HP Hewlett Packard Calculator F1902 90001 User Manual
hp 10BII financial calculator  
user’s guide  
Edition 1  
HP part number F1902-90001  
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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  
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Welcome to the HP 10BII  
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Features  
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Welcome to the HP 10BII  
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Contents  
11  
11  
12  
13  
14  
15  
16  
17  
18  
19  
21  
At a Glance...  
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26  
27  
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28  
28  
28  
29  
30  
30  
31  
31  
32  
32  
Getting Started  
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Contents  
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5
2
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33  
33  
33  
34  
34  
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35  
35  
36  
Business Percentages  
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Number Storage and Arithmetic  
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Picturing Financial Problems  
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6
Contents  
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5
53  
53  
54  
55  
55  
60  
63  
67  
72  
72  
73  
Time Value of Money Calculations  
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7
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77  
77  
78  
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Cash Flow Calculations  
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87  
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93  
Statistical Calculations  
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Contents  
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Additional Examples  
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137 Messages  
139 Index  
Contents  
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At a Glance...  
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Percentages—At a Glance...  
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31.82  
&DOFXODWHVꢀPDUJLQꢁ  
,IꢀWKHꢀFRVWꢀLVꢀꢇꢊꢉꢁꢉꢉꢀDQGꢀWKHꢀPDUNXSꢀLVꢀꢋꢋꢆꢌꢀZKDWꢀLVꢀWKHꢀVHOOLQJꢀSULFH"  
20.00  
(QWHUVꢀFRVWꢁ  
33.00  
(QWHUVꢀPDUNXSꢁ  
26.60  
&DOFXODWHVꢀSULFHꢁ  
12 At a Glance...  
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Memory Keys—At a Glance…  
6WRUHVꢀDꢀFRQVWDQWꢀRSHUDWLRQꢁ  
6WRUHVꢀDꢀYDOXHꢀLQꢀWKHꢀ0ꢀUHJLVWHUꢀꢂPHPRU\ꢀORFDWLRQꢃꢁ  
5HFDOOVꢀDꢀYDOXHꢀIURPꢀWKHꢀ0ꢀUHJLVWHUꢁ  
$GGVꢀDꢀYDOXHꢀWRꢀWKHꢀQXPEHUꢀVWRUHGꢀLQꢀWKHꢀ0ꢀUHJLVWHUꢁ  
6WRUHVꢀDꢀYDOXHꢀLQꢀDꢀQXPEHUHGꢀUHJLVWHUꢁ  
5HFDOOVꢀDꢀYDOXHꢀIURPꢀDꢀQXPEHUHGꢀUHJLVWHUꢁ  
0XOWLSO\ꢀꢄꢈꢌꢀꢊꢊꢌꢀDQGꢀꢊꢅꢀE\ꢀꢈꢌꢀVWRULQJꢀ´ïꢀꢈµꢀDVꢀDꢀFRQVWDQWꢀRSHUDWLRQꢁ  
Keys:  
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Description:  
7.00  
6WRUHVꢀ´ïꢀꢈµꢀDVꢀDꢀ  
FRQVWDQWꢀRSHUDWLRQꢁ  
119.00  
154.00  
175.00  
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0XOWLSOLHVꢀꢊꢊꢀïꢀꢈꢁ  
0XOWLSOLHVꢀꢊꢅꢀïꢀꢈꢁ  
6WRUHꢀꢅꢄꢍꢀLQꢀUHJLVWHUꢀꢊꢌꢀWKHQꢀUHFDOOꢀLWꢁ  
519.00  
0.00  
6WRUHVꢀLQꢀUHJLVWHUꢀꢊꢁ  
&OHDUVꢀGLVSOD\ꢁ  
519.00  
5HFDOOVꢀUHJLVWHUꢀꢊꢁ  
At a Glance... 13  
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Time Value of Money (TVM)—At a Glance…  
(QWHUꢀDQ\ꢀIRXUꢀRIꢀWKHꢀILYHꢀYDOXHVꢀDQGꢀVROYHꢀIRUꢀWKHꢀILIWKꢁ  
$ꢀQHJDWLYHꢀVLJQꢀLQꢀWKHꢀGLVSOD\ꢀUHSUHVHQWVꢀPRQH\ꢀSDLGꢀRXWꢎꢀ  
PRQH\ꢀUHFHLYHGꢀLVꢀSRVLWLYHꢁ  
1XPEHUꢀRIꢀSD\PHQWVꢁ  
,QWHUHVWꢀSHUꢀ\HDUꢁ  
3UHVHQWꢀYDOXHꢁ  
3D\PHQWꢁ  
)XWXUHꢀYDOXHꢁ  
%HJLQꢀRUꢀ(QGꢀPRGHꢁ  
1XPEHUꢀRIꢀSD\PHQWVꢀSHUꢀ\HDUꢀPRGHꢁ  
,Iꢀ\RXꢀERUURZꢀꢇꢄꢏꢌꢉꢉꢉꢀꢂ39ꢃꢀIRUꢀꢋꢐꢉꢀPRQWKVꢀꢂ1ꢃꢀDWꢀꢄꢉꢆꢀLQWHUHVWꢀꢂ,ꢑ<5ꢃꢌꢀ  
ZKDWꢀLVꢀWKHꢀPRQWKO\ꢀUHSD\PHQW"  
6HWꢀWRꢀ(QGꢀPRGHꢁꢀ3UHVVꢀ  
ꢀLIꢀBEGIN DQQXQFLDWRUꢀLVꢀGLVSOD\HGꢁ  
Keys:  
Display:  
Description:  
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...  
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TVM What if…—At a Glance…  
,WꢀLVꢀQRWꢀQHFHVVDU\ꢀWRꢀUHHQWHUꢀ790ꢀYDOXHVꢀIRUꢀHDFKꢀH[DPSOHꢁꢀ  
8VLQJꢀWKHꢀYDOXHVꢀ\RXꢀMXVWꢀHQWHUHGꢀꢂSDJH ꢄꢏꢃꢌꢀKRZꢀPXFKꢀFDQꢀ  
\RXꢀERUURZꢀLIꢀ\RXꢀZDQWꢀDꢀSD\PHQWꢀRIꢀꢇꢄꢉꢉꢁꢉꢉ"  
Keys:  
Display:  
Description:  
–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  
&DOFXODWHVꢀRULJLQDOꢀ  
SD\PHQWꢁ  
At a Glance... 15  
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Amortization—At a Glance…  
$IWHUꢀFDOFXODWLQJꢀDꢀSD\PHQWꢀXVLQJꢀ7LPHꢀ9DOXHꢀRIꢀ0RQH\ꢀ  
ꢂ790ꢃꢌꢀHQWHUꢀWKHꢀSHULRGVꢀWRꢀDPRUWL]HꢀDQGꢀSUHVVꢀ ꢁꢀ  
7KHQꢀSUHVVꢀ WRꢀFRQWLQXDOO\ꢀF\FOHꢀWKURXJKꢀWKHꢀSULQFLSDOꢌꢀ  
LQWHUHVWꢌꢀDQGꢀEDODQFHꢀYDOXHVꢀꢂLQGLFDWHGꢀE\ꢀWKHꢀPRINꢌꢀINTꢌꢀ  
DQGꢀBALꢀDQQXQFLDWRUVꢀUHVSHFWLYHO\ꢃꢁ  
8VLQJꢀWKHꢀSUHYLRXVꢀ790ꢀH[DPSOHꢀꢂSDJH ꢄꢏꢃꢌꢀDPRUWL]HꢀDꢀ  
VLQJOHꢀSD\PHQWꢀDQGꢀWKHQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢁ  
$PRUWL]HꢀWKHꢀꢊꢉ ꢀSD\PHQWꢀRIꢀWKHꢀORDQꢁ  
Keys:  
Display:  
Description:  
