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
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HEWLETT-PACKARD
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WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL,
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prohibited without prior written permission of Hewlett-Packard Company,
except as allowed under the copyright laws.
Hewlett-Packard Company
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Suite 301
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Printing History
Edition 1
May 2003
Welcome to the HP 10BII
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Welcome to the HP 10BII
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Features
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Welcome to the HP 10BII
Contents
11
11
12
13
14
15
16
17
18
19
21
At a Glance...
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Getting Started
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Contents
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33
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36
Business Percentages
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Number Storage and Arithmetic
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Picturing Financial Problems
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Contents
5
53
53
54
55
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67
72
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Time Value of Money Calculations
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Cash Flow Calculations
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Statistical Calculations
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Contents
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95
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Additional Examples
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137 Messages
139 Index
Contents
9
At a Glance...
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At a Glance... 11
Percentages—At a Glance...
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6WRUHꢀꢅꢄꢍꢀLQꢀUHJLVWHUꢀꢊꢌꢀWKHQꢀUHFDOOꢀLWꢁ
519.00
0.00
6WRUHVꢀLQꢀUHJLVWHUꢀꢊꢁ
&OHDUVꢀGLVSOD\ꢁ
519.00
5HFDOOVꢀUHJLVWHUꢀꢊꢁ
At a Glance... 13
Time Value of Money (TVM)—At a Glance…
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Description:
12.00
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢁ
360.00
(QWHUVꢀQXPEHUꢀRIꢀ
SD\PHQWVꢁ
10.00
(QWHUVꢀLQWHUHVWꢀSHUꢀ
\HDUꢁ
14,000.00
0.00
(QWHUVꢀSUHVHQWꢀYDOXHꢁ
(QWHUVꢀIXWXUHꢀYDOXHꢁ
–122.86
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SDLGꢀDWꢀHQGꢀRIꢀSHULRGꢁ
14 At a Glance...
TVM What if…—At a Glance…
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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
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YDOXHꢀIRUꢀꢇꢄꢉꢉꢁꢉꢉꢀ
SD\PHQWꢀDQGꢀꢍꢁꢅꢆꢀ
LQWHUHVWꢁ
10.00
5HHQWHUVꢀRULJLQDOꢀ
LQWHUHVWꢀUDWHꢁ
14,000.00
–122.86
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At a Glance... 15
Amortization—At a Glance…
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7KHQꢀSUHVVꢀ WRꢀFRQWLQXDOO\ꢀF\FOHꢀWKURXJKꢀWKHꢀSULQFLSDOꢌꢀ
LQWHUHVWꢌꢀDQGꢀEDODQFHꢀYDOXHVꢀꢂLQGLFDWHGꢀE\ꢀWKHꢀPRINꢌꢀINTꢌꢀ
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8VLQJꢀWKHꢀSUHYLRXVꢀ790ꢀH[DPSOHꢀꢂSDJH ꢄꢏꢃꢌꢀDPRUWL]HꢀDꢀ
VLQJOHꢀSD\PHQWꢀDQGꢀWKHQꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢁ
$PRUWL]HꢀWKHꢀꢊꢉ ꢀSD\PHQWꢀRIꢀWKHꢀORDQꢁ
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Description:
20.00
(QWHUVꢀSHULRGꢀWRꢀ
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20 – 20
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DPRUWL]Hꢁ
–7.25
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–115.61
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13,865.83
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$PRUWL]HꢀWKHꢀꢄ ꢀWKURXJKꢀꢄꢊ ꢀORDQꢀSD\PHQWVꢁ
12_
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WRꢀDPRUWL]Hꢁ
1 – 12
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–1,396.50
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13,922.18
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16 At a Glance...
Interest Rate Conversion—At a Glance…
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HQWHUꢀWKHꢀNQRZQꢀUDWHꢀDQGꢀWKHꢀQXPEHUꢀRIꢀSHULRGVꢀSHUꢀ\HDUꢌꢀ
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3HULRGVꢀSHUꢀ\HDUꢁ
)LQGꢀWKHꢀDQQXDOꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHꢀRIꢀꢄꢉꢆꢀQRPLQDOꢀLQWHUHVWꢀ
FRPSRXQGHGꢀPRQWKO\ꢁ
Keys:
Display:
10.00
Description:
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12.00
(QWHUVꢀSD\PHQWVꢀSHUꢀ
\HDUꢁ
10.47
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HIIHFWLYHꢀLQWHUHVWꢁ
At a Glance... 17
IRR/YR and NPV—At a Glance…
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,QWHUQDOꢀUDWHꢀRIꢀUHWXUQꢀSHUꢀ\HDUꢁ
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LQIORZVꢀRIꢀꢇꢏꢌꢈꢉꢉꢌꢀꢇꢈꢌꢉꢉꢉꢌꢀꢇꢈꢌꢉꢉꢉꢌꢀDQGꢀꢇꢊꢋꢌꢉꢉꢉꢌꢀZKDWꢀLVꢀWKHꢀ,55ꢀ<5"ꢀ
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12.00
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(QWHUVꢀLQLWLDOꢀRXWIORZꢁ
(QWHUVꢀILUVWꢀFDVKꢀIORZꢁ
(QWHUVꢀVHFRQGꢀFDVKꢀIORZꢁ
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4,700.00
7,000.00
2.00
23,000.00
15.96
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1.33
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10.00
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622.85
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18 At a Glance...
