢀLQWHUHVWꢀDQGꢀSULQFLSDOꢀꢁꢋꢑꢃꢇꢆꢇꢄꢇꢒꢀꢔꢀꢋꢃꢇꢌꢆꢄꢆꢒꢀ ꢀ  
ꢋꢍꢃꢐꢇꢐꢄꢍꢋꢂꢀHTXDOVꢀWKHꢀWRWDOꢀRIꢀꢋꢈꢀPRQWKO\ꢀSD\PHQWVꢀꢁꢋꢈꢀïꢀꢋꢃꢈꢓꢒꢄꢍꢐꢀ ꢀ  
ꢋꢍꢃꢐꢇꢐꢄꢍꢋꢂꢄꢀ7KHꢀUHPDLQLQJꢀEDODQFHꢀHTXDOVꢀWKHꢀLQLWLDOꢀPRUWJDJHꢀOHVVꢀWKHꢀ  
DPRXQWꢀDSSOLHGꢀWRZDUGꢀSULQFLSDOꢀꢁꢋꢓꢌꢃꢌꢌꢌꢀ²ꢀꢋꢃꢍꢇꢒꢄꢓꢐꢀ²ꢀꢋꢃꢇꢌꢆꢄꢆꢒꢀ ꢀ  
ꢋꢇꢆꢃꢇꢋꢑꢄꢐꢒꢂꢄꢀ0RUHꢀPRQH\ꢀLVꢀDSSOLHGꢀWRꢀSULQFLSDOꢀGXULQJꢀWKHꢀVHFRQGꢀUDWKHUꢀ  
WKDQꢀWKHꢀILUVWꢀ\HDUꢄꢀ7KHꢀVXFFHHGLQJꢀ\HDUVꢀFRQWLQXHꢀLQꢀWKHꢀVDPHꢀIDVKLRQꢄ  
Example: Amortizing a Single Payment. $PRUWL]HꢀWKHꢀꢋ ꢃꢀꢈꢍ ꢃꢀDQGꢀ  
ꢍꢐ ꢀSD\PHQWVꢀRIꢀDꢀILYHꢀ\HDUꢀFDUꢀOHDVHꢄꢀ7KHꢀOHDVHꢀDPRXQWꢀLVꢀꢏꢋꢐꢃꢈꢍꢌꢀDQGꢀ  
WKHꢀLQWHUHVWꢀUDWHꢀLVꢀꢋꢋꢄꢍꢎꢄꢀ3D\PHQWVꢀDUHꢀPRQWKO\ꢀDQGꢀEHJLQꢀLPPHGLDWHO\ꢄ  
6HWꢀWRꢀ%HJLQꢀPRGHꢄꢀ3UHVVꢀ  
Keys:  
ꢀLIꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢄ  
Display:  
Description:  
12.00  
60.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
6WRUHVꢀQXPEHUꢀRIꢀ  
SD\PHQWVꢄ  
11.50  
6WRUHVꢀLQWHUHVWꢀSHUꢀ\HDUꢄ  
6WRUHVꢀSUHVHQWꢀYDOXHꢄ  
6WRUHVꢀWKHꢀIXWXUHꢀYDOXHꢄ  
14,250.00  
0.00  
–310.42  
&DOFXODWHVꢀPRQWKO\ꢀ  
SD\PHQWꢄ  
70 5: Time Value of Money Calculations  
$PRUWL]HꢀWKHꢀꢋ ꢃꢀꢈꢍ ꢃꢀDQGꢀꢍꢐ ꢀSD\PHQWVꢄ  
1.00  
(QWHUVꢀILUVWꢀSD\PHQWꢄ  
1– 1  
'LVSOD\Vꢀ3(5ꢀDQGꢀWKHꢀ  
DPRUWL]HGꢀSD\PHQWꢀSHULRGꢄ  
–310.42  
0.00  
'LVSOD\Vꢀ35,1ꢀDQGꢀWKHꢀILUVWꢀ  
SULQFLSDOꢀSD\PHQWꢄ  
'LVSOD\Vꢀ,17ꢀDQGꢀWKHꢀLQWHUꢉ  
HVWꢄ  
13,939.58  
25.00  
'LVSOD\Vꢀ%$/ꢀDQGꢀWKHꢀORDQꢀ  
EDODQFHꢀDIWHUꢀRQHꢀSD\PHQWꢄ  
(QWHUVꢀSD\PHQWꢀWRꢀDPRUꢉ  
WL]Hꢄ  
25– 25  
–220.21  
'LVSOD\Vꢀ3(5ꢀDQGꢀWKHꢀ  
DPRUWL]HGꢀSD\PHQWꢀSHULRGꢄ  
'LVSOD\Vꢀ35,1ꢀDQGꢀWKHꢀ  
SULQFLSDOꢀSDLGꢀRQꢀWKHꢀꢈꢍ ꢀ  
SD\PHQWꢄ  
–90.21  
'LVSOD\Vꢀ,17ꢀDQGꢀWKHꢀLQWHUꢉ  
HVWꢀSDLGꢀRQꢀWKHꢀꢈꢍ ꢀSD\ꢉ  
PHQWꢄ  
9,193.28  
'LVSOD\Vꢀ%$/ꢀDQGꢀWKHꢀEDOꢉ  
DQFHꢀDIWHUꢀWKHꢀꢈꢍ ꢀSD\ꢉ  
PHQWꢄ  
54.00  
(QWHUVꢀSD\PHQWꢀWRꢀDPRUꢉ  
WL]Hꢄ  
54– 54  
–290.37  
'LVSOD\Vꢀ3(5ꢀDQGꢀWKHꢀ  
DPRUWL]HGꢀSD\PHQWꢀSHULRGꢄ  
'LVSOD\Vꢀ35,1ꢀDQGꢀWKHꢀ  
SULQFLSDOꢀSDLGꢀRQꢀWKHꢀꢍꢐ ꢀ  
SD\PHQWꢄ  
–20.05  
'LVSOD\Vꢀ,17ꢀDQGꢀWKHꢀLQWHUꢉ  
HVWꢀSDLGꢀRQꢀWKHꢀꢍꢐ ꢀSD\ꢉ  
PHQWꢄ  
1,801.57  
'LVSOD\Vꢀ%$/ꢀDQGꢀWKHꢀEDOꢉ  
DQFHꢀDIWHUꢀWKHꢀꢍꢐ ꢀSD\ꢉ  
PHQWꢄ  
5: Time Value of Money Calculations 71  
Interest Rate Conversions  
7KHꢀ,QWHUHVWꢀ&RQYHUVLRQꢀDSSOLFDWLRQꢀXVHVꢀWKUHHꢀNH\Vꢅꢀ  
ꢃꢀ ꢃꢀDQGꢀ ꢄꢀ7KH\ꢀFRQYHUWꢀEHWZHHQꢀQRPLQDOꢀ  
DQGꢀDQQXDOꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHVꢄꢀ1RPLQDOꢀDQGꢀHIIHFWLYHꢀ  
LQWHUHVWꢀUDWHVꢀDUHꢀGHVFULEHGꢀRQꢀSDJH ꢐꢒꢄ  
,Iꢀ\RXꢀNQRZꢀDQꢀDQQXDOꢀQRPLQDOꢀLQWHUHVWꢀUDWHꢀDQGꢀ\RXꢀZLVKꢀ  
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ꢂꢁ (QWHUꢀWKHꢀQXPEHUꢀRIꢀFRPSRXQGLQJꢀSHULRGVꢀDQGꢀSUHVVꢀ  
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6ROYLQJꢀ790ꢀSUREOHPVꢀZKHUHꢀWKHꢀSD\PHQWꢀSHULRGꢀDQGꢀWKHꢀLQWHUHVWꢀ  
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Investments With Different Compounding Periods  
Example: Comparing Investments. <RXꢀDUHꢀFRQVLGHULQJꢀRSHQLQJꢀDꢀ  
VDYLQJVꢀDFFRXQWꢀLQꢀRQHꢀRIꢀWKUHHꢀEDQNVꢄꢀ:KLFKꢀEDQNꢀKDVꢀWKHꢀPRVWꢀ  
IDYRUDEOHꢀLQWHUHVWꢀUDWH"  
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ꢆꢄꢇꢌꢎꢀDQQXDOꢀLQWHUHVWꢃꢀFRPSRXQGHGꢀTXDUWHUO\ꢄ  
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7KLUGꢀ%DQN  
ꢆꢄꢆꢑꢎꢀDQQXDOꢀLQWHUHVWꢃꢀFRPSRXQGHGꢀꢑꢆꢌꢀWLPHVꢀSHUꢀ  
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72 5: Time Value of Money Calculations  
First Bank  
Keys:  
Display:  
6.70  
Description:  
6WRUHVꢀQRPLQDOꢀUDWHꢄ  
4.00  
6WRUHVꢀTXDUWHUO\ꢀ  
FRPSRXQGLQJꢀSHULRGVꢄ  
6.87  
&DOFXODWHVꢀDQQXDOꢀ  
HIIHFWLYHꢀUDWHꢄ  
Second Bank  
6.65  
6WRUHVꢀQRPLQDOꢀUDWHꢄ  
12.00  
6WRUHVꢀPRQWKO\ꢀFRPꢉ  
SRXQGLQJꢀSHULRGVꢄ  
6.86  
&DOFXODWHVꢀDQQXDOꢀ  
HIIHFWLYHꢀUDWHꢄ  
Third Bank  
6.63  
6WRUHVꢀQRPLQDOꢀUDWHꢄ  
360.00  
6WRUHVꢀFRPSRXQGLQJꢀ  
SHULRGVꢄ  
6.85  
&DOFXODWHVꢀDQQXDOꢀ  
HIIHFWLYHꢀUDWHꢄ  
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ꢆꢄꢓꢍꢄ  
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SD\PHQWꢀSHULRGꢀGLIIHUVꢀIURPꢀWKHꢀFRPSRXQGLQJꢀSHULRGꢃꢀ  
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5: Time Value of Money Calculations 73  
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SD\PHQWꢀSHULRGꢀFRPSOHWHꢀWKHꢀIROORZLQJꢀVWHSVꢅ  
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ꢄꢀ(QWHUꢀWKHꢀQXPEHUꢀRIꢀ  
ꢄꢀ6ROYHꢀIRUꢀWKHꢀHIIHFWLYHꢀ  
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UDWHꢀE\ꢀSUHVVLQJꢀ  
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FRPSRXQGHGꢀGDLO\ꢀꢁXVLQJꢀDꢀꢑꢆꢍꢀGD\ꢀ\HDUꢂꢄꢀ:KDWꢀZLOOꢀWKHꢀEDODQFHꢀEHꢀLQꢀ  
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Keys:  
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5.00  
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365.00  
5.13  
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SHULRGVꢀSHUꢀ\HDUꢄ  
&DOFXODWHVꢀDQQXDOꢀHIIHFWLYHꢀ  
UDWHꢄ  
12.00  
5.01  
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&DOFXODWHVꢀHTXLYDOHQWꢀ  
QRPLQDOꢀSHUFHQWDJHꢀUDWHꢀIRUꢀ  
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LQꢀWKHꢀUHVWꢀRIꢀWKHꢀSUREOHPꢄ  
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0.00  
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6WRUHVꢀWRWDOꢀQXPEHUꢀRIꢀ  
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–25.00  
84.00  
2,519.61  
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74 5: Time Value of Money Calculations  
6
Cash Flow Calculations  
How to Use the Cash Flow Application  
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ꢄꢁ (QWHUꢀWKHꢀDPRXQWꢀRIꢀWKHꢀLQLWLDOꢀLQYHVWPHQWꢁ  
ꢅꢁ (QWHUꢀWKHꢀDPRXQWꢀRIꢀWKHꢀQH[WꢀFDVKꢀIORZꢁ  
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HQWHUꢀWKHꢀQXPEHUꢀRIꢀWLPHVꢀLWꢀRFFXUVꢁ  