20.00  
(QWHUVꢀSHULRGꢀWRꢀ  
DPRUWL]Hꢁ  
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  
12_  
(QWHUVꢀUDQJHꢀRIꢀSHULRGVꢀ  
WRꢀDPRUWL]Hꢁ  
1 – 12  
'LVSOD\VꢀUDQJHꢀRIꢀ  
SHULRGVꢀꢂSD\PHQWVꢃꢁ  
–77.82  
'LVSOD\VꢀSULQFLSDOꢁ  
–1,396.50  
'LVSOD\VꢀLQWHUHVWꢁꢀ  
ꢂ0RQH\ꢀSDLGꢀRXWꢀLVꢀ  
QHJDWLYHꢁꢃ  
13,922.18  
'LVSOD\VꢀEDODQFHꢁ  
16 At a Glance...  
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Interest Rate Conversion—At a Glance…  
7RꢀFRQYHUWꢀEHWZHHQꢀQRPLQDOꢀDQGꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHVꢌꢀ  
HQWHUꢀWKHꢀNQRZQꢀUDWHꢀDQGꢀWKHꢀQXPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢌꢀ  
WKHQꢀVROYHꢀIRUꢀWKHꢀXQNQRZQꢀUDWHꢁ  
1RPLQDOꢀLQWHUHVWꢀSHUFHQWꢁ  
(IIHFWLYHꢀLQWHUHVWꢀSHUFHQWꢁ  
3HULRGVꢀSHUꢀ\HDUꢁ  
)LQGꢀWKHꢀDQQXDOꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHꢀRIꢀꢄꢉꢆꢀQRPLQDOꢀLQWHUHVWꢀ  
FRPSRXQGHGꢀPRQWKO\ꢁ  
Keys:  
Display:  
10.00  
Description:  
(QWHUVꢀQRPLQDOꢀUDWHꢁ  
12.00  
(QWHUVꢀSD\PHQWVꢀSHUꢀ  
\HDUꢁ  
10.47  
&DOFXODWHVꢀDQQXDOꢀ  
HIIHFWLYHꢀLQWHUHVWꢁ  
At a Glance... 17  
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IRR/YR and NPV—At a Glance…  
1XPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢀꢂGHIDXOWꢀLVꢀꢄꢊꢃꢁ  
&DVKꢀIORZVꢌꢀXSꢀWRꢀꢄꢅꢀꢂ´MµꢀLGHQWLILHVꢀWKHꢀFDVKꢀIORZꢀQXPEHUꢃꢁ  
1XPEHUꢀRIꢀFRQVHFXWLYHꢀWLPHVꢀFDVKꢀIORZꢀ´MµꢀRFFXUVꢁ  
,QWHUQDOꢀUDWHꢀRIꢀUHWXUQꢀSHUꢀ\HDUꢁ  
1HWꢀSUHVHQWꢀYDOXHꢁ  
,Iꢀ\RXꢀKDYHꢀDQꢀLQLWLDOꢀFDVKꢀRXWIORZꢀRIꢀꢇꢏꢉꢌꢉꢉꢉꢌꢀIROORZHGꢀE\ꢀPRQWKO\ꢀFDVKꢀ  
LQIORZVꢀRIꢀꢇꢏꢌꢈꢉꢉꢌꢀꢇꢈꢌꢉꢉꢉꢌꢀꢇꢈꢌꢉꢉꢉꢌꢀDQGꢀꢇꢊꢋꢌꢉꢉꢉꢌꢀZKDWꢀLVꢀWKHꢀ,55ꢀ<5"ꢀ  
:KDWꢀLVꢀWKHꢀ,55ꢀSHUꢀPRQWK"  
Keys:  
Display:  
0.00  
Description:  
&OHDUVꢀDOOꢀPHPRU\ꢁ  
12.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢁ  
(QWHUVꢀLQLWLDOꢀRXWIORZꢁ  
(QWHUVꢀILUVWꢀFDVKꢀIORZꢁ  
(QWHUVꢀVHFRQGꢀFDVKꢀIORZꢁ  
(QWHUVꢀQXPEHUꢀRIꢀFRQVHFꢒ  
XWLYHꢀWLPHVꢀFDVKꢀIORZꢀ  
RFFXUVꢁ  
–40,000.00  
4,700.00  
7,000.00  
2.00  
23,000.00  
15.96  
(QWHUVꢀWKLUGꢀFDVKꢀIORZꢁ  
&DOFXODWHVꢀ,55ꢀ<5ꢁ  
1.33  
&DOFXODWHVꢀ,55ꢀSHUꢀ  
PRQWKꢁ  
:KDWꢀLVꢀWKHꢀ139ꢀLIꢀWKHꢀGLVFRXQWꢀUDWHꢀLVꢀꢄꢉꢆ"  
10.00  
(QWHUVꢀ,ꢀ<5ꢁ  
622.85  
&DOFXODWHVꢀ139ꢁ  
18 At a Glance...  
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Statistics—At a Glance…  
&OHDUꢀVWDWLVWLFDOꢀUHJLVWHUVꢁ  
QXPEHUꢁ  
QXPEHUꢁ  
QXPEHUꢂꢁ  
QXPEHUꢂꢁ  
(QWHUꢀRQHꢒYDULDEOHꢀVWDWLVWLFDOꢀGDWDꢁ  
'HOHWHꢀRQHꢒYDULDEOHꢀVWDWLVWLFDOꢀGDWDꢁ  
(QWHUꢀWZRꢒYDULDEOHꢀVWDWLVWLFDOꢀGDWDꢁ  
'HOHWHꢀWZRꢒYDULDEOHꢀVWDWLVWLFDOꢀGDWDꢁ  
0HDQVꢀRIꢀ[ꢀDQGꢀ\ꢁ  
ꢀ
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QXPEHUꢃꢁ  
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3RSXODWLRQꢀVWDQGDUGꢀGHYLDWLRQVꢀRIꢀ[ꢀDQGꢀ\ꢁ  
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8VLQJꢀWKHꢀIROORZLQJꢀGDWDꢌꢀILQGꢀWKHꢀPHDQVꢀRIꢀ[ꢀDQGꢀ\ꢌꢀWKHꢀVDPSOHꢀVWDQGDUGꢀ  
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x-data  
y-data  
2
4
6
50  
90  
160  
At a Glance... 19  
Download from Www.Somanuals.com. All Manuals Search And Download.  
Keys:  
Display:  
0.00  
Description:  
&OHDUVꢀVWDWLVWLFVꢀUHJLVWHUVꢁ  
(QWHUVꢀILUVWꢀ[ꢅ\ꢀSDLUꢁ  
(QWHUVꢀVHFRQGꢀ[ꢅ\ꢀSDLUꢁ  
(QWHUVꢀWKLUGꢀ[ꢅ\ꢀSDLUꢁ  
'LVSOD\VꢀPHDQꢀRIꢀ[ꢁ  
'LVSOD\VꢀPHDQꢀRIꢀ\ꢁ  
1.00  
2.00  
3.00  
4.00  
100.00  
2.00  
'LVSOD\VꢀVDPSOHꢀVWDQꢒ  
GDUGꢀGHYLDWLRQꢀRIꢀ[ꢁ  
55.68  
'LVSOD\VꢀVDPSOHꢀVWDQꢒ  
GDUGꢀGHYLDWLRQꢀRIꢀ\ꢁ  
–10.00  
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UHJUHVVLRQꢀOLQHꢀꢂSUHꢒ  
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27.50  
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3.00  
'LVSOD\VꢀQꢌꢀQXPEHUꢀRIꢀ  
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1,420.00  
'LVSOD\VꢀΣ[\ꢌꢀVXPꢀRIꢀWKHꢀ  
SURGXFWVꢀRIꢀ[ꢒꢀDQGꢀ  
\ꢒYDOXHVꢁ  
20 At a Glance...  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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  
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1
Getting Started  
Power On and Off  
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RUꢀ ꢄ  
Simple Arithmetic Calculations  
Arithmetic Operators. 7KHꢀIROORZLQJꢀH[DPSOHVꢀGHPRQVWUDWHꢀXVLQJꢀWKHꢀ  
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ꢀ ꢃꢀDOOꢀDUHꢀLJQRUHGꢀH[FHSWꢀWKHꢀODVWꢀRQHꢄ  
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1: Getting Started 23  
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Keys:  
Display:  
Description:  
87.18  
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Negative Numbers. (QWHUꢀWKHꢀQXPEHUꢀDQGꢀSUHVVꢀ ꢀWRꢀFKDQJHꢀWKHꢀVLJQꢄꢀ  
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24 1: Getting Started  
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Understanding the Display and Keyboard  
Cursor  
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Clearing Memory  
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1: Getting Started 25  
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Annunciators  
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Annunciator  
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SHIFT  
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INPUT  
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26 1: Getting Started  
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Annunciator  
FULL  
Status (Continued)  
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Statistics Key  
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:KHQꢀ\RXꢀSUHVVꢀ ꢃꢀWKHꢀVWDWLVWLFVꢀDQQXQFLDWRUꢀꢅSTATSꢆꢀLVꢀ  