Statistics—At a Glance…
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x-data
y-data
2
4
6
50
90
160
At a Glance... 19
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2.00
3.00
4.00
100.00
2.00
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27.50
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3.00
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1,420.00
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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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1: Getting Started 23
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Description:
87.18
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240.92
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356.42
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36.92
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40.57
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13.00
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39.00
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Description:
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–25.00
24 1: Getting Started
Understanding the Display and Keyboard
Cursor
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Clearing Memory
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Description
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1: Getting Started 25
Annunciators
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Annunciator
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26 1: Getting Started
Annunciator
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Status (Continued)
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FUNC
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1: Getting Started 27
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28 1: Getting Started
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Keys:
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17.00
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1: Getting Started 29
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30 1: Getting Started
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1: Getting Started 31
Rounding Numbers
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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
&RPSOHWHVꢀVHFRQGꢀ
FDOFXODWLRQꢅ
:LWKꢀWKHꢀH[FHSWLRQꢀRIꢀVWDWLVWLFVꢁꢀ\RXꢀFDQꢀDOVRꢀXVHꢀ
ꢀDQGꢀ IRUꢀ
DSSOLFDWLRQꢀUHJLVWHUVꢅꢀ)RUꢀH[DPSOHꢁꢀ ꢀVWRUHVꢀWKHꢀQXPEHUꢀIURPꢀWKHꢀ
GLVSOD\ꢀLQꢀWKHꢀ ꢀUHJLVWHUꢅꢀ ꢀFRSLHVꢀWKHꢀFRQWHQWVꢀIURPꢀ ꢀWRꢀWKHꢀ
GLVSOD\ꢅ
,QꢀPRVWꢀFDVHVꢁꢀLWꢀLVꢀXQQHFHVVDU\ꢀWRꢀFOHDUꢀDꢀVWRUDJHꢀUHJLVWHUꢀVLQFHꢀVWRULQJꢀDꢀ
QXPEHUꢀUHSODFHVꢀWKHꢀSUHYLRXVꢀFRQWHQWVꢅꢀ+RZHYHUꢁꢀ\RXꢀFDQꢀFOHDUꢀDꢀVLQJOHꢀ
UHJLVWHUꢀE\ꢀVWRULQJꢀꢈꢀLQꢀLWꢅꢀ7RꢀFOHDUꢀDOOꢀWKHꢀUHJLVWHUVꢀDWꢀRQFHꢁꢀSUHVVꢀ
ꢅꢀ
40 3: Number Storage and Arithmetic
Doing Arithmetic Inside Registers
<RXꢀFDQꢀGRꢀDULWKPHWLFꢀLQVLGHꢀVWRUDJHꢀUHJLVWHUVꢀ5 ꢀWKURXJKꢀ5 ꢅꢀ7KHꢀUHVXOWꢀ
LVꢀVWRUHGꢀLQꢀWKHꢀUHJLVWHUꢅꢀ
Keys
New Number in Register
UHJLVWHUꢀQXPEHU
UHJLVWHUꢀQXPEHU