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Example: A Short Term Investment. 7KHꢀIROORZLQJꢀFDVKꢀIORZꢀGLDJUDPꢀ  
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PRQWKO\ꢀUDWHꢀRIꢀUHWXUQꢁ  
6: Cash Flow Calculations 75  
XXX  
Keys:  
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0.00  
Description:  
&OHDUVꢀDOOꢀUHJLVWHUVꢁ  
12.00  
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–5,000.00  
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–4,000.00  
11,765.29  
38.98  
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(QWHUVꢀILQDOꢀFDVKꢀIORZꢁ  
&DOFXODWHVꢀDQQXDOꢀ  
QRPLQDOꢀ\LHOGꢁ  
3.25  
0RQWKO\ꢀ\LHOGꢁ  
76 6: Cash Flow Calculations  
NPV and IRR/YR: Discontinuing Cash Flows  
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DGGꢀWKHPꢀWRJHWKHUꢁ  
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FDOFXODWHꢀ139ꢁ  
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6: Cash Flow Calculations 77  
:KHQHYHUꢀ\RXꢀHQWHUꢀDꢀVHULHVꢀRIꢀFDVKꢀIORZVꢂꢀLWꢀLVꢀLPSRUWDQWꢀWRꢀDFFRXQWꢀIRUꢀ  
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]HURꢁ  
Entering Cash Flows  
7KHꢀ+3ꢀꢃꢄ%,,ꢀFDQꢀVWRUHꢀDQꢀLQLWLDOꢀFDVKꢀIORZꢀSOXVꢀꢃꢈꢀDGGLWLRQDOꢀFDVKꢀIORZꢀ  
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IORZVꢀXVLQJꢀWKHꢀIROORZLQJꢀVWHSVꢍ  
ꢀꢁ 3UHVVꢀ  
ꢀWRꢀFOHDUꢀWKHꢀUHVLVWHUVꢁ  
ꢂꢁ (QWHUꢀWKHꢀQXPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢀDQGꢀSUHVVꢀ  
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ꢃꢁ (QWHUꢀWKHꢀDPRXQWꢀRIꢀWKHꢀLQLWLDOꢀLQYHVWPHQWꢂꢀWKHQꢀSUHVVꢀ ꢁꢀꢉ7KHꢀ´Mµꢀ  
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ꢄꢁ (QWHUꢀWKHꢀDPRXQWꢀRIꢀWKHꢀQH[WꢀFDVKꢀIORZꢀDQGꢀSUHVVꢀ  
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EHHQꢀHQWHUHGꢁ  
78 6: Cash Flow Calculations  
Example. (QWHUꢀWKHꢀFDVKꢀIORZVꢀIURPꢀWKHꢀSUHFHGLQJꢀGLDJUDPꢀDQGꢀ  
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WKHUHꢀDUHꢀꢃꢎꢀSHULRGVꢀSHUꢀ\HDUꢁꢀ  
Keys:  
Display:  
0.00  
Description:  
&OHDUVꢀDOOꢀUHJLVWHUVꢁ  
6HWVꢀ ꢀWRꢀꢃꢎꢁ  
12.00  
–11,000.00  
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6: Cash Flow Calculations 79  
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84 6: Cash Flow Calculations  
7
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86 7: Statistical Calculations  
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Keys  
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Mean, Standard Deviations, and Summation  
Statistics  
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7: Statistical Calculations 89  
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90 7: Statistical Calculations  
Linear Estimation. 7KHꢀVWUDLJKWꢀOLQHꢀFDOFXODWHGꢀE\ꢀOLQHDUꢀUHJUHVVLRQꢀFDQꢀ  
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Minutes of Advertising  
(x-values)  
Sales  
(y-values)  
Week  
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7: Statistical Calculations 91  
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92 7: Statistical Calculations  
Weighted Mean  
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4.00  
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7: Statistical Calculations 93  
8
Additional Examples  
Business Applications  
Setting a Sales Price  
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8: Additional Examples 95  
Forecasting Based on History  
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1
2
3
4
5
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13,060  
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5.00  
22,000.50  
(VWLPDWHVꢀVDOHVꢀIRUꢀ\HDUꢀ  
VL[ꢂ  
24,605.00  
(VWLPDWHVꢀVDOHVꢀIRUꢀ\HDUꢀ  
VHYHQꢂ  
96 8: Additional Examples  
Cost of Not Taking a Cash Discount  
$ꢀFDVKꢀGLVFRXQWꢀJLYHVꢀDꢀEX\HUꢀDꢀUHGXFWLRQꢀLQꢀSULFHꢀLIꢀWKHꢀSD\PHQWꢀLVꢀPDGHꢀ  
ZLWKLQꢀDꢀVSHFLILHGꢀWLPHꢀSHULRGꢂꢀ)RUꢀH[DPSOHꢁꢀ´ꢉꢎꢅꢇꢁꢀ1(7ꢎꢏꢇµꢀPHDQVꢀWKDWꢀ  
WKHꢀEX\HUꢀFDQꢀGHGXFWꢀꢉꢀSHUFHQWꢀLIꢀSD\PHQWꢀLVꢀPDGHꢀZLWKLQꢀꢅꢇꢀGD\Vꢂꢀ,Iꢀ  
SD\PHQWꢀLVꢀQRWꢀPDGHꢀZLWKLQꢀꢅꢇꢀGD\VꢁꢀWKHꢀIXOOꢀDPRXQWꢀPXVWꢀEHꢀSDLGꢀE\ꢀWKHꢀ  
ꢏꢇ ꢀGD\ꢂ  
<RXꢀFDQꢀXVHꢀWKHꢀHTXDWLRQꢀVKRZQꢀEHORZꢀWRꢀFDOFXODWHꢀWKHꢀFRVWꢀRIꢀIDLOLQJꢀWRꢀ  
WDNHꢀWKHꢀFDVKꢀGLVFRXQWꢂꢀ7KHꢀFRVWꢀLVꢀFDOFXODWHGꢀDVꢀDQꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀ  
FKDUJHGꢀIRUꢀGHOD\LQJꢀSD\PHQWꢂ  
',6&ꢌ × ꢏꢐꢇ × ꢅꢇꢇ  
&267ꢌ = -----------------------------------------------------------------------------------------------------------------------------  
((ꢅꢇꢇ – ',6&ꢌ) × (727$/ꢀ'$<6 – ',6&ꢀ'$<6))  
',6&ꢀꢀLVꢀWKHꢀGLVFRXQWꢀSHUFHQWꢀLIꢀWKHꢀSD\PHQWꢀLVꢀPDGHꢀHDUO\ꢂꢀ727$/ꢁ  
'$<6ꢀLVꢀWKHꢀWRWDOꢀQXPEHUꢀRIꢀGD\VꢀXQWLOꢀWKHꢀELOOꢀPXVWꢀEHꢀSDLGꢂꢀ',6&ꢁ'$<6ꢀ  
LVꢀWKHꢀQXPEHUꢀRIꢀGD\VꢀIRUꢀZKLFKꢀWKHꢀGLVFRXQWꢀLVꢀDYDLODEOHꢂ  
Example. <RXꢀUHFHLYHꢀDꢀELOOꢀZLWKꢀWKHꢀFUHGLWꢀWHUPVꢀꢉꢎꢅꢇꢁꢀ1(7ꢎꢏꢇꢂꢀ:KDWꢀ  
LVꢀWKHꢀFRVWꢀRIꢀQRWꢀWDNLQJꢀWKHꢀFDVKꢀGLVFRXQW"  
Keys:  
Display:  
Description:  
72,000.00  
&DOFXODWHVꢀQXPHUDWRUꢀ  
LQꢀHTXDWLRQꢂ  
98.00  
36.73  
3DUHQWKHVHVꢀIRUFHꢀ  
RUGHUꢀRIꢀFDOFXODWLRQꢂ  
&DOFXODWHVꢁꢀDVꢀDQꢀDQQXDOꢀ  
SHUFHQWDJHꢀUDWHꢁꢀFRVWꢀRIꢀ  
QRWꢀWDNLQJꢀGLVFRXQWꢂ  
8: Additional Examples 97  
Loans and Mortgages  
Simple Annual Interest  
Example. <RXUꢀJRRGꢀIULHQGꢀQHHGVꢀDꢀORDQꢀWRꢀVWDUWꢀKLVꢀODWHVWꢀHQWHUSULVHꢀDQGꢀ  
KDVꢀDVNHGꢀ\RXꢀWRꢀOHQGꢀKLPꢀꢊꢋꢑꢇꢀIRUꢀꢐꢇꢀGD\Vꢂꢀ<RXꢀOHQGꢀKLPꢀWKHꢀPRQH\ꢀDWꢀ  
ꢅꢇꢌꢀVLPSOHꢀDQQXDOꢀLQWHUHVWꢁꢀWRꢀEHꢀFDOFXODWHGꢀRQꢀDꢀꢏꢐꢑꢍGD\ꢀEDVLVꢂꢀ+RZꢀ  
PXFKꢀLQWHUHVWꢀZLOOꢀKHꢀRZHꢀ\RXꢀLQꢀꢐꢇꢀGD\VꢁꢀDQGꢀZKDWꢀLVꢀWKHꢀWRWDOꢀDPRXQWꢀ  
RZHG"  
7KLVꢀHTXDWLRQꢀLVꢀXVHGꢀIRUꢀFDOFXODWLQJꢀVLPSOHꢀDQQXDOꢀLQWHUHVWꢀXVLQJꢀDꢀꢏꢐꢑꢀ  
GD\ꢀ\HDUꢃ  
,17(5(67ꢀ  
/2$1ꢀ$02817 × ,17(5(67ꢌ × 7(50ꢀ2)ꢀ/2$1ꢀꢄ,1ꢀ'$<6ꢈ  