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DJDLQꢄ  
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1: Getting Started 27  
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INPUT Key  
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SWAP Key  
3UHVVLQJꢀ  
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Math Functions  
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28 1: Getting Started  
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Two-Number Functions. :KHQꢀDꢀIXQFWLRQꢀUHTXLUHVꢀWZRꢀ  
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Keys:  
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70.59  
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Display Format of Numbers  
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1: Getting Started 29  
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Specifying Displayed Decimal Places  
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Keys:  
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SODFHVꢄ  
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Scientific Notation  
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30 1: Getting Started  
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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  
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RUꢀꢁꢄꢂꢂꢂꢄꢂꢂꢂꢃꢂꢂꢄ  
1: Getting Started 31  
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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  
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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  
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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  
$GGVꢀꢉꢐꢊꢄꢇꢂꢀDQGꢀ  
ꢉꢁꢃꢆꢇꢂꢄꢂꢂꢀWRꢀVKRZꢀ  
UHSD\PHQWꢀDPRXQWꢄ  
Percent Change  
&DOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀWZRꢀQXPEHUVꢀꢋQ DQGꢀ  
Q ꢃꢀH[SUHVVHGꢀDVꢀDꢀSHUFHQWꢀRIꢀQ ꢌꢀE\ꢀHQWHULQJꢀQ ꢀQ ꢃꢀWKHQꢀ  
SUHVVꢀ  
ꢄ
Example. &DOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀꢆꢍꢁꢄꢊꢀDQGꢀ  
ꢎꢁꢏꢄꢐꢄ  
Keys:  
Display:  
Description:  
291.70  
(QWHUVꢀQ ꢄ  
8.60  
&DOFXODWHVꢀSHUFHQWꢀ  
FKDQJHꢄ  
Example. &DOFXODWHꢀWKHꢀSHUFHQWꢀFKDQJHꢀEHWZHHQꢀꢋꢁꢆꢀïꢀꢇꢌꢀDQGꢀꢋꢏꢇꢀꢑꢀꢁꢐꢌꢄ  
Keys:  
Display:  
Description:  
60.00  
&DOFXODWHVꢀDQGꢀHQWHUVꢀQ ꢄ  
38.33  
&DOFXODWHVꢀSHUFHQWꢀ  
FKDQJHꢄ  
34 2: Business Percentages  
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Margin and Markup Calculations  
7KHꢀ+3ꢀꢁꢂ%,,ꢀFDQꢀFDOFXODWHꢀFRVWꢃꢀVHOOLQJꢀSULFHꢃꢀPDUJLQꢃꢀRUꢀPDUNXSꢄ  
Application  
0DUJLQ  
Keys  
Description  
0DUJLQꢀLVꢀPDUNXSꢀH[SUHVVHGꢀDVꢀ  
DꢀSHUFHQWꢀRIꢀSULFHꢄ  
0DUNXSꢀFDOFXODWLRQVꢀDUHꢀ  
H[SUHVVHGꢀDVꢀDꢀSHUFHQWꢀRIꢀFRVWꢄ  
,
,
,
0DUNXS  
,
7RꢀVHHꢀDQ\ꢀYDOXHꢀXVHGꢀE\ꢀWKHꢀ0DUJLQꢀDQGꢀ0DUNXSꢀDSSOLFDWLRQꢃꢀSUHVVꢀ  
DQGꢀWKHQꢀWKHꢀNH\ꢀ\RXꢀZLVKꢀWRꢀVHHꢄꢀ)RUꢀH[DPSOHꢃꢀWRꢀVHHꢀWKHꢀYDOXHꢀVWRUHGꢀDVꢀ  
ꢃꢀSUHVVꢀ ꢄꢀ0DUJLQꢀDQGꢀ0DUNXSꢀVKDUHꢀWKHꢀVDPHꢀVWRUDJHꢀUHJLVWHUꢄꢀ  
ꢀ
)RUꢀH[DPSOHꢃꢀLIꢀ\RXꢀVWRUHꢀꢆꢂꢀLQꢀ ꢃꢀWKHQꢀSUHVVꢀ  
GLVSOD\HGꢄꢀ  
ꢃꢀ\RXꢀZLOOꢀVHHꢀꢆꢂꢄꢂꢂꢀ  
Margin Calculations  
Example. .LORZDWWꢀ(OHFWURQLFVꢀSXUFKDVHVꢀWHOHYLVLRQVꢀIRUꢀꢉꢆꢇꢇꢄꢀ7KHꢀ  
WHOHYLVLRQVꢀDUHꢀVROGꢀIRUꢀꢉꢎꢂꢂꢄꢀ:KDWꢀLVꢀWKHꢀPDUJLQ"  
Keys:  
Display:  
255.00  
Description:  
6WRUHVꢀFRVWꢀLQꢀ&67ꢄ  
300.00  
6WRUHVꢀVHOOLQJꢀSULFHꢀLQꢀ  
35&ꢄ  
15.00  
&DOFXODWHVꢀPDUJLQꢄ  
Markup on Cost Calculations  
Example. 7KHꢀVWDQGDUGꢀPDUNXSꢀRQꢀFRVWXPHꢀMHZHOU\ꢀDWꢀ.OHLQHU·Vꢀ  
.RVPHWLTXHꢀLVꢀꢏꢂꢈꢄꢀ7KH\ꢀMXVWꢀUHFHLYHGꢀDꢀVKLSPHQWꢀRIꢀFKRNHUVꢀFRVWLQJꢀ  
ꢉꢁꢍꢄꢂꢂꢀHDFKꢄꢀ:KDWꢀLVꢀWKHꢀUHWDLOꢀSULFHꢀSHUꢀFKRNHU"  
Keys:  
Display:  
19.00  
Description:  
6WRUHVꢀFRVWꢄ  
60.00  
6WRUHVꢀPDUNXSꢄ  
&DOFXODWHVꢀUHWDLOꢀSULFHꢄ  
30.40  
2: Business Percentages 35  
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Using Margin and Markup Together  
Example.$ꢀ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  
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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  
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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  
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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  
$GGVꢀꢇꢏꢅꢋꢉꢀWRꢀ0ꢀ  
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16.95  
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48 4: Picturing Financial Problems  
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4: Picturing Financial Problems 49  
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4: Picturing Financial Problems 51  
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5: Time Value of Money Calculations 53  
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54 5: Time Value of Money Calculations  
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GLVSOD\HGꢀZKHQꢀ\RXUꢀFDOFXODWRUꢀLVꢀLQꢀ%HJLQꢀPRGHꢄꢀ1RꢀDQQXQFLDWRUꢀLVꢀ  
GLVSOD\HGꢀZKHQꢀ\RXꢀDUHꢀLQꢀ(QGꢀPRGHꢄꢀ  
0RUWJDJHVꢀDQGꢀORDQVꢀW\SLFDOO\ꢀXVHꢀ(QGꢀPRGHꢄꢀ/HDVHVꢀDQGꢀVDYLQJVꢀSODQVꢀ  
W\SLFDOO\ꢀXVHꢀ%HJLQꢀPRGHꢄ  
Loan Calculations  
Example: A Car Loan. <RXꢀDUHꢀILQDQFLQJꢀDꢀQHZꢀFDUꢀZLWKꢀDꢀWKUHHꢀ\HDUꢀ  
ORDQꢀDWꢀꢋꢌꢄꢍꢎꢀDQQXDOꢀQRPLQDOꢀLQWHUHVWꢃꢀFRPSRXQGHGꢀPRQWKO\ꢄꢀ7KHꢀSULFHꢀ  
RIꢀWKHꢀFDUꢀLVꢀꢏꢋꢐꢃꢍꢌꢌꢄꢀ<RXUꢀGRZQꢀSD\PHQWꢀLVꢀꢏꢋꢃꢍꢌꢌꢄ  
Part 1. :KDWꢀDUHꢀ\RXUꢀPRQWKO\ꢀSD\PHQWVꢀDWꢀꢋꢌꢄꢍꢎꢀLQWHUHVW"ꢀꢁ$VVXPHꢀ  
\RXUꢀSD\PHQWVꢀVWDUWꢀRQHꢀPRQWKꢀDIWHUꢀWKHꢀSXUFKDVHꢀRUꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀ  