UHJLVWHUꢀQXPEHU
UHJLVWHUꢀQXPEHU
2OGꢀFRQWHQWVꢀꢊꢀGLVSOD\HGꢀQXPEHUꢅ
2OGꢀFRQWHQWVꢀ²ꢀGLVSOD\HGꢀQXPEHUꢅ
2OGꢀFRQWHQWVꢀïꢀGLVSOD\HGꢀQXPEHUꢅ
2OGꢀFRQWHQWVꢀ¸ꢀGLVSOD\HGꢀQXPEHUꢅ
Example. 6WRUHꢀꢏꢉꢅꢍꢀLQꢀ5 ꢁꢀPXOWLSO\ꢀE\ꢀꢋꢅꢉꢁꢀDQGꢀVWRUHꢀWKHꢀUHVXOWꢀLQꢀ5 ꢅ
Keys:
Display:
Description:
45.70
6WRUHVꢀꢏꢉꢅꢍꢀLQꢀ5 ꢅ
0XOWLSOLHVꢀꢏꢉꢅꢍꢀLQꢀ5 ꢀE\ꢀ
2.50
ꢋꢅꢉꢀDQGꢀVWRUHVꢀUHVXOWꢀ
ꢃꢇꢇꢏꢅꢋꢉꢄꢀLQꢀ5 ꢅ
114.25
'LVSOD\Vꢀ5 ꢅ
3: Number Storage and Arithmetic 41
Doing Arithmetic
0DWKꢀIXQFWLRQVꢀRSHUDWHꢀRQꢀWKHꢀQXPEHUꢀLQꢀWKHꢀGLVSOD\ꢅ
Example. &DOFXODWHꢀ ꢒ ꢁꢀWKHQꢀFDOFXODWHꢀ ꢋꢈ ꢀꢊꢀꢏꢍꢅꢋꢀꢊꢀꢇꢅꢇ ꢅ
Keys:
Display:
Description:
0.25
&DOFXODWHVꢀWKHꢀ
UHFLSURFDOꢀRIꢀꢏꢅ
4.47
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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
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
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
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DGYDQFHꢀSD\PHQWꢄ
97,877.55
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Step 3. )LQGꢀWKHꢀSUHVHQWꢀYDOXHꢀRIꢀWKHꢀEX\ꢀRSWLRQꢄ
48.00
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0.00
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VROXWLRQꢄ
–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
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
$QQXDOꢀQRPLQDOꢀLQWHUHVWꢀUDWHꢄ
6WDUWLQJꢀEDODQFHꢄ
(QGLQJꢀEDODQFHꢄ
3D\PHQWꢀDPRXQWꢀꢁURXQGHGꢀWRꢀWKHꢀGLVSOD\ꢀIRUPDWꢂꢄ
1XPEHUꢀRIꢀSD\PHQWVꢀSHUꢀ\HDUꢄ
7KHꢀQXPEHUVꢀGLVSOD\HGꢀIRUꢀLQWHUHVWꢃꢀSULQFLSDOꢃꢀDQGꢀEDODQFHꢀDUHꢀURXQGHGꢀWRꢀ
WKHꢀFXUUHQWꢀGLVSOD\ꢀVHWWLQJꢄꢀ
To Amortize. 7RꢀDPRUWL]HꢀDꢀVLQJOHꢀSD\PHQWꢃꢀHQWHUꢀWKHꢀSHULRGꢀQXPEHUꢀ
DQGꢀSUHVVꢀ
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E\ꢀWKHꢀVWDUWLQJꢀDQGꢀHQGLQJꢀSD\PHQWVꢀWKDWꢀZLOOꢀEHꢀDPRUWL]HGꢄ
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DQGꢀDJDLQꢀWRꢀVHHꢀWKHꢀEDODQFHꢀꢁBALꢂꢄꢀ&RQWLQXHꢀSUHVVLQJꢀ ꢀWRꢀF\FOHꢀWKURXJKꢀ
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7RꢀDPRUWL]HꢀDꢀUDQJHꢀRIꢀSD\PHQWVꢃꢀHQWHUꢀVWDUWLQJꢁSHULRGꢁQXPEHUꢀ ꢀHQGLQJꢁ
SHULRGꢁQXPEHUꢃꢀWKHQꢀSUHVVꢀ
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PERꢀIROORZHGꢀE\ꢀWKHꢀVWDUWLQJꢀDQGꢀHQGLQJꢀSD\PHQWVꢀWKDWꢀZLOOꢀEHꢀ
DPRUWL]HGꢄꢀ7KHQꢀSUHVVꢀ ꢀUHSHDWHGO\ꢀWRꢀF\FOHꢀWKURXJKꢀLQWHUHVWꢃꢀSULQFLSDOꢃꢀ
DQGꢀEDODQFHꢄ
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DQGꢀEDODQFHꢄꢀ7RꢀUHVXPHꢀDPRUWL]DWLRQꢀZLWKꢀWKHꢀVDPHꢀVHWꢀRIꢀSHULRGVꢃꢀSUHVVꢀ
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\HDUVꢀRIꢀWKHꢀDQQXDOꢀDPRUWL]DWLRQꢀVFKHGXOHꢀIRUꢀDꢀꢑꢌꢀ\HDUꢃꢀꢏꢋꢓꢌꢃꢌꢌꢌꢀ
PRUWJDJHꢃꢀDWꢀꢇꢄꢇꢍꢎꢀDQQXDOꢀLQWHUHVWꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢄ
6HWꢀWRꢀ(QGꢀPRGHꢄꢀ3UHVVꢀ
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68 5: Time Value of Money Calculations
Keys:
Display:
12.00
Description:
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢄ
360.00
6WRUHVꢀWRWDOꢀQXPEHUꢀRIꢀ
SD\PHQWVꢄ
7.75
6WRUHVꢀLQWHUHVWꢀSHUꢀ\HDUꢄ
6WRUHVꢀSUHVHQWꢀYDOXHꢄ
6WRUHVꢀIXWXUHꢀYDOXHꢄ
180,000.00
0.00
–1,289.54
&DOFXODWHVꢀPRQWKO\ꢀ
SD\PHQWꢄ
,Iꢀ\RXꢀDOUHDG\ꢀNQRZꢀWKHꢀPRUWJDJHꢀSD\PHQWꢃꢀ\RXꢀFDQꢀHQWHUꢀDQGꢀVWRUHꢀLWꢀMXVWꢀ
OLNHꢀ\RXꢀVWRUHꢀWKHꢀRWKHUꢀIRXUꢀYDOXHVꢄꢀ1H[WꢃꢀDPRUWL]HꢀWKHꢀILUVWꢀ\HDUꢄꢀ