-------------------------------------------------------------------------------------------------------------------------------------------------------------------  
ꢏꢐꢑ  
Keys:  
Display:  
0.10  
Description:  
6WRUHVꢀLQWHUHVWꢂ  
7.40  
&DOFXODWHVꢀLQWHUHVWꢀRZHGꢂ  
&DOFXODWHVꢀWRWDOꢀRZHGꢂ  
457.40  
Continuous Compounding  
7KHꢀHTXDWLRQꢀIRUꢀFDOFXODWLQJꢀDQꢀHIIHFWLYHꢀUDWHꢀIRUꢀFRQWLQXRXVꢀ  
FRPSRXQGLQJꢀLVꢃ  
÷
())ꢌ = (H(  
) – ꢅ) × ꢅꢇꢇ  
7RꢀVROYHꢀDꢀFRQWLQXRXVꢀFRPSRXQGLQJꢀSUREOHPꢀFRPSOHWHꢀWKHVHꢀVWHSVꢃ  
ꢀꢁ &RPSXWHꢀWKHꢀDQQXDOꢀHIIHFWLYHꢀUDWHꢀXVLQJꢀWKHꢀDERYHꢀHTXDWLRQꢂ  
ꢂꢁ (LWKHUꢀXVHꢀWKLVꢀHIIHFWLYHꢀUDWHꢀLQꢀ\RXUꢀFDOFXODWLRQVꢀZLWKꢀDQꢀDQQXDOꢀ  
SHULRGꢀꢄ3ꢂ<5ꢀ ꢀꢅꢈꢀRUꢀFRQYHUWꢀWKLVꢀUDWHꢀVRꢀWKDWꢀLWꢀDSSOLHVꢀWRꢀ\RXUꢀ  
SD\PHQWꢀSHULRGꢂꢀ,QꢀWKHꢀIROORZLQJꢀH[DPSOHꢁꢀ3ꢂ<5ꢀ ꢀꢅꢉꢀVRꢀ\RXꢀKDYHꢀ  
WRꢀFDOFXODWHꢀDꢀQHZꢀ120ꢀꢀXVLQJꢀWKHꢀLQWHUHVWꢀUDWHꢀFRQYHUVLRQꢀ  
DSSOLFDWLRQꢀZLWKꢀ3ꢂ<5ꢀHTXDOꢀWRꢀꢅꢉꢂ  
98 8: Additional Examples  
Example. <RXꢀFXUUHQWO\ꢀKDYHꢀꢊꢋꢁꢑꢒꢉꢂꢓꢇꢀLQꢀDQꢀDFFRXQWꢀDWꢀ'UHDPꢀ:RUOGꢀ  
,QYHVWPHQWVꢀWKDWꢀHDUQVꢀꢅꢓꢌꢀDQQXDOꢀLQWHUHVWꢀFRPSRXQGHGꢀFRQWLQXRXVO\ꢂꢀ  
$WꢀWKHꢀHQGꢀRIꢀHDFKꢀPRQWKꢁꢀ\RXꢀGHSRVLWꢀꢊꢉꢑꢇꢂꢇꢇꢀLQꢀWKHꢀDFFRXQWꢂꢀ:KDWꢀZLOOꢀ  
WKHꢀEDODQFHꢀEHꢀDIWHUꢀꢅꢑꢀ\HDUV"  
Keys:  
Display:  
Description:  
0.18  
'LYLGHVꢀQRPLQDOꢀUDWHꢀ  
E\ꢀꢅꢇꢇꢂ  
1.20  
5DLVHVꢀHꢀWRꢀꢇꢂꢅꢓꢀSRZHUꢂ  
19.72  
&DOFXODWHVꢀDQQXDOꢀ  
HIIHFWLYHꢀUDWHꢂ  
19.72  
12.00  
18.14  
6WRUHVꢀHIIHFWLYHꢀUDWHꢂ  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
&DOFXODWHVꢀDQQXDOꢀ  
QRPLQDOꢀUDWHꢀIRUꢀDꢀ  
PRQWKO\ꢀSD\PHQWꢀ  
SHULRGꢂ  
6HWꢀWRꢀ(QGꢀ0RGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
180.00  
6WRUHVꢀQXPEHUꢀRIꢀPRQWKVꢂ  
6WRUHVꢀUHJXODUꢀSD\PHQWꢂ  
6WRUHVꢀFXUUHQWꢀEDODQFHꢀDVꢀDꢀ  
QHJDWLYHꢀYDOXHꢀꢄOLNHꢀDQꢀ  
LQLWLDOꢀLQYHVWPHQWꢈꢂ  
–250.00  
–4,572.80  
297,640.27  
&DOFXODWHVꢀDFFRXQWꢀ  
EDODQFHꢀDIWHUꢀꢅꢑꢀ\HDUVꢀRIꢀ  
SD\PHQWVꢀZLWKꢀꢅꢓꢌꢀ  
LQWHUHVWꢀFRPSRXQGHGꢀ  
FRQWLQXRXVO\ꢂ  
Yield of a Discounted (or Premium) Mortgage  
7KHꢀDQQXDOꢀ\LHOGꢀRIꢀDꢀPRUWJDJHꢀERXJKWꢀDWꢀDꢀGLVFRXQWꢀRUꢀSUHPLXPꢀFDQꢀEHꢀ  
FDOFXODWHGꢀJLYHQꢀWKHꢀRULJLQDOꢀPRUWJDJHꢀDPRXQWꢀꢄ39ꢈꢁꢀLQWHUHVWꢀUDWHꢀꢄ,ꢂ<5ꢈꢁꢀ  
SHULRGLFꢀSD\PHQWꢀꢄ307ꢈꢁꢀEDOORRQꢀSD\PHQWꢀDPRXQWꢀꢄ)9ꢈꢁꢀDQGꢀWKHꢀSULFHꢀ  
SDLGꢀIRUꢀWKHꢀPRUWJDJHꢀꢄQHZꢀ39ꢈꢂ  
5HPHPEHUꢀWKHꢀFDVKꢀIORZꢀVLJQꢀFRQYHQWLRQꢃꢀPRQH\ꢀSDLGꢀRXWꢀLVꢀQHJDWLYHꢔꢀ  
PRQH\ꢀUHFHLYHGꢀLVꢀSRVLWLYHꢂ  
8: Additional Examples 99  
Example. $QꢀLQYHVWRUꢀZLVKHVꢀWRꢀSXUFKDVHꢀDꢀꢊꢅꢇꢇꢁꢇꢇꢇꢀPRUWJDJHꢀWDNHQꢀ  
RXWꢀDWꢀꢕꢌꢀIRUꢀꢉꢇꢀ\HDUVꢂꢀ6LQFHꢀWKHꢀPRUWJDJHꢀZDVꢀLVVXHGꢁꢀꢋꢉꢀPRQWKO\ꢀ  
SD\PHQWVꢀKDYHꢀEHHQꢀPDGHꢂꢀ7KHꢀORDQꢀLVꢀWRꢀEHꢀSDLGꢀLQꢀIXOOꢀꢄDꢀEDOORRQꢀ  
SD\PHQWꢈꢀDWꢀWKHꢀHQGꢀRIꢀLWVꢀILIWKꢀ\HDUꢂꢀ:KDWꢀLVꢀWKHꢀ\LHOGꢀWRꢀWKHꢀSXUFKDVHUꢀLIꢀ  
WKHꢀSULFHꢀRIꢀWKHꢀPRUWJDJHꢀLVꢀꢊꢒꢕꢁꢇꢇꢇ"  
Step 1. &DOFXODWHꢀ307ꢂꢀ0DNHꢀVXUHꢀ)9ꢀ ꢀꢇꢂ  
6HWꢀWRꢀ(QGꢀ0RGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
12.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀLQWHUHVWꢀUDWHꢂ  
9.00  
240.00  
–100,000.00  
6WRUHVꢀQXPEHUꢀRIꢀPRQWKVꢂ  
6WRUHVꢀRULJLQDOꢀDPRXQWꢀRIꢀ  
PRUWJDJHꢂ  
0.00  
(QWHUVꢀDPRXQWꢀOHIWꢀWRꢀSD\ꢀ  
DIWHUꢀꢉꢇꢀ\HDUVꢂ  
899.73  
&DOFXODWHVꢀUHJXODUꢀ  
SD\PHQWꢂ  
Step 2. (QWHUꢀWKHꢀQHZꢀYDOXHꢀIRUꢀ1ꢀLQGLFDWLQJꢀZKHQꢀWKHꢀEDOORRQꢀRFFXUVꢁꢀ  
WKHQꢀILQGꢀ)9ꢁꢀWKHꢀDPRXQWꢀRIꢀWKHꢀEDOORRQꢂ  
Keys:  
Display:  
Description:  
899.73  
5RXQGVꢀSD\PHQWꢀWRꢀ  
WZRꢀGHFLPDOꢀSODFHVꢀIRUꢀ  
DFFXUDF\ꢂ  
60.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
SD\PHQWVꢀXQWLOꢀEDOORRQꢂ  
88,706.74  
&DOFXODWHVꢀEDOORRQꢀ  
SD\PHQWꢀꢄDGGꢀWRꢀILQDOꢀ  
SD\PHQWꢈꢂ  
100 8: Additional Examples  
Step 3. (QWHUꢀDFWXDOꢁꢀFXUUHQWꢀYDOXHVꢀIRUꢀ1ꢀDQGꢀ39ꢔꢀWKHQꢀILQGꢀWKHꢀQHZꢀ  
,ꢂ<5ꢀIRUꢀWKHꢀGLVFRXQWHGꢀPRUWJDJHꢀZLWKꢀEDOORRQꢂ  
Keys:  
Display:  
Description:  
18.00  
6WRUHVꢀUHPDLQLQJꢀ  
QXPEHUꢀRIꢀSD\PHQWVꢂ  
–79,000.00  
20.72  
6WRUHVꢀSULFHꢀRIꢀ  
PRUWJDJHꢂ  
&DOFXODWHVꢀWKHꢀUHWXUQꢀ  
RQꢀWKLVꢀGLVFRXQWHGꢀ  
PRUWJDJHꢂ  
Annual Percentage Rate for a Loan With Fees  
7KHꢀDQQXDOꢀSHUFHQWDJHꢀUDWHꢁꢀ$35ꢁꢀLQFRUSRUDWHVꢀIHHVꢀXVXDOO\ꢀFKDUJHGꢀZKHQꢀ  
DꢀPRUWJDJHꢀLVꢀLVVXHGꢁꢀZKLFKꢀHIIHFWLYHO\ꢀUDLVHVꢀWKHꢀLQWHUHVWꢀUDWHꢂꢀ7KHꢀDFWXDOꢀ  
DPRXQWꢀUHFHLYHGꢀE\ꢀWKHꢀERUURZHUꢀꢄWKHꢀ39ꢈꢀLVꢀUHGXFHGꢁꢀZKLOHꢀWKHꢀSHULRGLFꢀ  
SD\PHQWVꢀUHPDLQꢀWKHꢀVDPHꢂꢀ7KHꢀ$35ꢀFDQꢀEHꢀFDOFXODWHGꢀJLYHQꢀWKHꢀWHUPꢀRIꢀ  
WKHꢀPRUWJDJHꢀꢄ1ꢀSHULRGVꢈꢁꢀWKHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀꢄ,ꢂ35ꢈꢁꢀWKHꢀPRUWJDJHꢀ  
DPRXQWꢀꢄQHZꢀ39ꢈꢁꢀDQGꢀWKHꢀDPRXQWꢀRIꢀWKHꢀIHHꢂ  
5HPHPEHUꢀWKHꢀFDVKꢀIORZꢀVLJQꢀFRQYHQWLRQꢃꢀPRQH\ꢀSDLGꢀRXWꢀLVꢀQHJDWLYHꢔꢀ  
PRQH\ꢀUHFHLYHGꢀLVꢀSRVLWLYHꢂ  
Example: APR for a Loan With Fees. $ꢀERUURZHUꢀLVꢀFKDUJHGꢀWZRꢀ  
SRLQWVꢀIRUꢀWKHꢀLVVXDQFHꢀRIꢀDꢀPRUWJDJHꢂꢀꢄ2QHꢀSRLQWꢀLVꢀHTXDOꢀWRꢀꢅꢌꢀRIꢀWKHꢀ  
PRUWJDJHꢀDPRXQWꢂꢈꢀ,IꢀWKHꢀPRUWJDJHꢀDPRXQWꢀLVꢀꢊꢅꢐꢇꢁꢇꢇꢇꢀIRUꢀꢏꢇꢀ\HDUVꢀDQGꢀ  
WKHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀLVꢀꢓꢂꢑꢌꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢁꢀZKDWꢀ$35ꢀLVꢀWKHꢀ  
ERUURZHUꢀSD\LQJ"  
6HWꢀWRꢀ(QGꢀ0RGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
12.00  
8.50  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀLQWHUHVWꢀUDWHꢂ  
360.00  
6WRUHVꢀOHQJWKꢀRIꢀ  
PRUWJDJHꢂ  
160,000.00  
6WRUHVꢀRULJLQDOꢀDPRXQWꢀ  
RIꢀPRUWJDJHꢂ  
8: Additional Examples 101  
0.00  
7KHꢀORDQꢀZLOOꢀEHꢀ  
FRPSOHWHO\ꢀSDLGꢀRIIꢀLQꢀ  
ꢏꢇꢀ\HDUVꢂ  
–1,230.26  
160,000.00  
156,800  
8.72  
&DOFXODWHVꢀSD\PHQWꢂ  
5HFDOOVꢀORDQꢀDPRXQWꢂ  
6XEWUDFWVꢀSRLQWVꢂ  
&DOFXODWHVꢀ$35ꢁꢀ  
FRQVLGHULQJꢀIHHVꢂ  
Example: Interest-Only Loan With Fee. $ꢀꢊꢅꢁꢇꢇꢇꢁꢇꢇꢇꢁꢀꢅꢇꢍ\HDUꢁꢀꢅꢉꢌꢀ  
ꢄDQQXDOꢀLQWHUHVWꢈꢀLQWHUHVWꢃRQO\ꢀORDQꢀKDVꢀDQꢀRULJLQDWLRQꢀIHHꢀRIꢀWKUHHꢀSRLQWVꢂꢀ  
:KDWꢀLVꢀWKHꢀ\LHOGꢀWRꢀWKHꢀOHQGHU"ꢀ$VVXPHꢀWKDWꢀPRQWKO\ꢀSD\PHQWVꢀRIꢀ  
LQWHUHVWꢀDUHꢀPDGHꢂ  
6HWꢀWRꢀ(QGꢀPRGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
12.00  
12.00  
120.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀLQWHUHVWꢀUDWHꢂ  