ILUVWꢀSHULRGꢄꢂ  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄꢀ  
5: Time Value of Money Calculations 55  
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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  
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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  
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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  
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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  
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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  
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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  
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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  
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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  
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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  
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Example: Lease With Advance Payments. <RXUꢀFRPSDQ\ꢃꢀ4XLFNꢉ.LWꢀ  
3ROHꢀ%DUQVꢃꢀSODQVꢀWRꢀOHDVHꢀDꢀIRUNOLIWꢀIRUꢀWKHꢀZDUHKRXVHꢄꢀ7KHꢀOHDVHꢀLVꢀZULWWHQꢀ  
IRUꢀDꢀWHUPꢀRIꢀꢐꢀ\HDUVꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢀRIꢀꢏꢈꢃꢐꢌꢌꢄꢀ3D\PHQWVꢀDUHꢀGXHꢀ  
DWꢀWKHꢀEHJLQQLQJꢀRIꢀWKHꢀPRQWKꢀZLWKꢀWKHꢀILUVWꢀDQGꢀODVWꢀSD\PHQWVꢀGXHꢀDWꢀWKHꢀ  
RQVHWꢀRIꢀWKHꢀOHDVHꢄꢀ<RXꢀKDYHꢀDQꢀRSWLRQꢀWRꢀEX\ꢀWKHꢀIRUNOLIWꢀIRUꢀꢏꢋꢍꢃꢌꢌꢌꢀDWꢀ  
WKHꢀHQGꢀRIꢀWKHꢀOHDVLQJꢀSHULRGꢄ  
,IꢀWKHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀLVꢀꢒꢎꢃꢀZKDWꢀLVꢀWKHꢀFDSLWDOL]HGꢀYDOXHꢀRIꢀWKHꢀOHDVH"  
7KLVꢀVROXWLRQꢀUHTXLUHVꢀIRXUꢀVWHSVꢄ  
ꢀꢁ &DOFXODWHꢀWKHꢀSUHVHQWꢀYDOXHꢀRIꢀWKHꢀꢐꢇꢀPRQWKO\ꢀSD\PHQWVꢅꢀ  
ꢁꢐꢀïꢀꢋꢈꢂꢀ²ꢀꢋꢀ ꢀꢐꢇꢄ  
ꢂꢁ $GGꢀWKHꢀYDOXHꢀRIꢀWKHꢀDGGLWLRQDOꢀDGYDQFHꢀSD\PHQWꢄ  
ꢃꢁ )LQGꢀWKHꢀSUHVHQWꢀYDOXHꢀRIꢀWKHꢀEX\ꢀRSWLRQꢄ  
ꢄꢁ 6XPꢀWKHꢀYDOXHVꢀFDOFXODWHGꢀLQꢀVWHSVꢀꢈꢀDQGꢀꢑꢄ  
Step 1ꢄꢀ)LQGꢀWKHꢀSUHVHQWꢀYDOXHꢀRIꢀWKHꢀPRQWKO\ꢀSD\PHQWVꢄ  
6HWꢀWRꢀ%HJLQꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀDQQXQFLDWRUꢀLVꢀQRWꢀGLVSOD\HGꢄ  
5: Time Value of Money Calculations 65  
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Keys:  
Display:  
12.00  
Description:  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
47.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
SD\PHQWVꢄ  
–2,400.00  
6WRUHVꢀPRQWKO\ꢀ  
SD\PHQWꢄ  
0.00  
6WRUHVꢀ)9ꢀIRUꢀVWHSꢀꢋꢄ  
9.00  
6WRUHVꢀLQWHUHVWꢀUDWHꢄ  
95,477.55  
&DOFXODWHVꢀSUHVHQWꢀ  
YDOXHꢀRIꢀꢐꢇꢀPRQWKO\ꢀ  
SD\PHQWVꢄ  
Step 2. $GGꢀWKHꢀDGGLWLRQDOꢀDGYDQFHꢀSD\PHQWꢀWRꢀ39ꢄꢀ6WRUHꢀWKHꢀDQVZHUꢄ  
97,877.55  
$GGVꢀDGGLWLRQDOꢀ  
DGYDQFHꢀSD\PHQWꢄ  
97,877.55  
6WRUHVꢀUHVXOWꢀLQꢀ0ꢀ  
UHJLVWHUꢄ  
Step 3. )LQGꢀWKHꢀSUHVHQWꢀYDOXHꢀRIꢀWKHꢀEX\ꢀRSWLRQꢄ  
48.00  
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EX\ꢀRSWLRQꢀRFFXUVꢄ  
0.00  
6WRUHVꢀ]HURꢀSD\PHQWꢀ  
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–15,000.00  
6WRUHVꢀYDOXHꢀWRꢀ  
GLVFRXQWꢄ  
10,479.21  
&DOFXODWHVꢀSUHVHQWꢀ  
YDOXHꢀRIꢀODVWꢀFDVKꢀIORZꢄ  
Step 4. $GGꢀWKHꢀUHVXOWVꢀRIꢀVWHSVꢀꢈꢀDQGꢀꢑꢄ  
Keys:  
Display:  
Description:  
108,356.77  
&DOFXODWHVꢀSUHVHQWꢀ  
ꢁFDSLWDOL]HGꢂꢀYDOXHꢀRIꢀ  
OHDVHꢄꢀꢁ5RXQGLQJꢀ  
GLVFUHSDQFLHVꢀDUHꢀ  
H[SODLQHGꢀRQꢀSDJH ꢍꢒꢄꢂ  
66 5: Time Value of Money Calculations  
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Amortization  
$PRUWL]DWLRQꢀLVꢀWKHꢀSURFHVVꢀRIꢀGLYLGLQJꢀDꢀSD\PHQWꢀLQWRꢀWKHꢀ  
DPRXQWꢀWKDWꢀDSSOLHVꢀWRꢀLQWHUHVWꢀDQGꢀWKHꢀDPRXQWꢀWKDWꢀ  
DSSOLHVꢀWRꢀSULQFLSDOꢄꢀ3D\PHQWVꢀQHDUꢀWKHꢀEHJLQQLQJꢀRIꢀDꢀORDQꢀ  
FRQWULEXWHꢀPRUHꢀLQWHUHVWꢃꢀDQGꢀOHVVꢀSULQFLSDOꢃꢀWKDQꢀSD\PHQWVꢀ  
QHDUꢀWKHꢀHQGꢀRIꢀDꢀORDQꢄ  
7KHꢀ  
7KHꢀ  
ꢀNH\ꢀRQꢀWKHꢀ+3ꢀꢋꢌ%,,ꢀDOORZVꢀ\RXꢀWRꢀFDOFXODWHꢄ  
7KHꢀDPRXQWꢀDSSOLHGꢀWRꢀLQWHUHVWꢀLQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢄ  
7KHꢀDPRXQWꢀDSSOLHGꢀWRꢀSULQFLSDOꢀLQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢄ  
7KHꢀORDQꢁEDODQFHꢀDIWHUꢀDꢀVSHFLILHGꢀQXPEHUꢀRIꢀSD\PHQWVꢀDUHꢀPDGHꢄ  
ꢀIXQFWLRQꢀDVVXPHVꢀ\RXꢀKDYHꢀMXVWꢀFDOFXODWHGꢀDꢀSD\PHQWꢀRUꢀ\RXꢀ  
KDYHꢀVWRUHGꢀWKHꢀDSSURSULDWHꢀDPRUWL]DWLRQꢀYDOXHVꢀLQꢀ,ꢀ<5ꢃꢀ39ꢃꢀ)9ꢃꢀ307ꢃꢀ  
DQGꢀ3ꢀ<5ꢄ  
5: Time Value of Money Calculations 67  
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$QQXDOꢀQRPLQDOꢀLQWHUHVWꢀUDWHꢄ  
6WDUWLQJꢀEDODQFHꢄ  
(QGLQJꢀEDODQFHꢄ  
3D\PHQWꢀDPRXQWꢀꢁURXQGHGꢀWRꢀWKHꢀGLVSOD\ꢀIRUPDWꢂꢄ  
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  
ꢄꢀ7KHꢀ+3ꢀꢋꢌ%,,ꢀGLVSOD\VꢀWKHꢀDQQXQFLDWRUꢀ  
PERꢀIROORZHGꢀE\ꢀWKHꢀVWDUWLQJꢀDQGꢀHQGLQJꢀSD\PHQWVꢀWKDWꢀZLOOꢀEHꢀ  
DPRUWL]HGꢄꢀ7KHQꢀSUHVVꢀ ꢀUHSHDWHGO\ꢀWRꢀF\FOHꢀWKURXJKꢀLQWHUHVWꢃꢀSULQFLSDOꢃꢀ  
DQGꢀEDODQFHꢄ  
3UHVVꢀ  
ꢀDJDLQꢀWRꢀPRYHꢀWRꢀWKHꢀQH[WꢀVHWꢀRIꢀSHULRGVꢄꢀ7KLVꢀDXWRꢉ  
LQFUHPHQWꢀIHDWXUHꢀVDYHVꢀ\RXꢀWKHꢀNH\VWURNHVꢀRIꢀHQWHULQJꢀWKHꢀQHZꢀVWDUWLQJꢀ  
DQGꢀHQGLQJꢀSHULRGVꢄ  
,Iꢀ\RXꢀVWRUHꢃꢀUHFDOOꢃꢀRUꢀSHUIRUPꢀDQ\ꢀRWKHUꢀFDOFXODWLRQVꢀGXULQJꢀ  
DPRUWL]DWLRQꢃꢀSUHVVLQJꢀ ꢀZLOOꢀQRꢀORQJHUꢀF\FOHꢀWKURXJKꢀLQWHUHVWꢃꢀSULQFLSDOꢃꢀ  
DQGꢀEDODQFHꢄꢀ7RꢀUHVXPHꢀDPRUWL]DWLRQꢀZLWKꢀWKHꢀVDPHꢀVHWꢀRIꢀSHULRGVꢃꢀSUHVVꢀ  
ꢄ
Example: Amortizing a Range of Payments. &DOFXODWHꢀWKHꢀILUVWꢀWZRꢀ  
\HDUVꢀRIꢀWKHꢀDQQXDOꢀDPRUWL]DWLRQꢀVFKHGXOHꢀIRUꢀDꢀꢑꢌꢀ\HDUꢃꢀꢏꢋꢓꢌꢃꢌꢌꢌꢀ  
PRUWJDJHꢃꢀDWꢀꢇꢄꢇꢍꢎꢀDQQXDOꢀLQWHUHVWꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢄ  
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢄꢀ  
68 5: Time Value of Money Calculations  