12_
(QWHUVꢀVWDUWLQJꢀDQGꢀ
HQGLQJꢀSHULRGVꢄ
1– 12
'LVSOD\VꢀWKHꢀ3(5ꢀ
DQQXQFLDWRUꢀDQGꢀUDQJHꢄ
–1,579.82
'LVSOD\VꢀWKHꢀ35,1ꢀ
DQQXQFLDWRUꢀDQGꢀWKHꢀ
SULQFLSDOꢀSDLGꢀLQꢀWKHꢀ
ILUVWꢀ\HDUꢄ
–13,894.66
'LVSOD\VꢀWKHꢀ,17ꢀ
DQQXQFLDWRUꢀDQGꢀWKHꢀ
LQWHUHVWꢀSDLGꢀLQꢀWKHꢀILUVWꢀ
\HDUꢄ
178,420.18
'LVSOD\VꢀWKHꢀ%$/ꢀ
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
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DQGꢀDQQXDOꢀHIIHFWLYHꢀLQWHUHVWꢀUDWHVꢄꢀ1RPLQDOꢀDQGꢀHIIHFWLYHꢀ
LQWHUHVWꢀUDWHVꢀDUHꢀGHVFULEHGꢀRQꢀSDJH ꢐꢒꢄ
,Iꢀ\RXꢀNQRZꢀDQꢀDQQXDOꢀQRPLQDOꢀLQWHUHVWꢀUDWHꢀDQGꢀ\RXꢀZLVKꢀ
WRꢀVROYHꢀIRUꢀWKHꢀFRUUHVSRQGLQJꢀDQQXDOꢀHIIHFWLYHꢀUDWHꢅ
ꢀꢁ (QWHUꢀWKHꢀQRPLQDOꢀUDWHꢀDQGꢀSUHVVꢀ
ꢄ
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ꢄ
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ꢀꢁ (QWHUꢀWKHꢀHIIHFWLYHꢀUDWHꢀDQGꢀSUHVVꢀ
ꢂꢁ (QWHUꢀWKHꢀQXPEHUꢀRIꢀFRPSRXQGLQJꢀSHULRGVꢀDQGꢀSUHVVꢀ
ꢃꢁ &DOFXODWHꢀWKHꢀQRPLQDOꢀUDWHꢀE\ꢀSUHVVLQJꢀ
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Investments With Different Compounding Periods
Example: Comparing Investments. <RXꢀDUHꢀFRQVLGHULQJꢀRSHQLQJꢀDꢀ
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6HFRQGꢀ%DQN ꢆꢄꢆꢍꢎꢀDQQXDOꢀLQWHUHVWꢃꢀFRPSRXQGHGꢀPRQWKO\ꢄ
7KLUGꢀ%DQN
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\HDUꢄ
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
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HIIHFWLYHꢀUDWHꢄ
Third Bank
6.63
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360.00
6WRUHVꢀFRPSRXQGLQJꢀ
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6.85
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LQVWDOOPHQWVꢀRUꢀVDYLQJVꢀGHSRVLWVꢀDQGꢀZLWKGUDZDOVꢀGRꢀQRWꢀ
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EHIRUHꢀVROYLQJꢀWKHꢀSUREOHPꢄ
5: Time Value of Money Calculations 73
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SD\PHQWꢀSHULRGꢀFRPSOHWHꢀWKHꢀIROORZLQJꢀVWHSVꢅ
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Keys:
Display:
Description:
5.00
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365.00
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7: Statistical Calculations 91
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Weighted Mean
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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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96 8: Additional Examples
Cost of Not Taking a Cash Discount
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8: Additional Examples 97
Loans and Mortgages
Simple Annual Interest
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Yield of a Discounted (or Premium) Mortgage
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8: Additional Examples 99
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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
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6WRUHVꢀRULJLQDOꢀDPRXQWꢀRIꢀ
PRUWJDJHꢂ
0.00
(QWHUVꢀDPRXQWꢀOHIWꢀWRꢀSD\ꢀ
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899.73
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SD\PHQWꢂ