6WRUHVꢀOHQJWKꢀRIꢀ  
PRUWJDJHꢂ  
1,000,000.00  
–1,000,000.00  
6WRUHVꢀRULJLQDOꢀDPRXQWꢀ  
RIꢀPRUWJDJHꢂ  
(QWHUVꢀDPRXQWꢀGXHꢀDWꢀ  
HQGꢀRIꢀWHUPꢂꢀ3D\PHQWVꢀ  
DUHꢀLQWHUHVWꢀRQO\ꢀVRꢀ  
HQWLUHꢀORDQꢀDPRXQWꢀLVꢀ  
GXHꢂ  
–10,000.00  
&DOFXODWHVꢀLQWHUHVWꢍRQO\ꢀ  
SD\PHQWVꢂ  
1,000,000.00  
970,000.00  
12.53  
5HFDOOVꢀORDQꢀDPRXQWꢂ  
6XEWUDFWVꢀSRLQWVꢂ  
&DOFXODWHVꢀ$35ꢂ  
102 8: Additional Examples  
Loan With a Partial (Odd) First Period  
790ꢀFDOFXODWLRQVꢀDSSO\ꢀWRꢀILQDQFLDOꢀWUDQVDFWLRQVꢀZKHUHꢀHDFKꢀSD\PHQWꢀ  
SHULRGꢀLVꢀWKHꢀVDPHꢀOHQJWKꢂꢀ+RZHYHUꢁꢀVLWXDWLRQVꢀH[LVWꢀZKHUHꢀWKHꢀILUVWꢀ  
SD\PHQWꢀSHULRGꢀLVꢀQRWꢀWKHꢀVDPHꢀOHQJWKꢀDVꢀWKHꢀUHPDLQLQJꢀSHULRGVꢂꢀ7KLVꢀILUVWꢀ  
SHULRGꢀLVꢀVRPHWLPHVꢀFDOOHGꢀDQꢀRGGꢀRUꢀSDUWLDOꢁILUVWꢁSHULRGꢂ  
,IꢀLQWHUHVWꢀLVꢀDSSOLHGꢀWRꢀDQꢀRGGꢀILUVWꢀSHULRGꢁꢀLWꢀLVꢀXVXDOO\ꢀFDOFXODWHGꢀDVꢀ  
VLPSOHꢀLQWHUHVWꢂꢀ6RꢀXVLQJꢀWKHꢀ+3ꢀꢅꢇ%,,ꢀWRꢀGRꢀDꢀSD\PHQWꢀFDOFXODWLRQꢀZLWKꢀ  
DQꢀRGGꢀILUVWꢀSHULRGꢀLVꢀDꢀWZRꢀVWHSꢀSURFHVVꢃ  
ꢀꢁ &DOFXODWHꢀWKHꢀDPRXQWꢀRIꢀVLPSOHꢀLQWHUHVWꢀWKDWꢀDFFUXHVꢀGXULQJꢀWKHꢀ  
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1.25  
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4,530.00  
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8: Additional Examples 103  
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–157.03  
&DOFXODWHVꢀSD\PHQWꢀ  
DPRXQWꢂ  
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3.50  
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104 8: Additional Examples  
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12.36  
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11.71  
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130,000  
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360.00  
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8: Additional Examples 105  
What if … TVM Calculations  
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12.00  
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735,000.00  
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106 8: Additional Examples  
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514.82  
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19.80  
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180.00  
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SDLGꢀRQꢀFRQWUDFWꢂ  
8: Additional Examples 107  
Savings  
Saving for College Costs  
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12.00  
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108 8: Additional Examples  
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8: Additional Examples 109  
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144.00  
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9.00  
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Gains That Go Untaxed Until Withdrawal  
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GLYLGHQGꢀUDWHꢀRIꢀꢓꢂꢅꢒꢑꢌꢂꢀ,Iꢀ\RXꢀLQYHVWꢀꢊꢉꢁꢇꢇꢇꢀDWꢀWKHꢀEHJLQQLQJꢀRIꢀHDFKꢀ  
\HDUꢀIRUꢀꢏꢑꢀ\HDUVꢁꢀKRZꢀPXFKꢀZLOOꢀEHꢀLQꢀWKHꢀDFFRXQWꢀDWꢀUHWLUHPHQW"ꢀ+RZꢀ  
PXFKꢀZLOOꢀ\RXꢀKDYHꢀSDLGꢀLQWRꢀWKHꢀDFFRXQW"ꢀ+RZꢀPXFKꢀLQWHUHVWꢀZLOOꢀ\RXꢀ  
KDYHꢀHDUQHG"ꢀ,Iꢀ\RXUꢀSRVWꢍUHWLUHPHQWꢀWD[ꢀUDWHꢀLVꢀꢅꢑꢌꢁꢀZKDWꢀZLOOꢀWKHꢀDIWHUꢍ  
WD[ꢀIXWXUHꢀYDOXHꢀRIꢀWKHꢀDFFRXQWꢀEH"ꢀ$VVXPHꢀWKDWꢀRQO\ꢀWKHꢀLQWHUHVWꢀLVꢀWD[HGꢀ  
ꢄDVVXPHꢀWKHꢀSULQFLSDOꢀZDVꢀWD[HGꢀEHIRUHꢀGHSRVLWꢈꢂꢀ:KDWꢀLVꢀWKHꢀSXUFKDVLQJꢀ  
SRZHUꢀRIꢀWKDWꢀDPRXQWꢁꢀLQꢀWRGD\·VꢀGROODUVꢁꢀDVVXPLQJꢀDꢀꢋꢌꢀLQIODWLRQꢀUDWH"  
110 8: Additional Examples  
6HWꢀWRꢀ%HJLQꢀPRGHꢂꢀ3UHVVꢀ  
Keys:  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢂ  
Display:  
Description:  
1.00  
6HWVꢀꢅꢀSD\PHQWꢀSHUꢀ  
\HDUꢂ  
35.00  
8.18  
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SHULRGVꢀDQGꢀLQWHUHVWꢀ  
UDWHꢂ  
0.00  
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VWDUWꢀZLWKꢂ  
–2,000.00  
387,640.45  
–70,000.00  
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DQQXDOꢀSD\PHQWꢂ  
&DOFXODWHVꢀDPRXQWꢀLQꢀ  
DFFRXQWꢀDWꢀUHWLUHPHQWꢂ  
&DOFXODWHVꢀDPRXQWꢀ\RXꢀ  
KDYHꢀSDLGꢀLQWRꢀDFFRXQWꢀ  
E\ꢀUHWLUHPHQWꢂ  
317,640.45  
47,646.07  
&DOFXODWHVꢀLQWHUHVWꢀ  
DFFRXQWꢀKDVꢀHDUQHGꢀE\ꢀ  
UHWLUHPHQWꢂ  
&DOFXODWHVꢀWD[HVꢀDWꢀꢅꢑꢌꢀ  
RIꢀLQWHUHVWꢂ  
339,994.39  
339,994.39  
&DOFXODWHVꢀDIWHUꢍWD[ꢀ)9ꢂ  
6WRUHVꢀDIWHUꢍWD[ꢀIXWXUHꢀ  
YDOXHꢀLQꢀ)9ꢂ  
–86,159.84  
&DOFXODWHVꢀSUHVHQWꢍ  
YDOXHꢀSXUFKDVLQJꢀSRZHUꢀ  
RIꢀDIWHUꢍWD[ꢀ)9ꢁꢀ  
DVVXPLQJꢀDꢀꢋꢌꢀ  
LQIODWLRQꢀUDWHꢂ  
8: Additional Examples 111  
Value of a Taxable Retirement Account  
7KLVꢀSUREOHPꢀXVHVꢀWKHꢀ790ꢀDSSOLFDWLRQꢀWRꢀFDOFXODWHꢀWKHꢀIXWXUHꢀYDOXHꢀRIꢀDꢀ  
WD[DEOHꢀUHWLUHPHQWꢀDFFRXQWꢀWKDWꢀUHFHLYHVꢀUHJXODUꢁꢀDQQXDOꢀSD\PHQWVꢀ  
EHJLQQLQJꢀWRGD\ꢀꢄ%HJLQꢀPRGHꢈꢂꢀ7KHꢀDQQXDOꢀWD[ꢀRQꢀWKHꢀLQWHUHVWꢀLVꢀSDLGꢀRXWꢀ  
RIꢀWKHꢀDFFRXQWꢂꢀꢄ$VVXPHꢀWKHꢀGHSRVLWVꢀKDYHꢀEHHQꢀWD[HGꢀDOUHDG\ꢂꢈ  
Example. ,Iꢀ\RXꢀLQYHVWꢀꢊꢏꢁꢇꢇꢇꢀHDFKꢀ\HDUꢀIRUꢀꢏꢑꢀ\HDUVꢁꢀZLWKꢀGLYLGHQGVꢀ  
WD[HGꢀDVꢀRUGLQDU\ꢀLQFRPHꢁꢀKRZꢀPXFKꢀZLOOꢀ\RXꢀKDYHꢀLQꢀWKHꢀDFFRXQWꢀDWꢀ  
UHWLUHPHQW"ꢀ$VVXPHꢀDQꢀDQQXDOꢀGLYLGHQGꢀUDWHꢀRIꢀꢓꢂꢅꢒꢑꢌꢁꢀDꢀWD[ꢀUDWHꢀRIꢀꢉꢓꢌꢁꢀ  
DQGꢀWKDWꢀSD\PHQWVꢀEHJLQꢀWRGD\ꢂꢀ:KDWꢀLVꢀWKHꢀSXUFKDVLQJꢀSRZHUꢀRIꢀWKDWꢀ  
DPRXQWꢀLQꢀWRGD\·VꢀGROODUVꢁꢀDVVXPLQJꢀꢋꢌꢀLQIODWLRQ"  
6HWꢀWRꢀ%HJLQꢀPRGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
1.00  
6HWVꢀꢅꢀSD\PHQWꢀSHUꢀ  
\HDUꢂ  
35.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
SD\PHQWꢀSHULRGVꢀXQWLOꢀ  
UHWLUHPHQWꢂ  
5.89  
5.89  
0.00  
&DOFXODWHVꢀLQWHUHVWꢀUDWHꢀ  
GLPLQLVKHGꢀE\ꢀWD[ꢀUDWHꢂ  
6WRUHVꢀDGMXVWHGꢀLQWHUHVWꢀ  
UDWHꢂ  
6WRUHVꢀDPRXQWꢀ\RXꢀDUHꢀ  
VWDUWLQJꢀZLWKꢂ  
–3,000.00  
345,505.61  
–87,556.47  
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DQQXDOꢀSD\PHQWꢂ  
&DOFXODWHVꢀDPRXQWꢀLQꢀ  