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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%$/ꢀ  
DQQXQFLDWRUꢀDQGꢀWKHꢀ  
ORDQꢀEDODQFHꢀDIWHUꢀRQHꢀ  
\HDUꢄ  
7KHꢀDPRXQWꢀSDLGꢀWRZDUGꢀLQWHUHVWꢀDQGꢀSULQFLSDOꢀꢁꢋꢑꢃꢓꢒꢐꢄꢆꢇꢀꢔꢀꢋꢃꢍꢇꢒꢄꢓꢐꢀ ꢀ  
ꢋꢍꢃꢐꢇꢐꢄꢍꢋꢂꢀHTXDOVꢀWKHꢀWRWDOꢀRIꢀꢋꢈꢀPRQWKO\ꢀSD\PHQWVꢀꢁꢋꢈꢀïꢀꢋꢃꢈꢓꢒꢄꢍꢐꢀ ꢀ  
ꢋꢍꢃꢐꢇꢐꢄꢍꢋꢂꢄꢀ7KHꢀUHPDLQLQJꢀEDODQFHꢀHTXDOVꢀWKHꢀLQLWLDOꢀPRUWJDJHꢃꢀOHVVꢀWKHꢀ  
DPRXQWꢀDSSOLHGꢀWRZDUGꢀSULQFLSDOꢀꢁꢋꢓꢌꢃꢌꢌꢌꢀ²ꢀꢋꢃꢍꢇꢒꢄꢓꢐꢀ ꢀꢋꢇꢓꢃꢐꢈꢌꢄꢋꢆꢂꢄ  
5: Time Value of Money Calculations 69  
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$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:  
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Description:  
12.00  
60.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ  
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11.50  
6WRUHVꢀLQWHUHVWꢀSHUꢀ\HDUꢄ  
6WRUHVꢀSUHVHQWꢀYDOXHꢄ  
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70 5: Time Value of Money Calculations  
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25.00  
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–90.21  
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5: Time Value of Money Calculations 71  
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Interest Rate Conversions  
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72 5: Time Value of Money Calculations  
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First Bank  
Keys:  
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6.65  
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12.00  
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6.86  
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6.63  
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360.00  
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6.85  
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5: Time Value of Money Calculations 73  
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74 5: Time Value of Money Calculations  
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6
Cash Flow Calculations  
How to Use the Cash Flow Application  
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6: Cash Flow Calculations 75  
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76 6: Cash Flow Calculations  
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NPV and IRR/YR: Discontinuing Cash Flows  
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6: Cash Flow Calculations 77  
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78 6: Cash Flow Calculations  
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6: Cash Flow Calculations 79  
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80 6: Cash Flow Calculations  
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6: Cash Flow Calculations 81  
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82 6: Cash Flow Calculations  
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6: Cash Flow Calculations 83  
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84 6: Cash Flow Calculations  
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7: Statistical Calculations 85  
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86 7: Statistical Calculations  
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92 7: Statistical Calculations  
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Weighted Mean  
7KHꢀIROORZLQJꢀSURFHGXUHꢀFDOFXODWHVꢀWKHꢀZHLJKWHGꢀPHDQꢀRIꢀGDWDꢀSRLQWVꢀ[ ꢃꢀ  
[ ꢃꢀ«ꢃꢀ[ ꢀRFFXUULQJꢀZLWKꢀZHLJKWVꢀ\ ꢃꢀ\ ꢃꢀ«ꢃꢀ\ ꢂ  
ꢀꢁ 8VHꢀ ꢀDQGꢀ ꢀWRꢀHQWHUꢀ[ꢃ\ꢀSDLUVꢂꢀ7KHꢀ\ꢁYDOXHVꢀDUHꢀWKHꢀZHLJKWVꢀRIꢀ  
WKHꢀ[ꢁYDOXHVꢂ  
ꢂꢁ 3UHVVꢀ  
ꢂ
Example. $ꢀVXUYH\ꢀRIꢀꢌꢒꢒꢀRQHꢁEHGURRPꢀUHQWDOꢀDSDUWPHQWVꢀUHYHDOVꢀWKDWꢀ  
ꢋꢊꢀRIꢀWKHPꢀUHQWꢀIRUꢀꢓꢋꢆꢆꢀSHUꢀPRQWKꢃꢀꢍꢌꢀIRUꢀꢓꢋꢆꢋꢃꢀꢐꢐꢀIRUꢀꢓꢋꢅꢆꢃꢀDQGꢀꢏꢌꢀIRUꢀ  
ꢓꢋꢅꢒꢂꢀ:KDWꢀLVꢀWKHꢀDYHUDJHꢀPRQWKO\ꢀUHQW"  
Keys:  
Display:  
Description:  
0.00  
&OHDUVꢀVWDWLVWLFVꢀ  
PHPRU\ꢂ  
1.00  
(QWHUVꢀILUVWꢀUHQWꢀDQGꢀLWVꢀ  
ZHLJKWꢂ  
2.00  
(QWHUVꢀVHFRQGꢀUHQWꢀDQGꢀ  
LWVꢀZHLJKWꢂ  
3.00  
(QWHUVꢀWKLUGꢀUHQWꢀDQGꢀ  
LWVꢀZHLJKWꢂ  
4.00  
(QWHUVꢀIRXUWKꢀUHQWꢀDQGꢀ  
LWVꢀZHLJKWꢂ  
509.44  
&DOFXODWHVꢀZHLJKWHGꢀ  
PHDQꢂ  
7: Statistical Calculations 93  
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8
Additional Examples  
Business Applications  
Setting a Sales Price  
2QHꢀPHWKRGꢀIRUꢀVHWWLQJꢀWKHꢀSHUꢀXQLWꢀVDOHVꢀSULFHꢀLVꢀWRꢀGHWHUPLQHꢀWKHꢀFRVWꢀRIꢀ  
SURGXFWLRQꢀSHUꢀXQLWꢁꢀDQGꢀWKHQꢀPXOWLSO\ꢀE\ꢀWKHꢀGHVLUHGꢀUDWHꢀRIꢀUHWXUQꢂꢀ)RUꢀ  
WKLVꢀPHWKRGꢀWRꢀEHꢀDFFXUDWHꢁꢀ\RXꢀPXVWꢀLGHQWLI\ꢀDOOꢀFRVWVꢀDVVRFLDWHGꢀZLWKꢀWKHꢀ  
SURGXFWꢂ  
7KHꢀIROORZLQJꢀHTXDWLRQꢀFDOFXODWHVꢀXQLWꢀSULFHꢀEDVHGꢀRQꢀWRWDOꢀFRVWꢀDQGꢀUDWHꢀ  
RIꢀUHWXUQꢃ  
35,&(ꢀ ꢀ727$/ꢀ&267ꢀ÷ꢀ180%(5ꢀ2)ꢀ81,76ꢀïꢀꢄꢅꢀꢆꢀꢄꢀ571ꢀ÷ꢀꢅꢇꢇꢈꢈ  
Example. 7RꢀSURGXFHꢀꢉꢁꢇꢇꢇꢀXQLWVꢁꢀ\RXUꢀFRVWꢀLVꢀꢊꢋꢇꢁꢇꢇꢇꢂꢀ<RXꢀZDQWꢀDꢀꢉꢇꢌꢀ  
UDWHꢀRIꢀUHWXUQꢂꢀ:KDWꢀSULFHꢀVKRXOGꢀ\RXꢀFKDUJHꢀSHUꢀXQLW"  
Keys:  
Display:  
40,000.00  
20.00  
Description:  
(QWHUVꢀFRVWꢂ  
&DOFXODWHVꢀXQLWꢀFRVWꢂ  
24.00  
&DOFXODWHVꢀXQLWꢀVDOHVꢀ  
SULFHꢂ  
8: Additional Examples 95  
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Forecasting Based on History  
2QHꢀPHWKRGꢀRIꢀIRUHFDVWLQJꢀVDOHVꢁꢀPDQXIDFWXULQJꢀUDWHVꢁꢀRUꢀH[SHQVHVꢀLVꢀ  
UHYLHZLQJꢀKLVWRULFDOꢀWUHQGVꢂꢀ2QFHꢀ\RXꢀKDYHꢀKLVWRULFDOꢀGDWDꢁꢀWKHꢀGDWDꢀDUHꢀILWꢀ  
WRꢀDꢀFXUYHꢀWKDWꢀKDVꢀWLPHꢀRQꢀWKHꢀ[ꢍD[LVꢀDQGꢀTXDQWLW\ꢀRQꢀWKHꢀ\ꢍD[LVꢂ  
Example. *LYHQꢀWKHꢀIROORZLQJꢀVDOHVꢀGDWDꢁꢀZKDWꢀDUHꢀWKHꢀVDOHVꢀHVWLPDWHVꢀIRUꢀ  
\HDUVꢀVL[ꢀDQGꢀVHYHQ"  
Year  
Sales $  
1
2
3
4
5