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Keys:
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Description:
899.73
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60.00
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88,706.74
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100 8: Additional Examples
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Keys:
Display:
Description:
18.00
6WRUHVꢀUHPDLQLQJꢀ
QXPEHUꢀRIꢀSD\PHQWVꢂ
–79,000.00
20.72
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PRUWJDJHꢂ
&DOFXODWHVꢀWKHꢀUHWXUQꢀ
RQꢀWKLVꢀGLVFRXQWHGꢀ
PRUWJDJHꢂ
Annual Percentage Rate for a Loan With Fees
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DꢀPRUWJDJHꢀLVꢀLVVXHGꢁꢀZKLFKꢀHIIHFWLYHO\ꢀUDLVHVꢀWKHꢀLQWHUHVWꢀUDWHꢂꢀ7KHꢀDFWXDOꢀ
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WKHꢀPRUWJDJHꢀꢄ1ꢀSHULRGVꢈꢁꢀWKHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀꢄ,ꢂ35ꢈꢁꢀWKHꢀPRUWJDJHꢀ
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Example: APR for a Loan With Fees. $ꢀERUURZHUꢀLVꢀFKDUJHGꢀWZRꢀ
SRLQWVꢀIRUꢀWKHꢀLVVXDQFHꢀRIꢀDꢀPRUWJDJHꢂꢀꢄ2QHꢀSRLQWꢀLVꢀHTXDOꢀWRꢀꢅꢌꢀRIꢀWKHꢀ
PRUWJDJHꢀDPRXQWꢂꢈꢀ,IꢀWKHꢀPRUWJDJHꢀDPRXQWꢀLVꢀꢊꢅꢐꢇꢁꢇꢇꢇꢀIRUꢀꢏꢇꢀ\HDUVꢀDQGꢀ
WKHꢀDQQXDOꢀLQWHUHVWꢀUDWHꢀLVꢀꢓꢂꢑꢌꢀZLWKꢀPRQWKO\ꢀSD\PHQWVꢁꢀZKDWꢀ$35ꢀLVꢀWKHꢀ
ERUURZHUꢀSD\LQJ"
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ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ
Keys:
Display:
Description:
12.00
8.50
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6WRUHVꢀLQWHUHVWꢀUDWHꢂ
360.00
6WRUHVꢀOHQJWKꢀRIꢀ
PRUWJDJHꢂ
160,000.00
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RIꢀPRUWJDJHꢂ
8: Additional Examples 101
0.00
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ꢏꢇꢀ\HDUVꢂ
–1,230.26
160,000.00
156,800
8.72
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&DOFXODWHVꢀ$35ꢁꢀ
FRQVLGHULQJꢀIHHVꢂ
Example: Interest-Only Loan With Fee. $ꢀꢊꢅꢁꢇꢇꢇꢁꢇꢇꢇꢁꢀꢅꢇꢍ\HDUꢁꢀꢅꢉꢌꢀ
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:KDWꢀLVꢀWKHꢀ\LHOGꢀWRꢀWKHꢀOHQGHU"ꢀ$VVXPHꢀWKDWꢀPRQWKO\ꢀSD\PHQWVꢀRIꢀ
LQWHUHVWꢀDUHꢀPDGHꢂ
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ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ
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12.00
12.00
120.00
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6WRUHVꢀLQWHUHVWꢀUDWHꢂ
6WRUHVꢀOHQJWKꢀRIꢀ
PRUWJDJHꢂ
1,000,000.00
–1,000,000.00
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RIꢀPRUWJDJHꢂ
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DUHꢀLQWHUHVWꢀRQO\ꢀVRꢀ
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–10,000.00
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SD\PHQWVꢂ
1,000,000.00
970,000.00
12.53
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6XEWUDFWVꢀSRLQWVꢂ
&DOFXODWHVꢀ$35ꢂ
102 8: Additional Examples
Loan With a Partial (Odd) First Period
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PRQWKꢂꢈ
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Example. $ꢀꢏꢐꢍPRQWKꢀORDQꢀIRUꢀꢊꢋꢁꢑꢇꢇꢀKDVꢀDQꢀDQQXDOꢀUDWHꢀRIꢀꢅꢑꢌꢂꢀ,IꢀWKHꢀ