DFFRXQWꢀDWꢀUHWLUHPHQWꢂ  
&DOFXODWHVꢀSUHVHQWꢍ  
YDOXHꢀSXUFKDVLQJꢀSRZHUꢀ  
RIꢀ)9ꢁꢀDVVXPLQJꢀDꢀꢋꢌꢀ  
LQIODWLRQꢀUDWHꢂ  
112 8: Additional Examples  
Cash Flow Examples  
Wrap-Around Mortgages  
$ꢀZUDSꢍDURXQGꢀPRUWJDJHꢀLVꢀDꢀFRPELQDWLRQꢀRIꢀUHILQDQFLQJꢀDꢀPRUWJDJHꢀDQGꢀ  
ERUURZLQJꢀDJDLQVWꢀUHDOꢀHVWDWHꢀHTXLW\ꢂꢀ8VXDOO\ꢀWKHꢀWZRꢀXQNQRZQꢀTXDQWLWLHVꢀ  
LQꢀWKHꢀZUDSSHGꢀPRUWJDJHꢀDUHꢀWKHꢀQHZꢀSD\PHQWꢀDQGꢀWKHꢀUDWHꢀRIꢀUHWXUQꢀWRꢀ  
WKHꢀOHQGHUꢂꢀ7RꢀDUULYHꢀDWꢀDꢀVROXWLRQꢁꢀ\RXꢀQHHGꢀWRꢀXVHꢀERWKꢀWKHꢀ790ꢀDQGꢀWKHꢀ  
FDVKꢀIORZꢀDSSOLFDWLRQVꢂ  
Example. <RXꢀKDYHꢀꢓꢉꢀPRQWKO\ꢀSD\PHQWVꢀRIꢀꢊꢒꢑꢋꢀOHIWꢀRQꢀ\RXUꢀꢓꢌꢀ  
PRUWJDJHꢁꢀOHDYLQJꢀDꢀUHPDLQLQJꢀEDODQFHꢀRIꢀꢊꢋꢒꢁꢑꢅꢇꢂꢉꢉꢂꢀ<RXꢀZRXOGꢀOLNHꢀWRꢀ  
ZUDSꢀWKDWꢀPRUWJDJHꢀDQGꢀERUURZꢀDQꢀDGGLWLRQDOꢀꢊꢏꢑꢁꢇꢇꢇꢀIRUꢀDQRWKHUꢀ  
LQYHVWPHQWꢂꢀ<RXꢀILQGꢀDꢀOHQGHUꢀZKRꢀLVꢀZLOOLQJꢀWRꢀ´ZUDSµꢀDQꢀꢊꢓꢉꢁꢑꢅꢇꢂꢉꢉꢀ  
PRUWJDJHꢀDWꢀꢕꢂꢑꢌꢀIRUꢀꢅꢑꢀ\HDUVꢂꢀ:KDWꢀDUHꢀ\RXUꢀQHZꢀSD\PHQWVꢀDQGꢀZKDWꢀ  
UHWXUQꢀLVꢀWKHꢀOHQGHUꢀJHWWLQJꢀRQꢀWKLVꢀZUDSꢍDURXQGꢀPRUWJDJH"  
7KHꢀSD\PHQWꢀFDOFXODWLRQꢀLVꢀDꢀVWUDLJKWIRUZDUGꢀ790ꢀSD\PHQWꢀFDOFXODWLRQꢀ  
XVLQJꢀWKHꢀQHZꢀDPRXQWꢀDVꢀWKHꢀ39ꢂ  
6HWꢀWRꢀ(QGꢀPRGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
0.00  
&OHDUVꢀDOOꢀUHJLVWHUVꢂ  
12.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
82,510.22  
6WRUHVꢀORDQꢀDPRXQWꢀRQꢀ  
ZKLFKꢀ\RXUꢀQHZꢀ  
SD\PHQWꢀLVꢀFDOFXODWHGꢂ  
9.50  
6WRUHVꢀLQWHUHVWꢀUDWHꢂ  
6WRUHVꢀILQDOꢀEDODQFHꢂ  
0.00  
180.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
PRQWKO\ꢀSD\PHQWVꢀ\RXꢀ  
ZLOOꢀPDNHꢂ  
–861.59  
&DOFXODWHVꢀ\RXUꢀQHZꢀ  
SD\PHQWꢂ  
8: Additional Examples 113  
7KHQꢁꢀWRꢀFDOFXODWHꢀWKHꢀOHQGHU·VꢀUHWXUQꢁꢀHQWHUꢀFDVKꢀIORZVꢀWKDWꢀUHSUHVHQWꢀWKHꢀ  
FRPSOHWHꢀSLFWXUHꢀRIꢀWKHꢀZUDSꢍDURXQGꢀPRUWJDJHꢀIURPꢀWKHꢀOHQGHU·VꢀSRLQWꢀRIꢀ  
YLHZꢃ  
:KHQꢀ\RXꢀJURXSꢀWKHꢀDERYHꢀFDVKꢀIORZVꢁꢀ\RX·OOꢀILQGꢀWKDWꢃ  
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&)   ꢓꢐꢅꢂꢑꢕꢀ²ꢀꢒꢑꢋꢂꢇꢇꢀ ꢀꢅꢇꢒꢂꢑꢕ  
1
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1
  ꢅꢓꢇꢀ²ꢀꢓꢉꢀ ꢀꢕꢓ  
Keys:  
Display:  
Description:  
CF0  
–35,000.00  
(QWHUVꢀꢊꢏꢑꢁꢇꢇꢇꢀIRUꢀORDQꢀ  
DPRXQWꢂ  
CF1  
107.59  
(QWHUVꢀQHWꢀSD\PHQWꢀIRUꢀ  
ILUVWꢀꢓꢉꢀPRQWKVꢂ  
n1  
82.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
WLPHVꢀSD\PHQWꢀRFFXUVꢂ  
CF2  
861.59  
(QWHUVꢀQHWꢀSD\PHQWꢀIRUꢀ  
QH[WꢀꢕꢓꢀPRQWKVꢂ  
n2  
98.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
WLPHVꢀSD\PHQWꢀRFFXUVꢂ  
10.16  
&DOFXODWHVꢀDQQXDOꢀ  
UHWXUQꢂ  
114 8: Additional Examples  
Net Future Value  
7KHꢀQHWꢀIXWXUHꢀYDOXHꢀFDQꢀEHꢀFDOFXODWHGꢀE\ꢀXVLQJꢀWKHꢀ790ꢀNH\VꢀWRꢀVOLGHꢀWKHꢀ  
QHWꢀSUHVHQWꢀYDOXHꢀꢄ139ꢈꢀIRUZDUGꢀRQꢀWKHꢀFDVKꢀIORZꢀGLDJUDPꢂ  
Example: Value of a Fund. <RXꢀKDYHꢀPDGHꢀWKHꢀIROORZLQJꢀGHSRVLWVꢀRYHUꢀ  
WKHꢀSDVWꢀWZRꢀ\HDUVꢀLQWRꢀDꢀPRQH\ꢀPDUNHWꢀIXQGꢀHDUQLQJꢀꢓꢂꢓꢌꢂꢀ:KDWꢀLVꢀWKHꢀ  
FXUUHQWꢀEDODQFHꢀRIꢀWKHꢀDFFRXQW"  
6HWꢀWRꢀ(QGꢀPRGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
&OHDUVꢀDOOꢀUHJLVWHUVꢂ  
12.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
(QWHUVꢀLQLWLDOꢀFDVKꢀIORZꢂ  
CF0  
–12,000.00  
CF1  
0.00  
(QWHUVꢀDPRXQWꢀLQꢀ  
JURXSꢀꢅꢂ  
n1  
2.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
WLPHVꢀSD\PHQWꢀRFFXUVꢂ  
CF2  
–3,000.00  
(QWHUVꢀDPRXQWꢀLQꢀ  
JURXSꢀꢉꢂ  
n2  
3.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
WLPHVꢀSD\PHQWꢀRFFXUVꢂ  
n3  
9.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
WLPHVꢀSD\PHQWꢀRFFXUVꢂ  
CF4  
–7,500.00  
(QWHUVꢀFDVKꢀIORZꢀJURXSꢀ  
ꢋꢂ  
n5  
3.00  
(QWHUVꢀQXPEHUꢀRIꢀ  
WLPHVꢀSD\PHQWꢀRFFXUVꢂ  
8: Additional Examples 115  
CF6  
–2,000.00  
(QWHUVꢀFDVKꢀIORZꢀJURXSꢀ  
ꢐꢂ  
8.80  
6WRUHVꢀDQQXDOꢀLQWHUHVWꢀ  
UDWHꢂ  
–29,203.14  
&DOFXODWHVꢀQHWꢀSUHVHQWꢀ  
YDOXHꢀꢄ139ꢈꢁꢀ  
DXWRPDWLFDOO\ꢀVWRUHGꢀDVꢀ  
39ꢂ  
24.00  
6WRUHVꢀNQRZQꢀYDOXHVꢂ  
0.00  
34,800.58  
&DOFXODWHVꢀQHWꢀIXWXUHꢀ  
YDOXHꢂ  
116 8: Additional Examples  
A
Assistance, Batteries, and Service  
+HZOHWWꢀ3DFNDUGꢁLVꢁFRPPLWWHGꢁWRꢁSURYLGLQJꢁ\RXꢁZLWKꢁRQJRLQJꢁVXSSRUWꢂꢁ  
<RXꢁFDQꢁREWDLQꢁDQVZHUVꢁWRꢁTXHVWLRQVꢁDERXWꢁXVLQJꢁ\RXUꢁFDOFXODWRUꢁIURPꢁ  
RXUꢁ&DOFXODWRUꢁ6XSSRUWꢁGHSDUWPHQWꢂ  
3OHDVHꢁUHDGꢁ´$QVZHUVꢁWRꢁ&RPPRQꢁ4XHVWLRQVµꢁEHIRUHꢁFRQWDFWLQJꢁXVꢂꢁ2XUꢁ  
H[SHULHQFHꢁKDVꢁVKRZQꢁWKDWꢁPDQ\ꢁRIꢁRXUꢁFXVWRPHUVꢁKDYHꢁVLPLODUꢁTXHVWLRQVꢁ  
DERXWꢁRXUꢁSURGXFWVꢂꢁ,Iꢁ\RXꢁGRQ·WꢁILQGꢁDQꢁDQVZHUꢁWRꢁ\RXUꢁTXHVWLRQꢃꢁ\RXꢁFDQꢁ  
FRQWDFWꢁXVꢁXVLQJꢁWKHꢁDGGUHVVꢁRUꢁSKRQHꢁQXPEHUꢁOLVWHGꢁRQꢁWKHꢁLQVLGHꢁEDFNꢁ  
FRYHUꢂ  
Answers to Common Questions  
Q: ,·PꢁQRWꢁVXUHꢁLIꢁWKHꢁFDOFXODWRUꢁLVꢁPDOIXQFWLRQLQJꢁRUꢁLIꢁ,·PꢁGRLQJꢁ  
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SURSHUO\"  
A: 6HHꢁ´'HWHUPLQLQJꢁLIꢁWKHꢁ&DOFXODWRUꢁ5HTXLUHVꢁ6HUYLFHµꢁRQꢁ  
SDJH ꢄꢅꢄꢂ  
Q: 0\ꢁQXPEHUVꢁFRQWDLQꢁFRPPDVꢁLQVWHDGꢁRIꢁSHULRGVꢁDVꢁGHFLPDOꢁSRLQWVꢂꢁ  
+RZꢁGRꢁ,ꢁUHVWRUHꢁWKHꢁSHULRGV"  
A: 3UHVVꢁ  
ꢁꢆSDJH ꢇꢄꢈꢂ  
Q: +RZꢁGRꢁ,ꢁFKDQJHꢁWKHꢁQXPEHUꢁRIꢁGHFLPDOꢁSODFHVꢁWKDWꢁWKHꢁ+3 ꢄꢉ%,,ꢁ  
GLVSOD\V"  
A: 3UHVVꢁ  
ꢆSDJH ꢇꢄꢈꢂ  
ꢁDQGꢁWKHꢁQXPEHUꢁRIꢁGHFLPDOꢁSODFHVꢁWKDWꢁ\RXꢁZDQWꢁ  
A: Assistance, Batteries, and Service 117  
Q: :KDWꢁGRHVꢁDQꢁ´(µꢁLQꢁDꢁQXPEHUꢁꢆIRUꢁH[DPSOHꢃꢁꢅꢂꢊꢄ(²ꢄꢇꢈꢁPHDQ"  
A: ([SRQHQWꢁRIꢁWHQꢁꢆIRUꢁH[DPSOHꢃꢁꢅꢂꢊꢄꢁïꢁꢄꢉ ꢈꢂꢁ5HIHUꢁWRꢁ´6FLHQWLILFꢁ  
1RWDWLRQµꢁRQꢁSDJH ꢇꢉꢂ  
Q: :K\ꢁGRꢁ,ꢁJHWꢁDꢁZURQJꢁDQVZHUꢁRUꢁWKHꢁNo Solution PHVVDJHꢁ  
ZKHQꢁXVLQJꢁ790"  
A: %HꢁVXUHꢁWRꢁHQWHUꢁDꢁYDOXHꢁIRUꢁIRXUꢁRIꢁWKHꢁILYHꢁ790ꢁYDOXHVꢁEHIRUHꢁ\RXꢁ  
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Dꢁ]HURꢁIRUꢁ ꢁLIꢁ\RXꢁFRPSOHWHO\ꢁSD\ꢁRIIꢁDꢁORDQꢂꢈꢁ&OHDULQJꢁDOOꢁWKHꢁUHJLVWHUVꢁ  
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ꢆ%HJLQꢁRUꢁ(QGꢁPRGHꢈꢁDQGꢁWKDWꢁ3ꢀ<5ꢁLVꢁVHWꢁFRUUHFWO\ꢂ  
Q: +RZꢁFDQꢁ,ꢁFKDQJHꢁWKHꢁVLJQꢁRIꢁDꢁQXPEHUꢁLQꢁDꢁOLVWꢁRIꢁFDVKꢁIORZV"  
A: <RXꢁPXVWꢁUHSODFHꢁWKHꢁFDVKꢁIORZꢁHQWU\ꢂꢁ6HHꢁ´9LHZLQJꢁDQGꢁ  
5HSODFLQJꢁ&DVKꢁ)ORZVµꢁRQꢁSDJH ꢋꢌꢂ  
Q: :KDWꢁGRHVꢁPENDꢁLQꢁWKHꢁGLVSOD\ꢁPHDQ"  