10,000  
11,210  
13,060  
16,075  
20,590  
Keys:  
Display:  
Description:  
0.00  
1.00  
&OHDUVꢀVWDWLVWLFVꢀUHJLVWHUVꢂ  
(QWHUVꢀILUVWꢀ\HDUꢀDQGꢀVDOHVꢀ  
IRUꢀWKDWꢀ\HDUꢂ  
2.00  
(QWHUVꢀVHFRQGꢀ\HDU·VꢀGDWDꢂ  
&RQWLQXHVꢀGDWDꢀHQWU\ꢂ  
3.00  
4.00  
5.00  
22,000.50  
(VWLPDWHVꢀVDOHVꢀIRUꢀ\HDUꢀ  
VL[ꢂ  
24,605.00  
(VWLPDWHVꢀVDOHVꢀIRUꢀ\HDUꢀ  
VHYHQꢂ  
96 8: Additional Examples  
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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  
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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  
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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  
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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  
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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  
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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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
Loan With a Partial (Odd) First Period  
790ꢀFDOFXODWLRQVꢀDSSO\ꢀWRꢀILQDQFLDOꢀWUDQVDFWLRQVꢀZKHUHꢀHDFKꢀSD\PHQWꢀ  
SHULRGꢀLVꢀWKHꢀVDPHꢀOHQJWKꢂꢀ+RZHYHUꢁꢀVLWXDWLRQVꢀH[LVWꢀZKHUHꢀWKHꢀILUVWꢀ  
SD\PHQWꢀSHULRGꢀLVꢀQRWꢀWKHꢀVDPHꢀOHQJWKꢀDVꢀWKHꢀUHPDLQLQJꢀSHULRGVꢂꢀ7KLVꢀILUVWꢀ  
SHULRGꢀLVꢀVRPHWLPHVꢀFDOOHGꢀDQꢀRGGꢀRUꢀSDUWLDOꢁILUVWꢁSHULRGꢂ  
,IꢀLQWHUHVWꢀLVꢀDSSOLHGꢀWRꢀDQꢀRGGꢀILUVWꢀSHULRGꢁꢀLWꢀLVꢀXVXDOO\ꢀFDOFXODWHGꢀDVꢀ  
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DQꢀRGGꢀILUVWꢀSHULRGꢀLVꢀDꢀWZRꢀVWHSꢀSURFHVVꢃ  
ꢀꢁ &DOFXODWHꢀWKHꢀDPRXQWꢀRIꢀVLPSOHꢀLQWHUHVWꢀWKDWꢀDFFUXHVꢀGXULQJꢀWKHꢀ  
IUDFWLRQDOꢀILUVWꢀSHULRGꢀDQGꢀDGGꢀLWꢀWRꢀWKHꢀORDQꢀDPRXQWꢂꢀ7KLVꢀLVꢀWKHꢀQHZꢀ  
39ꢂꢀ<RXꢀPXVWꢀEHꢀDEOHꢀWRꢀFDOFXODWHꢀWKHꢀOHQJWKꢀRIꢀWKHꢀRGGꢀILUVWꢀSHULRGꢀ  
DVꢀDꢀIUDFWLRQꢀRIꢀWKHꢀZKROHꢀSHULRGꢂꢀꢄ)RUꢀH[DPSOHꢁꢀDꢀꢅꢑꢍGD\ꢀRGGꢀILUVWꢀ  
SHULRGꢀZRXOGꢀEHꢀꢇꢂꢑꢀSHULRGVꢀDVVXPLQJꢀDꢀZKROHꢀSHULRGꢀWRꢀEHꢀDꢀꢏꢇꢍGD\ꢀ  
PRQWKꢂꢈ  
ꢂꢁ &DOFXODWHꢀWKHꢀSD\PHQWꢀXVLQJꢀWKHꢀQHZꢀ39ꢁꢀZLWKꢀ1ꢀHTXDOꢀWRꢀWKHꢀ  
QXPEHUꢀRIꢀIXOOꢀSHULRGVꢂꢀ8VHꢀ%HJLQꢀPRGHꢀLIꢀWKHꢀQXPEHUꢀRIꢀGD\VꢀXQWLOꢀ  
WKHꢀILUVWꢀSD\PHQWꢀLVꢀOHVVꢀWKDQꢀꢏꢇꢔꢀRWKHUZLVHꢀXVHꢀ(QGꢀPRGHꢂ  
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ILUVWꢀPRQWKO\ꢀSD\PHQWꢀLVꢀPDGHꢀLQꢀꢋꢐꢀGD\VꢁꢀZKDWꢀLVꢀWKHꢀPRQWKO\ꢀSD\PHQWꢀ  
DPRXQWꢀDVVXPLQJꢀꢏꢇꢍGD\ꢀPRQWKV"  
7KHꢀRGGꢀILUVWꢀSHULRGꢀLQꢀWKLVꢀH[DPSOHꢀLVꢀꢅꢐꢀGD\Vꢂ  
6HWꢀWRꢀ(QGꢀPRGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
12.00  
15.00  
1.25  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀLQWHUHVWꢀUDWHꢂ  
&DOFXODWHVꢀSHULRGLFꢀ  
LQWHUHVWꢀUDWHꢂ  
0.67  
0XOWLSOLHVꢀE\ꢀIUDFWLRQꢀ  
RIꢀDꢀSHULRGꢂ  
30.00  
&DOFXODWHVꢀDPRXQWꢀRIꢀ  
VLPSOHꢀLQWHUHVWꢀRZHGꢀ  
IRUꢀRGGꢀSHULRGꢂ  
4,530.00  
$GGVꢀWKLVꢀVLPSOHꢀ  
LQWHUHVWꢀWRꢀSUHVHQWꢀ  
YDOXHꢂ  
8: Additional Examples 103  
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36.00  
0.00  
6WRUHVꢀWHUPꢀRIꢀORDQꢂ  
(QWHUVꢀDPRXQWꢀOHIWꢀWRꢀ  
SD\ꢀDIWHUꢀꢏꢐꢀSD\PHQWVꢂ  
–157.03  
&DOFXODWHVꢀSD\PHQWꢀ  
DPRXQWꢂ  
Automobile Loan  
Example. <RXꢀDUHꢀEX\LQJꢀDꢀQHZꢀꢊꢅꢋꢁꢇꢇꢇꢂꢇꢇꢀVHGDQꢂꢀ<RXUꢀGRZQꢀSD\PHQWꢀ  
LVꢀꢊꢅꢁꢑꢇꢇꢀDQGꢀ\RXꢀDUHꢀJRLQJꢀWRꢀILQDQFHꢀWKHꢀUHPDLQLQJꢀꢊꢅꢉꢁꢑꢇꢇꢂꢀ7KHꢀFDUꢀ  
GHDOHUꢀLVꢀRIIHULQJꢀWZRꢀFKRLFHVꢀIRUꢀILQDQFLQJꢃ  
$ꢀꢏꢍ\HDUꢀORDQꢀZLWKꢀDQꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀRIꢀꢏꢂꢑꢌꢂ  
$ꢀꢏꢍ\HDUꢀORDQꢀZLWKꢀDQꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀRIꢀꢕꢂꢑꢌꢀDQGꢀDꢀꢊꢅꢁꢇꢇꢇꢂꢇꢇꢀ  
UHEDWHꢂ  
:LWKꢀZKLFKꢀFKRLFHꢀGRꢀ\RXꢀSD\ꢀOHVVꢀIRUꢀWKHꢀFDU"  
6HWꢀWRꢀ(QGꢀPRGHꢂꢀ3UHVVꢀ  
&DOFXODWHꢀWKHꢀILUVWꢀRSWLRQꢃ  
Keys:  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Display:  
12.00  
Description:  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀNQRZQꢀYDOXHVꢂ  
36.00  
12,500.00  
0.00  
3.50  
6WRUHVꢀILUVWꢀLQWHUHVWꢀ  
UDWHꢂ  
–366.28  
&DOFXODWHVꢀSD\PHQWꢂ  
–13,185.94  
&DOFXODWHVꢀWRWDOꢀLQWHUHVWꢀ  
DQGꢀSULQFLSDOꢂ  
104 8: Additional Examples  
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&DOFXODWHꢀWKHꢀVHFRQGꢀRSWLRQꢃ  
Keys: Display:  
Description:  
11,500.00  
6WRUHVꢀORDQꢀDPRXQWꢀZLWKꢀ  
UHEDWHꢂ  
9.50  
6WRUHVꢀVHFRQGꢀLQWHUHVWꢀUDWHꢂ  
&DOFXODWHVꢀSD\PHQWꢂ  
&DOFXODWHVꢀWRWDOꢀLQWHUHVWꢀDQGꢀ  
SULQFLSDOꢂ  
–368.38  
–13,261.64  
7KHꢀILUVWꢀRSWLRQꢀFRVWVꢀVOLJKWO\ꢀOHVVꢂ  
Canadian Mortgages  
,Qꢀ&DQDGLDQꢀPRUWJDJHVꢁꢀWKHꢀFRPSRXQGLQJꢀDQGꢀSD\PHQWꢀSHULRGVꢀDUHꢀQRWꢀ  
WKHꢀVDPHꢂꢀ,QWHUHVWꢀLVꢀFRPSRXQGHGꢀVHPLꢍDQQXDOO\ꢀZKLOHꢀSD\PHQWVꢀDUHꢀ  
PDGHꢀPRQWKO\ꢂꢀ7RꢀXVHꢀWKHꢀ790ꢀDSSOLFDWLRQꢀLQꢀWKHꢀ+3ꢀꢅꢇ%,,ꢁꢀ\RXꢀQHHGꢀWRꢀ  
FDOFXODWHꢀDꢀ&DQDGLDQꢁPRUWJDJHꢁIDFWRUꢀꢄZKLFKꢀLVꢀDQꢀDGMXVWHGꢀLQWHUHVWꢀUDWHꢈꢀWRꢀ  
VWRUHꢀLQꢀ,ꢂ<5ꢂ  
)RUꢀDGGLWLRQDOꢀLQIRUPDWLRQꢀRQꢀLQWHUHVWꢀUDWHꢀFRQYHUVLRQVꢁꢀVHHꢀ´,QWHUHVWꢀ  
5DWHꢀ&RQYHUVLRQVµꢀRQꢀSDJH ꢒꢉꢂ  
Example. :KDWꢀLVꢀWKHꢀPRQWKO\ꢀSD\PHQWꢀUHTXLUHGꢀWRꢀIXOO\ꢀDPRUWL]HꢀDꢀꢏꢇꢍ  
\HDUꢁꢀꢊꢅꢏꢇꢁꢇꢇꢇꢀ&DQDGLDQꢀPRUWJDJHꢀLIꢀWKHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀLVꢀꢅꢉꢌ"  
Keys:  
Display:  
Description:  
12.00  
2.00  
6WRUHVꢀNQRZQꢀQRPLQDOꢀ  
SHUFHQWDJHꢀDQGꢀQXPEHUꢀRIꢀ  
FRPSRXQGLQJꢀSHULRGVꢂ  
12.36  
&DOFXODWHVꢀDQQXDOꢀHIIHFWLYHꢀ  
UDWHꢂ  
12.00  
11.71  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
&DOFXODWHVꢀ&DQDGLDQꢁPRUWJDJHꢁ  
IDFWRUꢀꢄDGMXVWHGꢀLQWHUHVWꢀUDWHꢈꢂ  
130,000  
6WRUHVꢀRWKHUꢀNQRZQꢀYDOXHVꢀ  
IRUꢀPRUWJDJHꢂ  
360.00  
–1,308.30  
&DOFXODWHVꢀPRQWKO\ꢀSD\PHQWꢀ  
IRUꢀ&DQDGLDQꢀPRUWJDJHꢂ  
8: Additional Examples 105  
Download from Www.Somanuals.com. All Manuals Search And Download.  