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ꢀLIꢀBEGINꢀDQQXQFLDWRUꢀLVꢀGLVSOD\HGꢂ
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12.00
15.00
1.25
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6WRUHVꢀLQWHUHVWꢀUDWHꢂ
&DOFXODWHVꢀSHULRGLFꢀ
LQWHUHVWꢀUDWHꢂ
0.67
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RIꢀDꢀSHULRGꢂ
30.00
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4,530.00
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LQWHUHVWꢀWRꢀSUHVHQWꢀ
YDOXHꢂ
8: Additional Examples 103
36.00
0.00
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(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"
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12.00
Description:
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6WRUHVꢀNQRZQꢀYDOXHVꢂ
36.00
12,500.00
0.00
3.50
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–366.28
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–13,185.94
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104 8: Additional Examples
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Keys: Display:
Description:
11,500.00
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9.50
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&DOFXODWHVꢀSD\PHQWꢂ
&DOFXODWHVꢀWRWDOꢀLQWHUHVWꢀDQGꢀ
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–368.38
–13,261.64
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Canadian Mortgages
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WKHꢀVDPHꢂꢀ,QWHUHVWꢀLVꢀFRPSRXQGHGꢀVHPLꢍDQQXDOO\ꢀZKLOHꢀSD\PHQWVꢀDUHꢀ
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12.00
2.00
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12.36
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12.00
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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106 8: Additional Examples
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8: Additional Examples 107
Savings
Saving for College Costs
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108 8: Additional Examples
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8: Additional Examples 109
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Gains That Go Untaxed Until Withdrawal
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110 8: Additional Examples
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8: Additional Examples 111
Value of a Taxable Retirement Account
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112 8: Additional Examples
Cash Flow Examples
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8: Additional Examples 113
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FRPSOHWHꢀSLFWXUHꢀRIꢀWKHꢀZUDSꢍDURXQGꢀPRUWJDJHꢀIURPꢀWKHꢀOHQGHU·VꢀSRLQWꢀRIꢀ
YLHZꢃ
:KHQꢀ\RXꢀJURXSꢀWKHꢀDERYHꢀFDVKꢀIORZVꢁꢀ\RX·OOꢀILQGꢀWKDWꢃ
&) ꢋꢒꢁꢑꢅꢇꢂꢉꢉꢀ²ꢀꢓꢉꢁꢑꢅꢇꢂꢉꢉꢀ ꢀ²ꢏꢑꢁꢇꢇꢇ
&) ꢓꢐꢅꢂꢑꢕꢀ²ꢀꢒꢑꢋꢂꢇꢇꢀ ꢀꢅꢇꢒꢂꢑꢕ
1
ꢓꢉ
&) ꢀ ꢓꢐꢅꢂꢑꢕ
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
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Keys:
Display:
Description:
&OHDUVꢀDOOꢀUHJLVWHUVꢂ
12.00