A: $QꢁDULWKPHWLFꢁRSHUDWLRQꢁLVꢁSHQGLQJꢁꢆLQꢁSURJUHVVꢈꢂ  
Q: :KDWꢁGRHVꢁINPUTꢀLQꢁWKHꢁGLVSOD\ꢁPHDQ"  
A:7KHꢁ ꢁNH\ꢁKDVꢁEHHQꢁSUHVVHGꢁꢆSDJH ꢅꢍꢈꢂ  
Q: :K\ꢁLVꢁ,55ꢀ<5ꢁODUJHUꢁWKDQꢁ,ꢁH[SHFWHG"  
A: 7KLVꢁLVꢁ,55ꢁSHUꢁ\HDUꢂꢁ7RꢁVHHꢁDꢁSHULRGLFꢁ,55ꢃꢁGLYLGHꢁ,55ꢀ<5ꢁE\ꢁ3ꢀ<5ꢂ  
Environmental Limits  
7RꢁPDLQWDLQꢁSURGXFWꢁUHOLDELOLW\ꢃꢁ\RXꢁVKRXOGꢁDYRLGꢁJHWWLQJꢁWKHꢁFDOFXODWRUꢁ  
ZHWꢁDQGꢁREVHUYHꢁWKHꢁIROORZLQJꢁWHPSHUDWXUHꢁDQGꢁKXPLGLW\ꢁOLPLWVꢎ  
2SHUDWLQJꢁWHPSHUDWXUHꢎꢁꢉƒꢁWRꢁꢏꢉƒ&ꢁꢆꢇꢅƒꢁWRꢁꢄꢉꢏƒ)ꢈꢂ  
6WRUDJHꢁWHPSHUDWXUHꢎꢁ²ꢅꢉƒꢁWRꢁꢐꢊƒ&ꢁꢆ²ꢏƒꢁWRꢁꢄꢏꢌƒ)ꢈꢂ  
2SHUDWLQJꢁDQGꢁVWRUDJHꢁKXPLGLW\ꢎꢁꢌꢉꢑꢁUHODWLYHꢁKXPLGLW\ꢁDWꢁꢏꢉƒ&ꢁ  
ꢆꢄꢉꢏƒ)ꢈꢁPD[LPXPꢂ  
Noise Declaration. ,QꢁWKHꢁRSHUDWRUꢁSRVLWLRQꢁXQGHUꢁQRUPDOꢁRSHUDWLRQꢁ  
ꢆSHUꢁ,62ꢁꢋꢋꢋꢌꢈꢎꢁ/S$ꢁꢒꢁꢋꢉG%ꢂ  
118 A: Assistance, Batteries, and Service  
Power and Batteries  
7KHꢁFDOFXODWRUꢁLVꢁSRZHUHGꢁE\ꢁWZRꢁꢇꢀYROWꢁOLWKLXPꢁEXWWRQꢀFHOOꢁ  
EDWWHULHVꢂ  
:KHQꢁFKDQJLQJꢁEDWWHULHVꢃꢁXVHꢁRQO\ꢁIUHVKꢁEXWWRQꢀFHOOꢁEDWWHULHVꢂꢁ  
%RWKꢁEDWWHULHVꢁPXVWꢁEHꢁFKDQJHGꢁDWꢁWKHꢁVDPHꢁWLPHꢂ  
'RꢁQRWꢁXVHꢁUHFKDUJHDEOHꢁEDWWHULHVꢂ  
Low Power Annunciator  
:KHQꢁWKHꢁORZꢁEDWWHU\ꢀSRZHUꢁDQQXQFLDWRUꢁꢆ  
ꢈꢁFRPHVꢁRQꢃꢁ\RXꢁ  
VKRXOGꢁUHSODFHꢁWKHꢁEDWWHULHVꢁDVꢁVRRQꢁDVꢁSRVVLEOHꢂꢁ,IꢁWKHꢁEDWWHU\ꢁ  
DQQXQFLDWRUꢁLVꢁRQꢁDQGꢁWKHꢁGLVSOD\ꢁGLPVꢃꢁ\RXꢁPD\ꢁORVHꢁGDWDꢂꢁ7KHꢁ  
All Clear PHVVDJHꢁLVꢁGLVSOD\HGꢁLIꢁGDWDꢁLVꢁORVWꢁGXHꢁWRꢁORZꢁSRZHUꢂ  
Battery Specifications  
<RXUꢁ+3ꢁFDOFXODWRUꢁUHTXLUHVꢁWZRꢁIUHVKꢁ&5ꢅꢉꢇꢅꢁOLWKLXPꢁEDWWHULHVꢂꢁ  
Installing Batteries  
ꢁꢂ +DYHꢁWZRꢁIUHVKꢁ&5ꢅꢉꢇꢅꢁEDWWHULHVꢁDWꢁKDQGꢂꢁ2QO\ꢁWRXFKꢁWKHꢁ  
EDWWHULHVꢁE\ꢁWKHLUꢁHGJHVꢂꢁ:LSHꢁHDFKꢁEDWWHU\ꢁZLWKꢁDꢁOLQWꢀIUHHꢁ  
FORWKꢁWRꢁUHPRYHꢁGLUWꢁDQGꢁRLOꢂ  
ꢃꢂ 0DNHꢁVXUHꢁWKHꢁFDOFXODWRUꢁLVꢁRIIꢂꢁ1RWHꢁWKDWꢁ\RXꢁZLOOꢁORVHꢁWKHꢁFRQWHQWVꢁ  
RIꢁPHPRU\ꢁZKHQꢁFKDQJLQJꢁWKHꢁEDWWHULHVꢃꢁVRꢁZULWHꢁGRZQꢁDQ\ꢁGDWDꢁWKDWꢁ  
\RXꢁKDYHꢁVWRUHGꢁDQGꢁQHHGꢁIRUꢁODWHUꢁXVHꢂ  
ꢄꢂ 7XUQꢁWKHꢁFDOFXODWRUꢁRYHUꢁDQGꢁSULVHꢁRIIꢁWKHꢁEDWWHU\ꢁFRYHUꢂ  
Accessing the battery compartment  
A: Assistance, Batteries, and Service 119  
ꢅꢂ 5HPRYHꢁERWKꢁEDWWHULHVꢂ  
7KHUHꢀLVꢀDꢀGDQJHUꢀRIꢀH[SORVLRQꢀLIꢀEDWWHULHVꢀDUHꢀ  
LQFRUUHFWO\ꢀUHSODFHGꢂ  
Warning  
5HSODFHꢀRQO\ꢀZLWKꢀWKHꢀVDPHꢀW\SHꢀRIꢀEDWWHU\ꢀRUꢀZLWKꢀ  
HTXLYDOHQWꢀEDWWHULHVꢀꢉDVꢀUHFRPPHQGHGꢀE\ꢀWKHꢀ  
PDQXIDFWXUHUꢊꢂꢀ'LVSRVHꢀRIꢀXVHGꢀEDWWHULHVꢀDFFRUGLQJꢀWRꢀ  
WKHꢀPDQXIDFWXUHU·VꢀLQVWUXFWLRQVꢂ  
'RꢀQRWꢀPXWLODWHꢋꢀSXQFWXUHꢋꢀRUꢀGLVSRVHꢀRIꢀEDWWHULHVꢀLQꢀ  
ILUHꢂꢀ7KHꢀEDWWHULHVꢀFDQꢀEXUVWꢀRUꢀH[SORGHꢋꢀUHOHDVLQJꢀ  
KD]DUGRXVꢀFKHPLFDOVꢂ  
'RꢀQRWꢀXVHꢀQHZꢀDQGꢀROGꢀEDWWHULHVꢀWRJHWKHUꢋꢀDQGꢀGRꢀQRWꢀ  
PL[ꢀEDWWHULHVꢀRIꢀGLIIHUHQWꢀW\SHVꢂ  
ꢆꢂ ,QVHUWꢁWKHꢁQHZꢁEDWWHULHVꢃꢁPDNLQJꢁVXUHꢁWKDWꢁWKHꢁSRVLWLYHꢁVLJQꢁ  
ꢆꢓꢈꢁRQꢁHDFKꢁEDWWHU\ꢁLVꢁIDFLQJꢁRXWZDUGꢂ  
ꢇꢂ 5HSODFHꢁWKHꢁEDWWHU\ꢀFRPSDUWPHQWꢁOLGꢂ  
ꢈꢂ 3UHVVꢁ  
ꢂ
,IꢁWKHꢁFDOFXODWRUꢁGRHVꢁQRWꢁWXUQꢁRQꢃꢁIROORZꢁWKHꢁSURFHGXUHVꢁLQꢁWKHꢁQH[Wꢁ  
VHFWLRQꢂ  
120 A: Assistance, Batteries, and Service  
Determining if the Calculator Requires Service  
8VHꢁWKHVHꢁJXLGHOLQHVꢁWRꢁGHWHUPLQHꢁLIꢁWKHꢁFDOFXODWRUꢁUHTXLUHVꢁVHUYLFHꢂꢁ,Iꢁ  
WKHVHꢁSURFHGXUHVꢁFRQILUPꢁWKDWꢁWKHꢁFDOFXODWRUꢁLVꢁQRWꢁIXQFWLRQLQJꢁSURSHUO\ꢃꢁ  
UHDGꢁWKHꢁVHFWLRQꢁ´,IꢁWKHꢁ&DOFXODWRUꢁ5HTXLUHVꢁ6HUYLFHµꢁRQꢁSDJH ꢄꢅꢇꢂ  
The calculator won’t turn on (nothing is in the display):  
7KLVꢁFRQGLWLRQꢁPRVWꢁOLNHO\ꢁLQGLFDWHVꢁWKDWꢁWKHꢁEDWWHULHVꢁKDYHꢁUXQꢁRXWꢂꢁ  
,QVWDOOꢁQHZꢁEDWWHULHVꢂ  
,IꢁWKHꢁFDOFXODWRUꢁVWLOOꢁGRHVꢁQRWꢁWXUQꢁRQꢁZKHQꢁ\RXꢁSUHVVꢁ  
ꢁꢂ UHVHWꢁWKHꢁFDOFXODWRUꢁꢆVHHꢁEHORZꢈꢁDQGꢃꢁLIꢁQHFHVVDU\ꢃ  
ꢃꢂ HUDVHꢁWKHꢁPHPRU\ꢁꢆVHHꢁEHORZꢈꢂ  
ꢎ
7KH All Clear PHVVDJHꢁVKRXOGꢁQRZꢁEHꢁGLVSOD\HGꢂꢁ,IꢁWKLVꢁLVꢁQRWꢁWKHꢁ  
FDVHꢃꢁWKHꢁFDOFXODWRUꢁUHTXLUHVꢁDꢁVHUYLFHꢂ  
Resetting the calculator  
ꢁꢂ 7XUQꢁWKHꢁFDOFXODWRUꢁRYHUꢁDQGꢁUHPRYHꢁWKHꢁEDWWHU\ꢁFRYHUꢂ  
ꢃꢂ ,QVHUWꢁWKHꢁHQGꢁRIꢁDꢁSDSHUꢁFOLSꢁLQWRꢁWKHꢁVPDOOꢃꢁURXQGꢁKROHꢁORFDWHGꢁ  
EHWZHHQꢁWKHꢁEDWWHULHVꢂꢁ,QVHUWꢁWKHꢁFOLSꢁDVꢁIDUꢁDVꢁLWꢁZLOOꢁJRꢂꢁ+ROGꢁIRUꢁ  
RQHꢁVHFRQGꢁDQGꢁWKHQꢁWKHQꢁUHPRYHꢁWKHꢁFOLSꢂ  
ꢄꢂ 3UHVVꢁ  
ꢂ
ꢅꢂ ,IꢁWKHꢁFDOFXODWRUꢁLVꢁVWLOOꢁQRWꢁUHVSRQGLQJꢃꢁHUDVHꢁWKHꢁPHPRU\ꢁꢆVHHꢁ  
EHORZꢈꢁDQGꢁUHSHDWꢁVWHSVꢁꢄꢁWRꢁꢇꢁDERYHꢁRQHꢁPRUHꢁWLPHꢂ  
Erasing the calculator’s memory  
ꢁꢂ +ROGꢁGRZQꢁWKHꢁ ꢁNH\ꢂ  
ꢃꢂ +ROGꢁGRZQꢁWKHꢁ ꢁDQGꢁWKHQꢁWKHꢁ ꢁNH\ꢂ  
ꢄꢂ 5HOHDVHꢁDOOꢁWKUHHꢁNH\Vꢂ  
0HPRU\ꢁLVꢁFOHDUHGꢁDQGꢁAll ClearꢁVKRXOGꢁEHꢁGLVSOD\HGꢂ  
The calculator doesn’t respond to keystrokes (nothing  
happens when you press the keys):  
ꢁꢂ 5HVHWꢁWKHꢁFDOFXODWRUꢁꢆVHHꢁDERYHꢈꢁDQGꢃꢁLIꢁQHFHVVDU\ꢃ  
ꢃꢂ HUDVHꢁWKHꢁPHPRU\ꢁꢆVHHꢁDERYHꢈꢂ  
7KH All Clear PHVVDJHꢁVKRXOGꢁQRZꢁEHꢁGLVSOD\HGꢂꢁ,IꢁWKLVꢁLVꢁQRWꢁWKHꢁ  
FDVHꢃꢁWKHꢁFDOFXODWRUꢁUHTXLUHVꢁDꢁVHUYLFHꢂ  
A: Assistance, Batteries, and Service 121  
The calculator responds to keystrokes but you suspect that it  
is malfunctioning:  
ꢁꢂ ,WꢁLVꢁOLNHO\ꢁWKDWꢁ\RX·YHꢁPDGHꢁDꢁPLVWDNHꢁLQꢁRSHUDWLQJꢁWKHꢁ  
FDOFXODWRUꢂꢁ7U\ꢁUHUHDGLQJꢁSRUWLRQVꢁRIꢁWKHꢁPDQXDOꢃꢁDQGꢁ  
FKHFNꢁ´$QVZHUVꢁWRꢁ&RPPRQꢁ4XHVWLRQVµꢁRQꢁSDJH ꢄꢄꢋꢂ  
ꢃꢂ &RQWDFWꢁWKHꢁ&DOFXODWRUꢁ6XSSRUWꢁGHSDUWPHQWꢂꢁ7KHꢁDGGUHVVꢁDQGꢁ  
SKRQHꢁQXPEHUꢁDUHꢁOLVWHGꢁRQꢁWKHꢁLQVLGHꢁEDFNꢁFRYHUꢂ  
Limited One-Year Warranty  
What Is Covered  
7KHꢁFDOFXODWRUꢁꢆH[FHSWꢁIRUꢁWKHꢁEDWWHULHVꢃꢁRUꢁGDPDJHꢁFDXVHGꢁE\ꢁWKHꢁEDWWHULHVꢈꢁ  
LVꢁZDUUDQWHGꢁE\ꢁ+HZOHWWꢃ3DFNDUGꢁDJDLQVWꢁGHIHFWVꢁLQꢁPDWHULDOVꢁDQGꢁZRUNPDQVKLSꢁIRUꢁ  
RQHꢁ\HDUꢁIURPꢁWKHꢁGDWHꢁRIꢁRULJLQDOꢁSXUFKDVHꢂꢁ,Iꢁ\RXꢁVHOOꢁ\RXUꢁXQLWꢁRUꢁJLYHꢁLWꢁDVꢁDꢁ  
JLIWꢃꢁWKHꢁZDUUDQW\ꢁLVꢁDXWRPDWLFDOO\ꢁWUDQVIHUUHGꢁWRꢁWKHꢁQHZꢁRZQHUꢁDQGꢁ  
UHPDLQVꢁLQꢁHIIHFWꢁIRUꢁWKHꢁRULJLQDOꢁRQHꢀ\HDUꢁSHULRGꢂꢁ'XULQJꢁWKHꢁZDUUDQW\ꢁ  
SHULRGꢃꢁZHꢁZLOOꢁUHSDLUꢁRUꢃꢁDWꢁRXUꢁRSWLRQꢃꢁUHSODFHꢁDWꢁQRꢁFKDUJHꢁDꢁSURGXFWꢁ  
WKDWꢁSURYHVꢁWRꢁEHꢁGHIHFWLYHꢃꢁSURYLGHGꢁ\RXꢁUHWXUQꢁWKHꢁSURGXFWꢃꢁVKLSSLQJꢁ  
SUHSDLGꢃꢁWRꢁDꢁ+HZOHWWꢀ3DFNDUGꢁVHUYLFHꢁFHQWHUꢂꢁꢆ5HSODFHPHQWꢁPD\ꢁEHꢁZLWKꢁDꢁ  
QHZHUꢁPRGHOꢁRIꢁHTXLYDOHQWꢁRUꢁEHWWHUꢁIXQFWLRQDOLW\ꢂꢈ  