What if … TVM Calculations  
2QHꢀRIꢀWKHꢀPRVWꢀYDOXDEOHꢀDVSHFWVꢀRIꢀWKHꢀ+3ꢀꢅꢇ%,,·Vꢀ790ꢀDSSOLFDWLRQꢀLVꢀ  
WKHꢀHDVHꢀZLWKꢀZKLFKꢀLWꢀKDQGOHVꢀWKHꢀTXHVWLRQꢀ´ZKDWꢀLIꢀ«µꢀLQꢀILQDQFLDOꢀ  
FDOFXODWLRQVꢂꢀ)RUꢀH[DPSOHꢁꢀRQHꢀRIꢀWKHꢀPRVWꢀSRSXODUꢀ´ZKDWꢀLIꢀ«µꢀ  
TXHVWLRQVꢀLVꢁꢀ´:KDWꢀLIꢀWKHꢀLQWHUHVWꢀUDWHꢀFKDQJHVꢀWRꢀ«"ꢀ+RZꢀZLOOꢀWKDWꢀDIIHFWꢀ  
P\ꢀSD\PHQW"µꢀ7RꢀDQVZHUꢀWKLVꢀTXHVWLRQꢁꢀRQFHꢀ\RXꢀKDYHꢀFDOFXODWHGꢀDꢀ  
SD\PHQWꢀEDVHGꢀRQꢀRQHꢀLQWHUHVWꢀUDWHꢁꢀDOOꢀ\RXꢀQHHGꢀWRꢀGRꢀLVꢀHQWHUꢀWKHꢀQHZꢀ  
LQWHUHVWꢀUDWHꢀDQGꢀUHFDOFXODWHꢀ307ꢂ  
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HQFRXQWHUVꢀZLWKꢀ´ZKDWꢀLIꢀ«µꢀTXHVWLRQVꢁꢀEXWꢀDꢀPRUHꢀFRPSOHWHꢀH[DPSOHꢀ  
IROORZVꢂ  
Example. <RXꢀDUHꢀDERXWꢀWRꢀVLJQꢀRQꢀWKHꢀGRWWHGꢀOLQHꢀIRUꢀDꢀꢏꢇꢍ\HDUꢁꢀ  
ꢊꢒꢏꢑꢁꢇꢇꢇꢀPRUWJDJHꢁꢀRQꢀDꢀYDFDWLRQꢀKRPHꢂꢀ7KHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀLVꢀ  
ꢅꢅꢂꢉꢌꢂ  
Part 1. :KDWꢀZLOOꢀ\RXUꢀSD\PHQWVꢀEHꢀDWꢀWKHꢀHQGꢀRIꢀWKHꢀPRQWK"  
6HWꢀWRꢀ(QGꢀPRGHꢂꢀ3UHVVꢀ  
ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ  
Keys:  
Display:  
Description:  
12.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀNQRZQꢀYDOXHVꢂ  
735,000.00  
11.20  
360.00  
0.00  
–7,110.88  
&DOFXODWHVꢀSD\PHQWꢂ  
106 8: Additional Examples  
Download from Www.Somanuals.com. All Manuals Search And Download.  
Part 2. <RXUꢀFRPSDQ\·VꢀUHJXODUꢀSD\UROOꢀLVꢀJHQHUDWHGꢀHYHU\ꢀRWKHUꢀ)ULGD\ꢂꢀ  
7KHꢀEDQNꢀDJUHHVꢀWRꢀDXWRPDWLFDOO\ꢀGUDZꢀSD\PHQWVꢀRIꢀꢊꢏꢁꢑꢑꢑꢂꢇꢇꢀRXWꢀRIꢀHDFKꢀ  
SD\FKHFNꢀꢄDSSUR[LPDWHO\ꢀKDOIꢀRIꢀZKDWꢀDꢀPRQWKO\ꢀSD\PHQWꢀZRXOGꢀEHꢈꢀDQGꢀ  
DGMXVWꢀWKHꢀSD\PHQWꢀSHULRGꢀDFFRUGLQJO\ꢀꢄꢉꢐꢀFRPSRXQGLQJꢀSHULRGVꢀSHUꢀ  
\HDUꢈꢂꢀ:KDWꢀZRXOGꢀEHꢀWKHꢀQHZꢀWHUPꢀRIꢀWKHꢀORDQ"  
–3,555.00  
(QWHUVꢀQHZꢀSD\PHQWꢂ  
26.00  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢀ  
IRUꢀHYHU\ꢀWZRꢀZHHNVꢂ  
514.82  
&DOFXODWHVꢀQXPEHUꢀRIꢀ  
ELZHHNO\ꢀSD\PHQWVꢂ  
19.80  
'LVSOD\Vꢀ\HDUVꢀUHTXLUHGꢀ  
WRꢀSD\ꢀRIIꢀORDQꢂ  
Part 3. :KDWꢀLIꢀ\RXꢀKDGꢀPRQWKO\ꢀSD\PHQWVꢀDVꢀLQꢀSDUWꢀꢅꢁꢀEXWꢀFKRVHꢀDꢀꢅꢑꢍ  
\HDUꢀWHUP"ꢀ:KDWꢀZRXOGꢀ\RXUꢀQHZꢀSD\PHQWꢀEH"ꢀ:KDWꢀZRXOGꢀEHꢀWKHꢀWRWDOꢀ  
LQWHUHVWꢀSDLGꢀRQꢀWKHꢀFRQWUDFW"  
Keys:  
Display:  
12.00  
Description:  
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ  
6WRUHVꢀQHZꢀWHUPꢂ  
180.00  
–8,446.53  
&DOFXODWHVꢀSD\PHQWꢀIRUꢀ  
VKRUWHUꢀWHUPꢂ  
–1,520,374.70  
–785,374.70  
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'LVSOD\VꢀWRWDOꢀLQWHUHVWꢀ  
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8: Additional Examples 107  
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Savings  
Saving for College Costs  
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9.00  
6WRUHVꢀDQQXDOꢀQRPLQDOꢀ  
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12.00  
6WRUHVꢀQXPEHUꢀRIꢀ  
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UDWHꢂ  
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HIIHFWLYHꢀUDWHꢂ  
108 8: Additional Examples  
Download from Www.Somanuals.com. All Manuals Search And Download.  
:KHQꢀFRPSRXQGLQJꢀRFFXUVꢀRQO\ꢀRQFHꢀSHUꢀ\HDUꢁꢀWKHꢀHIIHFWLYHꢀUDWHꢀDQGꢀWKHꢀ  
QRPLQDOꢀUDWHꢀDUHꢀWKHꢀVDPHꢂ  
9.38  
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1.00  
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15,000.00  
4.00  
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8: Additional Examples 109  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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144.00  
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110 8: Additional Examples  
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8: Additional Examples 111  
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Value of a Taxable Retirement Account  
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112 8: Additional Examples  
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Cash Flow Examples  
Wrap-Around Mortgages  
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180.00  
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8: Additional Examples 113  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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114 8: Additional Examples  
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Net Future Value  
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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  
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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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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  
VRPHWKLQJꢁLQFRUUHFWO\ꢂꢁ+RZꢁFDQꢁ,ꢁGHWHUPLQHꢁLIꢁWKHꢁFDOFXODWRUꢁLVꢁRSHUDWLQJꢁ  
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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
Q: :KDWꢁGRHVꢁDQꢁ´(µꢁLQꢁDꢁQXPEHUꢁꢆIRUꢁH[DPSOHꢃꢁꢅꢂꢊꢄ(²ꢄꢇꢈꢁPHDQ"  
A: ([SRQHQWꢁRIꢁWHQꢁꢆIRUꢁH[DPSOHꢃꢁꢅꢂꢊꢄꢁïꢁꢄꢉ ꢈꢂꢁ5HIHUꢁWRꢁ´6FLHQWLILFꢁ  
1RWDWLRQµꢁRQꢁSDJH ꢇꢉꢂ  
Q: :K\ꢁGRꢁ,ꢁJHWꢁDꢁZURQJꢁDQVZHUꢁRUꢁWKHꢁNo Solution PHVVDJHꢁ  
ZKHQꢁXVLQJꢁ790"  
A: %HꢁVXUHꢁWRꢁHQWHUꢁDꢁYDOXHꢁIRUꢁIRXUꢁRIꢁWKHꢁILYHꢁ790ꢁYDOXHVꢁEHIRUHꢁ\RXꢁ  
VROYHꢁIRUꢁWKHꢁILIWKꢃꢁHYHQꢁLIꢁRQHꢁRIꢁWKHꢁYDOXHVꢁLVꢁ]HURꢂꢁꢆ'RQ·WꢁIRUJHWꢁWRꢁVWRUHꢁ  
Dꢁ]HURꢁIRUꢁ ꢁLIꢁ\RXꢁFRPSOHWHO\ꢁSD\ꢁRIIꢁDꢁORDQꢂꢈꢁ&OHDULQJꢁDOOꢁWKHꢁUHJLVWHUVꢁ  
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ꢈꢁEHIRUHꢁHQWHULQJꢁ\RXUꢁNQRZQꢁYDOXHVꢁDFFRPSOLVKHVꢁWKHꢁVDPHꢁWKLQJꢂꢁ  
&KHFNꢁWRꢁVHHꢁWKDWꢁWKHꢁFDOFXODWRUꢁLVꢁLQꢁWKHꢁDSSURSULDWHꢁSD\PHQWꢁPRGHꢁ  
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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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):  
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,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  
Download from Www.Somanuals.com. All Manuals Search And Download.  