6HWVꢀSD\PHQWVꢀSHUꢀ\HDUꢂ
(QWHUVꢀLQLWLDOꢀFDVKꢀIORZꢂ
CF0
–12,000.00
CF1
0.00
(QWHUVꢀDPRXQWꢀLQꢀ
JURXSꢀꢅꢂ
n1
2.00
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WLPHVꢀSD\PHQWꢀRFFXUVꢂ
CF2
–3,000.00
(QWHUVꢀDPRXQWꢀLQꢀ
JURXSꢀꢉꢂ
n2
3.00
(QWHUVꢀQXPEHUꢀRIꢀ
WLPHVꢀSD\PHQWꢀRFFXUVꢂ
n3
9.00
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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
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39ꢂ
24.00
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0.00
34,800.58
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YDOXHꢂ
116 8: Additional Examples
A
Assistance, Batteries, and Service
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<RXꢁFDQꢁREWDLQꢁDQVZHUVꢁWRꢁTXHVWLRQVꢁDERXWꢁXVLQJꢁ\RXUꢁFDOFXODWRUꢁIURPꢁ
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FRYHUꢂ
Answers to Common Questions
Q: ,·PꢁQRWꢁVXUHꢁLIꢁWKHꢁFDOFXODWRUꢁLVꢁPDOIXQFWLRQLQJꢁRUꢁLIꢁ,·PꢁGRLQJꢁ
VRPHWKLQJꢁLQFRUUHFWO\ꢂꢁ+RZꢁFDQꢁ,ꢁGHWHUPLQHꢁLIꢁWKHꢁFDOFXODWRUꢁLVꢁRSHUDWLQJꢁ
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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
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Q: :K\ꢁGRꢁ,ꢁJHWꢁDꢁZURQJꢁDQVZHUꢁRUꢁWKHꢁNo Solution PHVVDJHꢁ
ZKHQꢁXVLQJꢁ790"
A: %HꢁVXUHꢁWRꢁHQWHUꢁDꢁYDOXHꢁIRUꢁIRXUꢁRIꢁWKHꢁILYHꢁ790ꢁYDOXHVꢁEHIRUHꢁ\RXꢁ
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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
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ZHWꢁDQGꢁREVHUYHꢁWKHꢁIROORZLQJꢁWHPSHUDWXUHꢁDQGꢁKXPLGLW\ꢁOLPLWVꢎ
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2SHUDWLQJꢁDQGꢁVWRUDJHꢁKXPLGLW\ꢎꢁꢌꢉꢑꢁUHODWLYHꢁKXPLGLW\ꢁDWꢁꢏꢉ&ꢁ
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118 A: Assistance, Batteries, and Service
Power and Batteries
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EDWWHULHVꢂ
:KHQꢁFKDQJLQJꢁEDWWHULHVꢃꢁXVHꢁRQO\ꢁIUHVKꢁEXWWRQꢀFHOOꢁEDWWHULHVꢂꢁ
%RWKꢁEDWWHULHVꢁPXVWꢁEHꢁFKDQJHGꢁDWꢁWKHꢁVDPHꢁWLPHꢂ
'RꢁQRWꢁXVHꢁUHFKDUJHDEOHꢁEDWWHULHVꢂ
Low Power Annunciator
:KHQꢁWKHꢁORZꢁEDWWHU\ꢀSRZHUꢁDQQXQFLDWRUꢁꢆ
ꢈꢁFRPHVꢁRQꢃꢁ\RXꢁ
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DQQXQFLDWRUꢁLVꢁRQꢁDQGꢁWKHꢁGLVSOD\ꢁGLPVꢃꢁ\RXꢁPD\ꢁORVHꢁGDWDꢂꢁ7KHꢁ
All Clear PHVVDJHꢁLVꢁGLVSOD\HGꢁLIꢁGDWDꢁLVꢁORVWꢁGXHꢁWRꢁORZꢁSRZHUꢂ
Battery Specifications
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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
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7KHUHꢀLVꢀDꢀGDQJHUꢀRIꢀH[SORVLRQꢀLIꢀEDWWHULHVꢀDUHꢀ
LQFRUUHFWO\ꢀUHSODFHGꢂ
Warning
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HTXLYDOHQWꢀEDWWHULHVꢀꢉDVꢀUHFRPPHQGHGꢀE\ꢀWKHꢀ
PDQXIDFWXUHUꢊꢂꢀ'LVSRVHꢀRIꢀXVHGꢀEDWWHULHVꢀDFFRUGLQJꢀWRꢀ
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ILUHꢂꢀ7KHꢀEDWWHULHVꢀFDQꢀEXUVWꢀRUꢀH[SORGHꢋꢀUHOHDVLQJꢀ
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PL[ꢀEDWWHULHVꢀRIꢀGLIIHUHQWꢀW\SHVꢂ
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ꢆꢓꢈꢁRQꢁHDFKꢁEDWWHU\ꢁLVꢁIDFLQJꢁRXWZDUGꢂ
ꢇꢂ 5HSODFHꢁWKHꢁEDWWHU\ꢀFRPSDUWPHQWꢁOLGꢂ