7KLVꢁZDUUDQW\ꢁJLYHVꢁ\RXꢁVSHFLILFꢁOHJDOꢁULJKWVꢃꢁDQGꢁ\RXꢁPD\ꢁDOVRꢁKDYHꢁRWKHUꢁ  
ULJKWVꢁWKDWꢁYDU\ꢁIURPꢁVWDWHꢁWRꢁVWDWHꢃꢁSURYLQFHꢁWRꢁSURYLQFHꢃꢁRUꢁFRXQWU\ꢁWRꢁ  
FRXQWU\ꢂ  
What Is Not Covered  
%DWWHULHVꢃꢁDQGꢁGDPDJHꢁFDXVHGꢁE\ꢁWKHꢁEDWWHULHVꢃꢁDUHꢁQRWꢁFRYHUHGꢁE\ꢁWKHꢁ  
+HZOHWWꢀ3DFNDUGꢁZDUUDQW\ꢂꢁ&KHFNꢁZLWKꢁWKHꢁEDWWHU\ꢁPDQXIDFWXUHUꢁDERXWꢁ  
EDWWHU\ꢁDQGꢁEDWWHU\ꢁOHDNDJHꢁZDUUDQWLHVꢂ  
7KLVꢁZDUUDQW\ꢁGRHVꢁQRWꢁDSSO\ꢁLIꢁWKHꢁSURGXFWꢁKDVꢁEHHQꢁGDPDJHGꢁE\ꢁ  
DFFLGHQWꢁRUꢁPLVXVHꢁRUꢁDVꢁWKHꢁUHVXOWꢁRIꢁVHUYLFHꢁRUꢁPRGLILFDWLRQꢁE\ꢁRWKHUꢁ  
WKDQꢁDQꢁDXWKRUL]HGꢁ+HZOHWWꢀ3DFNDUGꢁVHUYLFHꢁFHQWHUꢂ  
1RꢁRWKHUꢁH[SUHVVꢁZDUUDQW\ꢁLVꢁJLYHQꢂꢁ7KHꢁUHSDLUꢁRUꢁUHSODFHPHQWꢁRIꢁDꢁ  
SURGXFWꢁLVꢁ\RXUꢁH[FOXVLYHꢁUHPHG\ꢂꢀ$Q\ꢀRWKHUꢀLPSOLHGꢀZDUUDQW\ꢀRIꢀ  
PHUFKDQWDELOLW\ꢀRUꢀILWQHVVꢀLVꢀOLPLWHGꢀWRꢀWKHꢀRQHꢌ\HDUꢀGXUDWLRQꢀRIꢀWKLVꢀ  
ZULWWHQꢀZDUUDQW\ꢂꢁ  
122 A: Assistance, Batteries, and Service  
6RPHꢁVWDWHVꢃꢁSURYLQFHVꢃꢁRUꢁFRXQWULHVꢁGRꢁQRWꢁDOORZꢁOLPLWDWLRQVꢁRQꢁKRZꢁORQJꢁ  
DQꢁLPSOLHGꢁZDUUDQW\ꢁODVWVꢃꢁVRꢁWKHꢁDERYHꢁOLPLWDWLRQꢁPD\ꢁQRWꢁDSSO\ꢁWRꢁ\RXꢂꢁ  
,QꢀQRꢀHYHQWꢀVKDOOꢀ+HZOHWWꢌ3DFNDUGꢀ&RPSDQ\ꢀEHꢀOLDEOHꢀIRUꢀ  
FRQVHTXHQWLDOꢀGDPDJHVꢂꢁ6RPHꢁVWDWHVꢃꢁSURYLQFHVꢃꢁRUꢁFRXQWULHVꢁGRꢁQRWꢁ  
DOORZꢁWKHꢁH[FOXVLRQꢁRUꢁOLPLWDWLRQꢁRIꢁLQFLGHQWDOꢁRUꢁFRQVHTXHQWLDOꢁGDPDJHVꢃꢁ  
VRꢁWKHꢁDERYHꢁOLPLWDWLRQꢁRUꢁH[FOXVLRQꢁPD\ꢁQRWꢁDSSO\ꢁWRꢁ\RXꢂ  
3URGXFWVꢁDUHꢁVROGꢁRQꢁWKHꢁEDVLVꢁRIꢁVSHFLILFDWLRQVꢁDSSOLFDEOHꢁDWꢁWKHꢁWLPHꢁRIꢁ  
PDQXIDFWXUHꢂꢁ+HZOHWWꢀ3DFNDUGꢁVKDOOꢁKDYHꢁQRꢁREOLJDWLRQꢁWRꢁPRGLI\ꢁRUꢁ  
XSGDWHꢁSURGXFWVꢃꢁRQFHꢁVROGꢂ  
Consumer Transactions in the United Kingdom  
7KLVꢁZDUUDQW\ꢁVKDOOꢁQRWꢁDSSO\ꢁWRꢁFRQVXPHUꢁWUDQVDFWLRQVꢁDQGꢁVKDOOꢁQRWꢁ  
DIIHFWꢁWKHꢁVWDWXWRU\ꢁULJKWVꢁRIꢁDꢁFRQVXPHUꢂꢁ,QꢁUHODWLRQꢁWRꢁVXFKꢁWUDQVDFWLRQVꢃꢁ  
WKHꢁULJKWVꢁDQGꢁREOLJDWLRQVꢁRIꢁ6HOOHUꢁDQGꢁ%X\HUꢁVKDOOꢁEHꢁGHWHUPLQHGꢁE\ꢁ  
VWDWXWHꢂ  
If the Calculator Requires Service  
+HZOHWWꢀ3DFNDUGꢁPDLQWDLQVꢁVHUYLFHꢁFHQWHUVꢁLQꢁPDQ\ꢁFRXQWULHVꢂꢁ7KHVHꢁ  
FHQWHUVꢁZLOOꢁUHSDLUꢁDꢁFDOFXODWRUꢃꢁRUꢁUHSODFHꢁLWꢁZLWKꢁWKHꢁVDPHꢁPRGHOꢁRUꢁRQHꢁ  
RIꢁHTXDOꢁRUꢁJUHDWHUꢁYDOXHꢃꢁZKHWKHUꢁLWꢁLVꢁXQGHUꢁZDUUDQW\ꢁRUꢁQRWꢂꢁ7KHUHꢁLVꢁDꢁ  
VHUYLFHꢁFKDUJHꢁIRUꢁVHUYLFHꢁDIWHUꢁWKHꢁZDUUDQW\ꢁSHULRGꢂꢁ&DOFXODWRUVꢁQRUPDOO\ꢁ  
DUHꢁVHUYLFHGꢁDQGꢁUHVKLSSHGꢁZLWKLQꢁILYHꢁZRUNLQJꢁGD\Vꢂ  
Obtaining Service  
In the United States:ꢁ6HQGꢁWKHꢁFDOFXODWRUꢁWRꢁDQꢁDXWKRUL]HGꢁ+3ꢁ  
VHUYLFHꢁFHQWHUꢁOLVWHGꢁRQꢁWKHꢁLQVLGHꢁRIꢁWKHꢁEDFNꢁFRYHUꢂ  
In Europe:ꢁ&RQWDFWꢁ\RXUꢁ+HZOHWWꢀ3DFNDUGꢁVDOHVꢁRIILFHꢁRUꢁGHDOHUꢃꢁRUꢁ  
+HZOHWWꢀ3DFNDUG·Vꢁ(XURSHDQꢁKHDGTXDUWHUVꢁIRUꢁWKHꢁORFDWLRQꢁRIꢁWKHꢁ  
QHDUHVWꢁVHUYLFHꢁFHQWHUꢂꢁ'RꢁQRWꢁVKLSꢁWKHꢁFDOFXODWRUꢁIRUꢁVHUYLFHꢁZLWKRXWꢁILUVWꢁ  
FRQWDFWLQJꢁDꢁ+HZOHWWꢃ3DFNDUGꢁRIILFHꢂ  
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A: Assistance, Batteries, and Service 123  
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124 A: Assistance, Batteries, and Service  
Service Agreements  
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A: Assistance, Batteries, and Service 125  
Japan  
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 and 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.  
End-user terms and conditions  
HP 10B II 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  
126 A: Assistance, Batteries, and Service  
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. Hewlett-Packard 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 Hewlett-Packard 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. 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. 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.  
A: Assistance, Batteries, and Service 127  
B
More About Calculations  
IRR/YR Calculations  
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Possible Outcomes of Calculating IRR/YR  
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B: More About Calculations 129  
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HTXDOVꢀ]HURꢂꢀWKHꢀEHVWꢀHVWLPDWHꢀRIꢀ,55ꢀ<5ꢀLVꢀWKHꢀLQWHUHVWꢀUDWHꢀWKDWꢀ\LHOGVꢀ  
WKHꢀYDOXHꢀIRUꢀ139ꢀFORVHVWꢀWRꢀ]HURꢁ  
130 B: More About Calculations  
Effect of Using Σ– to Correct Data  
7KHꢀ+3ꢀꢉꢊ%,,ꢀVWRUHVꢀWKHꢀVWDWLVWLFDOꢀQXPEHUVꢀLQꢀDQꢀ´DFFXPXODWHGµꢀIDVKLRQꢁꢀ  
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LQWHUPHGLDWHꢀFDOFXODWLRQVꢀZKHQꢀ\RXꢀSUHVVꢀWKHꢀ ꢀNH\ꢁꢀ7KHꢀ  
ꢀNH\ꢀ  
SHUIRUPVꢀWKHꢀRSSRVLWHꢀLQWHUPHGLDWHꢀFDOFXODWLRQVꢀWRꢀHIIHFWLYHO\ꢀUHPRYHꢀDꢀ  
QXPEHUꢀRUꢀSDLUꢀRIꢀQXPEHUVꢀIURPꢀWKHꢀVWRUHGꢀUHVXOWVꢁ  
:KHQꢀFRUUHFWLQJꢀVWDWLVWLFDOꢀGDWDꢂꢀ  
ꢀGRHVꢀQRWꢀGHOHWHꢀURXQGLQJꢀHUURUVꢀ  
WKDWꢀPD\ꢀRFFXUꢀGXULQJꢀWKHꢀLQWHUPHGLDWHꢀFDOFXODWLRQVꢀGRQHꢀE\ꢀ ꢁꢀ7KXVꢂꢀ  
VXEVHTXHQWꢀUHVXOWVꢀIRUꢀFRUUHFWHGꢀGDWDꢀPD\ꢀEHꢀGLIIHUHQWꢀWKDQꢀIRUꢀGDWDꢀWKDWꢀ  
ZDVꢀHQWHUHGꢀRULJLQDOO\ꢀZLWKRXWꢀKDYLQJꢀWRꢀXVHꢀ  
ꢁꢀ+RZHYHUꢂꢀWKHꢀ  
GLIIHUHQFHꢀZLOOꢀQRWꢀEHꢀVHULRXVꢀXQOHVVꢀWKHꢀLQFRUUHFWꢀGDWDꢀKDVꢀDꢀYHU\ꢀODUJHꢀ  
PDJQLWXGHꢀFRPSDUHGꢀZLWKꢀWKHꢀFRUUHFWꢀYDOXHVꢋꢀLQꢀWKLVꢀFDVHꢂꢀ\RXꢀPD\ꢀZDQWꢀ  
WRꢀFOHDUꢀWKHꢀVWDWLVWLFDOꢀUHJLVWHUVꢀDQGꢀUHꢆHQWHUꢀWKHꢀGDWDꢁ  
Range of Numbers  
7KHꢀODUJHVWꢀSRVLWLYHꢀDQGꢀQHJDWLYHꢀQXPEHUVꢀDYDLODEOHꢀRQꢀWKHꢀFDOFXODWRUꢀDUHꢀ  
“ꢀꢌꢁꢌꢌꢌꢌꢌꢌꢌꢌꢌꢌꢌꢀïꢀꢉꢊ ꢋꢀWKHꢀVPDOOHVWꢀSRVLWLYHꢀDQGꢀQHJDWLYHꢀQXPEHUVꢀ  
DYDLODEOHꢀDUHꢀ“ꢉꢀïꢀꢉꢊ ꢁꢀ8QGHUIORZꢀEULHIO\ꢀGLSOD\VꢀUFLOꢀDQGꢀWKHQꢀ  
GLVSOD\Vꢀ]HURꢁꢀ5HIHUꢀWRꢀWKHꢀPHVVDJHVꢀOFLOꢀDQGꢀUFLOꢀLQꢀ´0HVVDJHVµꢀ  
IROORZLQJꢀWKLVꢀDSSHQGL[ꢁ  
B: More About Calculations 131  
Equations  
Margin and Markup Calculations  
35& – &267  
35& – &267  
ꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆ  
ꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆ  
× ꢉꢊꢊ  
0$5 =  
× ꢉꢊꢊ 08 =  
ꢀ
35&  
&267  
Time Value of Money (TVM)  
3D\PHQWꢀ0RGHꢀ)DFWRUꢅꢀ6ꢀ ꢀꢊꢀIRUꢀ(QGꢀPRGHꢋꢀꢉꢀIRUꢀ%HJLQꢀPRGHꢁ  
I/YR  
P/YR  
ꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆꢆ  