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  
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A: Assistance, Batteries, and Service 123  
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124 A: Assistance, Batteries, and Service  
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Service Agreements  
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A: Assistance, Batteries, and Service 125  
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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  
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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  
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IRR/YR Calculations  
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Possible Outcomes of Calculating IRR/YR  
7KHVHꢀDUHꢀWKHꢀSRVVLEOHꢀRXWFRPHVꢀRIꢀDQꢀ,55ꢀ<5ꢀFDOFXODWLRQꢅ  
Case 1.ꢀ7KHꢀFDOFXODWRUꢀGLVSOD\VꢀDꢀSRVLWLYHꢀDQVZHUꢁꢀ7KLVꢀLVꢀWKHꢀRQO\ꢀ  
SRVLWLYHꢀDQVZHUꢁꢀ+RZHYHUꢂꢀRQHꢀRUꢀPRUHꢀQHJDWLYHꢀDQVZHUVꢀPD\ꢀH[LVWꢁ  
Case 2.ꢀ7KHꢀFDOFXODWRUꢀILQGVꢀDꢀQHJDWLYHꢀDQVZHUꢀEXWꢀDꢀVLQJOHꢀSRVLWLYHꢀ  
DQVZHUꢀDOVRꢀH[LVWVꢁꢀ,WꢀGLVSOD\VꢅꢀPos Irr Alsoꢁꢀ7RꢀVHHꢀWKHꢀQHJDWLYHꢀ  
DQVZHUꢂꢀSUHVVꢀ ꢀWRꢀFOHDUꢀWKHꢀPHVVDJHꢁꢀ7RꢀVHDUFKꢀIRUꢀWKHꢀSRVLWLYHꢀ  
DQVZHUꢂꢀ\RXꢀPXVWꢀLQSXWꢀDꢀJXHVVꢁꢀꢃ5HIHUꢀWRꢀ´(QWHULQJꢀDꢀ*XHVVꢀIRUꢀ  
,55ꢀ<5ꢂµꢀEHORZꢄꢁꢀ7KHUHꢀPLJKWꢀDOVRꢀEHꢀDGGLWLRQDOꢀQHJDWLYHꢀDQVZHUVꢁ  
Case 3.ꢀ7KHꢀFDOFXODWRUꢀGLVSOD\VꢀDꢀQHJDWLYHꢀDQVZHUꢀDQGꢀQRꢀPHVVDJHꢁ  
7KLVꢀLVꢀWKHꢀRQO\ꢀDQVZHUꢁ  
Case 4.ꢀ7KHꢀFDOFXODWRUꢀGLVSOD\VꢀWKHꢀPHVVDJHꢅꢀNot Foundꢁꢀ7KLVꢀ  
LQGLFDWHVꢀWKDWꢀWKHꢀFDOFXODWLRQꢀLVꢀYHU\ꢀFRPSOH[ꢁꢀ,WꢀPLJKWꢀLQYROYHꢀPRUHꢀ  
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7RꢀFRQWLQXHꢀWKHꢀFDOFXODWLRQꢂꢀ\RXꢀPXVWꢀVWRUHꢀDꢀJXHVVꢀꢃVHHꢀEHORZꢄꢁ  
B: More About Calculations 129  
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Case 5.ꢀ7KHꢀFDOFXODWRUꢀGLVSOD\VꢅꢀNo Solutionꢁꢀ7KHUHꢀLVꢀQRꢀDQVZHUꢁꢀ  
7KLVꢀVLWXDWLRQꢀPLJKWꢀEHꢀWKHꢀUHVXOWꢀRIꢀDQꢀHUURUꢂꢀVXFKꢀDVꢀDꢀPLVWDNHꢀLQꢀ  
NH\LQJꢀLQꢀWKHꢀFDVKꢀIORZVꢁꢀ$ꢀFRPPRQꢀPLVWDNHꢀWKDWꢀUHVXOWVꢀLQꢀWKLVꢀ  
PHVVDJHꢀLVꢀSXWWLQJꢀWKHꢀZURQJꢀVLJQꢀRQꢀDꢀFDVKꢀIORZꢁꢀ$ꢀYDOLGꢀFDVKꢆIORZꢀ  
VHULHVꢀIRUꢀDQꢀ,55ꢀ<5ꢁFDOFXODWLRQꢀPXVWꢀKDYHꢀDWꢀOHDVWꢀRQHꢀSRVLWLYHꢀDQGꢀ  
RQHꢀQHJDWLYHꢀFDVKꢀIORZꢁ  
Halting and Restarting IRR/YR  
7KHꢀVHDUFKꢀIRUꢀ,55ꢀ<5ꢀPD\ꢀWDNHꢀDꢀUHODWLYHO\ꢀORQJꢀWLPHꢁꢀ<RXꢀFDQꢀKDOWꢀWKHꢀ  
FDOFXODWLRQꢀDWꢀDQ\ꢀWLPHꢀE\ꢀSUHVVLQJꢀWKHꢀ ꢀNH\ꢁꢀ7KHꢀPHVVDJHꢀInterruptedꢀLVꢀ  
GLVSOD\HGꢁꢀ3UHVVLQJꢀ ꢀQRZꢀGLVSOD\VꢀWKHꢀFXUUHQWꢀHVWLPDWHꢀIRUꢀ,55ꢀ<5ꢁꢀ  
<RXꢀFDQꢀUHVXPHꢀWKHꢀFDOFXODWLRQꢀE\ꢅ  
3UHVVLQJꢀ  
ꢀZKLOHꢀWKHꢀFXUUHQWꢀHVWLPDWHꢀLVꢀGLVSOD\HGꢀLQꢀWKHꢀ  
FDOFXODWRUꢀOLQHꢁꢀ7KLVꢀFRQWLQXHVꢀWKHꢀFDOFXODWLRQꢀIURPꢀZKHUHꢀLWꢀOHIWꢀRIIꢁ  
6WRULQJꢀDꢀJXHVVꢀIRUꢀ,55ꢀ<5ꢂꢀGLVFXVVHGꢀEHORZꢁ  
Entering a Guess for IRR/YR  
7RꢀHQWHUꢀDꢀJXHVVꢂꢀNH\ꢀLQꢀDQꢀHVWLPDWHꢀRIꢀ,55ꢀ<5ꢀDQGꢀWKHQꢀSUHVVꢀ  
ꢁꢀ<RXꢀFDQꢀHQWHUꢀDꢀJXHVVꢀIRUꢀ,55ꢀ<5ꢀDWꢀWKHVHꢀWLPHVꢅ  
%HIRUHꢀEHJLQQLQJꢀWKHꢀFDOFXODWLRQꢁꢀ$ꢀIDLUO\ꢀDFFXUDWHꢀJXHVVꢀFDQꢀUHGXFHꢀ  
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$IWHUꢀ\RX·YHꢀLQWHUUXSWHGꢀWKHꢀFDOFXODWLRQꢁ  
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DQRWKHUꢀVROXWLRQꢀE\ꢀKDOWLQJꢀWKHꢀFDOFXODWLRQꢀDQGꢀHQWHULQJꢀDꢀGLIIHUHQWꢀJXHVVꢁ  
2QHꢀZD\ꢀWRꢀREWDLQꢀDꢀJRRGꢀJXHVVꢀIRUꢀ,55ꢀ<5ꢀLVꢀWRꢀFDOFXODWHꢀWKHꢀ139ꢀIRUꢀ  
YDULRXVꢀLQWHUHVWꢀUDWHVꢁꢀ6LQFHꢀ,55ꢀ<5ꢀLVꢀWKHꢀLQWHUHVWꢀUDWHꢀDWꢀZKLFKꢀ139ꢀ  
HTXDOVꢀ]HURꢂꢀWKHꢀEHVWꢀHVWLPDWHꢀRIꢀ,55ꢀ<5ꢀLVꢀWKHꢀLQWHUHVWꢀUDWHꢀWKDWꢀ\LHOGVꢀ  
WKHꢀYDOXHꢀIRUꢀ139ꢀFORVHVWꢀWRꢀ]HURꢁ  
130 B: More About Calculations  
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Effect of Using Σ– to Correct Data  
7KHꢀ+3ꢀꢉꢊ%,,ꢀVWRUHVꢀWKHꢀVWDWLVWLFDOꢀQXPEHUVꢀLQꢀDQꢀ´DFFXPXODWHGµꢀIDVKLRQꢁꢀ  
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LQWHUPHGLDWHꢀFDOFXODWLRQVꢀZKHQꢀ\RXꢀSUHVVꢀWKHꢀ ꢀNH\ꢁꢀ7KHꢀ  
ꢀNH\ꢀ  
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:KHQꢀFRUUHFWLQJꢀVWDWLVWLFDOꢀGDWDꢂꢀ  
ꢀGRHVꢀQRWꢀGHOHWHꢀURXQGLQJꢀHUURUVꢀ  
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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  
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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  
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)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  
())ꢍ = 1 + -----------------------------  
ꢉꢊꢊ × 3 ⁄ <5  
– ꢉ × ꢉꢊꢊ  
B: More About Calculations 133  
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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  
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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  
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C
Messages  
3UHVVꢀ ꢀRUꢀ ꢀWRꢀFOHDUꢀDꢀPHVVDJHꢀIURPꢀWKHꢀGLVSOD\ꢁ  
All Clear  
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COPR HP 2000  
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