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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):
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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
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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:
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What Is Not Covered
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A: Assistance, Batteries, and Service 123
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Shipping Instructions
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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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PDWKHPDWLFDOꢀIRUPXODVꢀWKDWꢀVHDUFKꢀIRUꢀWKHꢀDQVZHUꢁꢀ7KHꢀSURFHVVꢀ
ILQGVꢀDꢀVROXWLRQꢀE\ꢀHVWLPDWLQJꢀDQꢀDQVZHUꢀDQGꢀWKHQꢀXVLQJꢀWKDWꢀ
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FDOFXODWLQJꢀ,55ꢀ<5ꢀIRUꢀFHUWDLQꢀVHWVꢀRIꢀFDVKꢀIORZVꢀLVꢀPRUHꢀFRPSOH[ꢁꢀ
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WKHꢀSUREOHPꢁꢀ,QꢀWKHVHꢀFDVHVꢂꢀWKHꢀFDOFXODWRUꢀGLVSOD\VꢀDꢀPHVVDJHꢀWRꢀ
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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
WKDQꢀRQHꢀSRVLWLYHꢀRUꢀQHJDWLYHꢀDQVZHUꢂꢀRUꢀWKHUHꢀPD\ꢀEHꢀQRꢀVROXWLRQꢁꢀ
7RꢀFRQWLQXHꢀWKHꢀFDOFXODWLRQꢂꢀ\RXꢀPXVWꢀVWRUHꢀDꢀJXHVVꢀꢃVHHꢀEHORZꢄꢁ
B: More About Calculations 129
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
WKHꢀWLPHꢀUHTXLUHGꢀWRꢀFDOFXODWHꢀDQꢀDQVZHUꢀDQGꢀUHGXFHꢀWKHꢀFKDQFHꢀRIꢀ
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$IWHUꢀ\RX·YHꢀLQWHUUXSWHGꢀWKHꢀFDOFXODWLRQꢁ
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ILQGVꢀDQꢀDQVZHUꢁꢀ+RZHYHUꢂꢀWKHUHꢀPD\ꢀEHꢀDGGLWLRQDOꢀSRVLWLYHꢀRUꢀQHJDWLYHꢀ
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DQRWKHUꢀVROXWLRQꢀE\ꢀKDOWLQJꢀWKHꢀFDOFXODWLRQꢀDQGꢀHQWHULQJꢀDꢀGLIIHUHQWꢀJXHVVꢁ
2QHꢀZD\ꢀWRꢀREWDLQꢀDꢀJRRGꢀJXHVVꢀIRUꢀ,55ꢀ<5ꢀLVꢀWRꢀFDOFXODWHꢀWKHꢀ139ꢀIRUꢀ
YDULRXVꢀLQWHUHVWꢀUDWHVꢁꢀ6LQFHꢀ,55ꢀ<5ꢀLVꢀWKHꢀLQWHUHVWꢀUDWHꢀDWꢀZKLFKꢀ139ꢀ
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130 B: More About Calculations
Effect of Using Σ– to Correct Data
7KHꢀ+3ꢀꢉꢊ%,,ꢀVWRUHVꢀWKHꢀVWDWLVWLFDOꢀQXPEHUVꢀLQꢀDQꢀ´DFFXPXODWHGµꢀIDVKLRQꢁꢀ
,WꢀGRHVQ·WꢀVWRUHꢀHYHU\ꢀQXPEHUꢀWKDWꢀ\RXꢀHQWHUꢂꢀEXWꢀUDWKHUꢀLWꢀSHUIRUPVꢀ
LQWHUPHGLDWHꢀFDOFXODWLRQVꢀZKHQꢀ\RXꢀSUHVVꢀWKHꢀ ꢀNH\ꢁꢀ7KHꢀ
ꢀNH\ꢀ
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VXEVHTXHQWꢀUHVXOWVꢀIRUꢀFRUUHFWHGꢀGDWDꢀPD\ꢀEHꢀGLIIHUHQWꢀWKDQꢀIRUꢀGDWDꢀWKDWꢀ
ZDVꢀHQWHUHGꢀRULJLQDOO\ꢀZLWKRXWꢀKDYLQJꢀWRꢀXVHꢀ
ꢁꢀ+RZHYHUꢂꢀWKHꢀ
GLIIHUHQFHꢀZLOOꢀQRWꢀEHꢀVHULRXVꢀXQOHVVꢀWKHꢀLQFRUUHFWꢀGDWDꢀKDVꢀDꢀYHU\ꢀODUJHꢀ
PDJQLWXGHꢀFRPSDUHGꢀZLWKꢀWKHꢀFRUUHFWꢀYDOXHVꢋꢀLQꢀWKLVꢀFDVHꢂꢀ\RXꢀPD\ꢀZDQWꢀ
WRꢀFOHDUꢀWKHꢀVWDWLVWLFDOꢀUHJLVWHUVꢀDQGꢀUHꢆHQWHUꢀWKHꢀGDWDꢁ
Range of Numbers
7KHꢀODUJHVWꢀSRVLWLYHꢀDQGꢀQHJDWLYHꢀQXPEHUVꢀDYDLODEOHꢀRQꢀWKHꢀFDOFXODWRUꢀDUHꢀ
ꢀꢌꢁꢌꢌꢌꢌꢌꢌꢌꢌꢌꢌꢌꢀïꢀꢉꢊ ꢋꢀWKHꢀVPDOOHVWꢀSRVLWLYHꢀDQGꢀQHJDWLYHꢀQXPEHUVꢀ
DYDLODEOHꢀDUHꢀꢉꢀïꢀꢉꢊ ꢁꢀ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
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COPR HP 2000
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