Lꢍ =  
–N  
Lꢍ  
ꢉꢊꢊ  
ꢉ – ꢉ ꢎ ꢆꢆꢆꢆꢆꢆꢆꢆ  
Lꢍ × S  
------------------------------------  
0 = PV + ꢉ + --------------- × PMT ×  
Lꢍ  
ꢉꢊꢊ  
-------  
ꢉꢊꢊ  
–N  
Lꢍ  
ꢉꢊꢊ  
+ FV × 1 + -------  
Amortization  
Σ,17   DFFXPXODWHGꢀLQWHUHVW  
Σ351   DFFXPXODWHGꢀSULQFLSDO  
L   SHULRGLFꢀLQWHUHVWꢀUDWH  
%$/ꢀLVꢀLQLWLDOO\ꢀ39ꢀURXQGHGꢀWRꢀWKHꢀFXUUHQWꢀGLVSOD\ꢀVHWWLQJꢁ  
307ꢀLVꢀLQLWLDOO\ꢀ307ꢀURXQGHGꢀWRꢀWKHꢀFXUUHQWꢀGLVSOD\ꢀVHWWLQJꢁ  
, ⁄ <5  
i = -----------------------------  
3 ⁄ <5 × ꢉꢊꢊ  
132 B: More About Calculations  
)RUꢀHDFKꢀSD\PHQWꢀDPRUWL]HGꢅ  
,17ꢂ %$/ꢀïꢀLꢁꢃ,17ꢂꢀLVꢀURXQGHGꢀWRꢀWKHꢀFXUUHQWꢀGLVSOD\ꢀVHWWLQJꢋꢀ  
 
,17·ꢁ ꢀꢊꢀIRUꢀSHULRGꢀꢊꢀLQꢀ%HJLQꢀPRGHꢁꢄ  
,17   ,17ꢂꢁꢃZLWKꢀVLJQꢀRIꢀ307ꢄ  
351   307ꢀꢎꢀ,17ꢂꢁ  
%$/  
Σ,17  
Σ351  
%$/ ꢀꢎꢀ351  
Σ,17 ꢀꢎꢀ,17  
Σ351 ꢀꢎꢀ351  
 
 
 
Interest Rate Conversions  
P ⁄ YR  
120ꢍ  
ꢉꢊꢊ × 3 ⁄ <5  
())ꢍ = 1 + -----------------------------  
– ꢉ × ꢉꢊꢊ  
B: More About Calculations 133  
Cash-Flow Calculations  
Lꢃ   SHULRGLFꢀLQWHUHVWꢀUDWHꢁ  
M   WKHꢀJURXSꢀQXPEHUꢀRIꢀWKHꢀFDVKꢀIORZꢁ  
&)   DPRXQWꢀRIꢀWKHꢀFDVKꢀIORZꢀIRUꢀJURXSꢀMꢁ  
Q   QXPEHUꢀRIꢀWLPHVꢀWKHꢀFDVKꢀIORZꢀRFFXUVꢀIRUꢀJURXSꢀMꢁ  
N   WKHꢀJURXSꢀQXPEHUꢀRIꢀWKHꢀODVWꢀJURXSꢀRIꢀFDVKꢀIORZVꢁ  
1M   
nl ꢀ ꢀWRWDOꢀQXPEHUꢀRIꢀFDVKꢀIORZVꢀSULRUꢀWRꢀJURXSꢀMꢁ  
∑
1 ≤ l < j  
–nj  
Lꢍ  
ꢉꢊꢊ  
1 – 1 + -------  
k
–nj  
Lꢍ  
ꢉꢊꢊ  
-------------------------------------  
NPV = CF0 +  
CF ×  
× 1 + -------  
∑
j
Lꢍ  
-------  
j = 1  
ꢉꢊꢊ  
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UHWXUQꢁ  
134 B: More About Calculations  
Statistics  
[
y
[\  
∑
∑
∑
[ = ------- ꢂꢀy = ------ ꢂꢀ[ = ---------  
Q
Q
\
∑
( [)2  
∑
[ – --------------  
∑
Q
Sx = ------------------------------  
Q – ꢉ  
( y)2  
∑
y – -------------  
∑
Q
Sy = -----------------------------  
Q – ꢉ  
( [)2  
( y)2  
∑
∑
[ – --------------  
y – -------------  
∑
∑
Q
Q
σx = ------------------------------ ꢀσy = ----------------------------- ꢀ  
Q
Q
x y  
∑ ∑  
xy – --------------  
∑
n
r = ---------------------------------------------------------------------------  
( x)2  
( y)2  
∑
∑
x2 – -------------  
y2 – -------------  
∑
∑
n
n
x y  
∑ ∑  
xy – --------------  
∑
n
m = -------------------------------  
( x)2  
∑
x2 – -------------  
∑
n
y – b  
m
ˆ
ˆ
b = y – mx ꢀx = ----------- ꢀy = mx + b  
B: More About Calculations 135  
C
Messages  
3UHVVꢀ ꢀRUꢀ ꢀWRꢀFOHDUꢀDꢀPHVVDJHꢀIURPꢀWKHꢀGLVSOD\ꢁ  
All Clear  
0HPRU\ꢀKDVꢀEHHQꢀHUDVHGꢀꢂSDJH ꢃꢄꢅꢁ  
COPR HP 2000  
&RS\ULJKWꢀPHVVDJHꢁ  
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UHWXUQHGꢀꢂ“ꢈꢁꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈꢈ(ꢉꢈꢈꢅꢁꢀ7KHꢀRYHUIORZꢀPHVVDJHꢀLVꢀDOVRꢀGLVSOD\HGꢀ  
LIꢀDQꢀLQWHUPHGLDWHꢀ790ꢀRUꢀFDVKIORZꢀFDOFXODWLRQꢀUHVXOWVꢀLQꢀDQꢀRYHUIORZꢀ  
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SURGXFHGꢀDꢀQHJDWLYHꢀVROXWLRQꢁꢀ$ꢀSRVLWLYHꢀVROXWLRQꢀDOVRꢀH[LVWVꢀꢂSDJH ꢇꢃꢈꢅꢁ  
C: Messages 137  
running  
ꢂ5XQQLQJꢅꢁꢀ$ꢀFDOFXODWLRQꢀLVꢀLQꢀSURFHVVꢁ  
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ꢂ8QGHUIORZꢅꢁꢀ$QꢀLQWHUPHGLDWHꢀUHVXOWꢀLQꢀ790ꢀLVꢀWRRꢀVPDOOꢀIRUꢀWKHꢀ+3ꢀ  
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138 C: Messages  
Index  
.H\VꢀQRWꢀOLVWHGꢀKHUHꢀFDQꢀEHꢀIRXQGꢀLQꢀWKHꢀ  
DOSKDEHWLFꢀVHFWLRQVꢀRIꢀWKLVꢀLQGH[ꢁ  
A
$GYDQFHꢀSD\PHQWV ꢆꢇ  
ꢆꢈ  
Special Keys  
AMORT ꢂꢆ  
$PRUWL]DWLRQ ꢆꢈ–ꢈꢅ  
EDODQFH ꢆꢈ  
ꢂꢃ  
ꢂꢃ  
ꢂꢃ  
HTXDWLRQV ꢅꢃꢂ  
LQWHUHVW ꢆꢈ  
SULQFLSDO ꢆꢈ  
ꢂꢃ  
ꢄꢂ  
ꢄꢂ  
ꢃꢅ  
ꢂꢄ  
ꢂꢆ  
ꢂꢆ  
ꢂꢃ, ꢂꢇ  
ꢃꢈ, ꢃꢉ  
ꢇꢄ  
UDQJHꢀRIꢀSD\PHQWV ꢆꢊ  
VLQJOHꢀSD\PHQW ꢆꢊ, ꢈꢋ  
$PRUWL]DWLRQꢀDWꢀDꢀJODQFH ꢅꢆ  
$QQXDOꢀHIIHFWLYHꢀUDWH ꢄꢉ  
$QQXDOꢀQRPLQDOꢀUDWH ꢄꢉ  
$QQXDOꢀSHUFHQWDJHꢀUDWH ꢅꢋꢅ  
$QQXDOL]HGꢀ\LHOG ꢊꢄ  
$QQXLW\ ꢆꢂ  
$QQXQFLDWRUV ꢂꢆ  
$35 ꢅꢋꢅ  
$ULWKPHWLF ꢄꢂ  
$ULWKPHWLFꢀRSHUDWRUV ꢂꢃ  
$YHUDJH ꢊꢈ  
ꢃꢃ  
ꢃꢄ  
ꢊꢊ  
ꢊꢊ  
ꢊꢊ  
ꢊꢊ  
ꢊꢊ  
ꢊꢇ  
ꢊꢇ, ꢅꢃꢅ  
ꢊꢊ  
ꢊꢈ  
B
%DFNVSDFH ꢂꢃ  
BAL ꢂꢆ  
%DODQFHꢀRIꢀORDQ ꢆꢈ  
%DOORRQꢀSD\PHQW ꢄꢇ, ꢇꢊ  
%DVLFVꢀDWꢀDꢀJODQFH ꢅꢅ  
%DWWHULHV ꢂꢃ, ꢅꢅꢉ  
LQVWDOOLQJ ꢅꢅꢉ  
ORZꢀSRZHU ꢂꢆ  
ꢊꢈ  
ꢊꢊ  
ꢊꢊ  
Index 139  
ꢇꢄ  
&RVW ꢅꢂ  
BEGIN ꢂꢆ, ꢇꢇ  
%HJLQꢀPRGH ꢇꢇ  
%RUURZLQJꢀHTXLW\ ꢅꢅꢃ  
%X\ꢀRXWꢀYDOXH ꢆꢃ  
&RVWꢀRIꢀQRꢀGLVFRXQW ꢉꢈ  
ꢃꢇ  
&XUVRU ꢂꢇ  
D
C
'HFLPDOꢀSODFHV ꢃꢋ  
'LJLWꢀVHSDUDWRU ꢃꢅ  
'LVFRXQW ꢉꢈ  
'LVFRXQWHGꢀPRUWJDJH ꢉꢉ  
'LVFRXQWLQJꢀFDVKꢀIORZV ꢈꢈ  
ꢃꢋ  
'LVSOD\ꢀFRQWUDVW ꢂꢃ  
'LVSOD\ꢀIRUPDW ꢂꢉ  
'RZQꢀSD\PHQW ꢇꢈ  
ꢂꢇ  
ꢂꢇ  
&DQDGLDQꢀPRUWJDJHV ꢅꢋꢇ  
&DSLWDOL]HGꢀYDOXH ꢆꢃ  
&DVKꢀIORZ ꢅꢊ, ꢄꢈ  
GLDJUDPV ꢄꢇ  
GLVFRXQW ꢈꢈ  
HQWHULQJ ꢈꢊ  
HTXDWLRQV ꢅꢃꢄ  
H[DPSOHV ꢅꢅꢃ  
LQLWLDO ꢈꢈ  
SUREOHPV ꢇꢅ, ꢈꢇ–ꢊꢄ  
UHSODFLQJ ꢈꢉ  
XQHYHQ ꢊꢋ  
YLHZLQJ ꢈꢉ  
E
ꢃꢋ  
ꢄꢂ  
ꢈꢂ  
(IIHFWLYHꢀLQWHUHVW ꢅꢈ  
(QGꢀPRGH ꢇꢇ  
(QYLURQPHQWDOꢀOLPLWV ꢅꢅꢊ  
(TXDWLRQV  
CF ꢂꢆ  
ꢈꢊ  
C-FLOW ꢂꢆ  
DPRUWL]DWLRQ ꢅꢃꢂ  
FDVKꢌIORZꢀFDOFXODWLRQV ꢅꢃꢄ  
LQWHUHVWꢀUDWHꢀFRQYHUVLRQV  
ꢅꢃꢃ  
PDUJLQVꢀDQGꢀPDUNXSV ꢅꢃꢂ  
VWDWLVWLFDO ꢅꢃꢇ  
790 ꢅꢃꢂ  
&KDLQꢀFDOFXODWLRQV ꢂꢄ  
&OHDULQJ  
GLVSOD\ ꢂꢇ  
PHPRU\ ꢂꢇ  
PHVVDJHV ꢂꢇ  
VWDWLVWLFV ꢊꢇ  
790 ꢇꢄ  
ꢂꢇ  
(TXLW\ ꢅꢅꢃ  
ERROR ꢂꢆ  
&RPPDꢀVHSDUDWRU ꢃꢅ, ꢅꢅꢈ  
&RPSRXQGꢀLQWHUHVW ꢄꢊ  
&RPSRXQGLQJꢀSHULRGV  
DQGꢀSD\PHQWꢀSHULRGV ꢈꢃ  
GLIIHUHQWꢀSHULRGV ꢈꢂ  
&RQVWDQWV ꢃꢈ  
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&RUUHODWLRQꢀFRHIILFLHQW ꢅꢉ, ꢊꢊ  
(UURUꢀPHVVDJHV ꢅꢃꢈ  
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F
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140 Index  
)UHTXHQWO\ꢀ$VNHGꢀ4XHVWLRQV ꢅꢅꢈ  
ꢄꢂ  
FULL ꢂꢈ  
/RDQV ꢇꢇ, ꢉꢊ  
FUNC ꢂꢈ  
LQWHUHVWꢌRQO\ ꢅꢋꢂ  
QXPEHUꢀRIꢀSD\PHQWV ꢇꢄ  
RGGꢀILUVWꢀSHULRG ꢅꢋꢃ  
/RJDULWKP ꢄꢂ  
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)XWXUHꢀYDOXH ꢄꢇ, ꢄꢉ  
ꢄꢉ  
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