HP NW239AA User Manual

HP 10bII+ Financial Calculator User’s Guide
HP Part Number: NW239-90001 Edition 1, May 2010
i

Legal Notice

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. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual.
Hewlett-Packard Company 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 © 2010 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 Palo Alto, CA 94304 USA
ii

HP 10bII+ Financial Calculator

iii

Keyboard Map Legend

Number
(row of keys)
1 12 character, seven-
2 Time Value of Money
3 Input key, markup, cost,
4 K memory register,
5 Change sign, recall
Primary Functions
(white)
segment screen display
(TVM)
price and margin
percent, cash flow amount, statistics entry, backspace
and memory
SHIFT Down \
(orange functions on
key bevel)
Payments per year, interest conversion, amortization,
Date and change of days, IRR per year, NPV, beginning/end of payment period
Swap, percent change, cash flow count, delete statistics, round
Scientific notation, store, clear statistics, parentheses
SHIFT Up ]
(blue functions above
keys)
Bond calculations
Calendar and coupon payment schedules, settlement and maturity dates (bonds)
Break-even calculation
Depreciation, hyperbolic and trigonometric functions
6 Shift (blue, up)
Shift (orange, down)
7 Numbered keys: 1, and
4-9 8 Clearing functions Clearing functions Clearing functions 9On Off Operating modes
10 Numbered keys: 0 and
2-3, decimal
11 Mathematical functions Common mathematical
12 A n n u n c i at o r s
Statistics, weighted mean and estimation
Common mathematical functions
functions, parentheses
Statistical functions and regression modes
Probability functions
Trigonometric functions
iv

Table of Contents

Legal Notice...............................................................................................................ii
HP 10bII+ Financial Calculator.................................................................................... iii
Keyboard Map Legend............................................................................................... iv
1 At a Glance........................................................................................................................ 1
Basics of Key Functions................................................................................................1
Shift Keys...................................................................................................................2
Boxed Key Functions ...................................................................................................2
Percentages ...............................................................................................................3
Memory Keys .............................................................................................................4
Time Value of Money (TVM) .........................................................................................6
TVM What if... ...........................................................................................................7
Amortization ..............................................................................................................8
Depreciation ..............................................................................................................9
Interest Rate Conversion.............................................................................................10
Cash Flows, IRR/YR, NPV, and NFV ...........................................................................11
Date and Calendar ...................................................................................................13
Bonds......................................................................................................................14
Break-even ...............................................................................................................16
Statistical Calculations...............................................................................................17
Probability ...............................................................................................................19
Trigonometric Functions .............................................................................................20
2 Getting Started................................................................................................................. 23
Power On and Off ....................................................................................................23
Manual Conventions and Examples.............................................................................23
Basics of Key Functions..............................................................................................24
Shift Keys.................................................................................................................25
Boxed Key Functions .................................................................................................25
Simple Arithmetic Calculations....................................................................................26
Understanding the Display and Keyboard....................................................................29
Cursor .....................................................................................................................29
Clearing the Calculator..............................................................................................29
Annunciators ............................................................................................................30
Input Key .................................................................................................................32
Swap Key ................................................................................................................32
Statistics Keys...........................................................................................................32
Time Value of Money (TVM), Cash Flows, Bond, and Break-even Keys ............................33
Math Functions .........................................................................................................33
Trigonometric and Hyperbolic Functions and Modes .....................................................35
Pi............................................................................................................................36
Hyperbolic Functions.................................................................................................36
Two-Number Functions ..............................................................................................37
In-line Functions ........................................................................................................37
1
Arithmetic with One-and Two-number Functions............................................................39
Last Answer ............................................................................................................. 41
Display Format of Numbers .......................................................................................41
Scientific Notation....................................................................................................43
Interchanging the Period and Comma ......................................................................... 43
Rounding Numbers................................................................................................... 43
Messages................................................................................................................44
3 Business Percentages.........................................................................................................45
The Business Percentage Keys .................................................................................... 45
Percent key.............................................................................................................. 45
Margin and Markup Calculations...............................................................................47
4 Number Storage and Storage Register Arithmetic ...............................................................49
Using Stored Numbers in Calculations ........................................................................49
5 Picturing Financial Problems ..............................................................................................55
How to approach a Financial Problem........................................................................ 55
Signs of Cash Flows .................................................................................................56
Periods and Cash Flows............................................................................................56
Simple and Compound Interest................................................................................... 56
Interest Rates............................................................................................................57
Two Types of Financial Problems................................................................................ 58
Recognizing a Cash Flow Problem .............................................................................59
6 Time Value of Money Calculations .....................................................................................61
Using the TVM Application ........................................................................................ 61
The TVM Keys.......................................................................................................... 61
Begin and End Modes...............................................................................................62
Loan Calculations.....................................................................................................62
Savings Calculations.................................................................................................67
Lease Calculations.................................................................................................... 71
Amortization............................................................................................................ 74
Interest Rate Conversions........................................................................................... 79
Resetting the TVM Keys .............................................................................................82
7 Depreciation .....................................................................................................................83
The Depreciation Keys .............................................................................................. 83
Resetting the TVM Keys .............................................................................................86
2
8 Cash Flow Calculations..................................................................................................... 87
How to Use the Cash Flow Application........................................................................87
Clearing the Cash Flow Memory.................................................................................88
Calculating Internal Rate of Return...............................................................................90
NPV and IRR/YR: Discounting Cash Flows ...................................................................91
Organizing Cash Flows.............................................................................................91
Viewing and Editing Cash Flows.................................................................................93
Calculating Net Present Value and Net Future Value .....................................................95
Automatic Storage of IRR/YR and NPV........................................................................98
9 Calendar Formats and Date Calculations ........................................................................... 99
Calendar Format.......................................................................................................99
Date Format .............................................................................................................99
Date Calculations and Number of Days.....................................................................101
Number of Days .....................................................................................................102
10 Bonds .......................................................................................................................... 105
The Bond Keys........................................................................................................105
Resetting the bond keys ...........................................................................................108
11 Break-even .................................................................................................................. 109
The Break-even Keys................................................................................................109
Resetting the Break-even keys ...................................................................................112
12 Statistical Calculations .................................................................................................. 113
Clearing Statistical Data ..........................................................................................114
Entering Statistical Data ...........................................................................................114
Viewing and Editing Statistical Data..........................................................................116
Summary of Statistical Calculations ...........................................................................119
Mean, Standard Deviations, and Summation Statistics.................................................120
Linear Regression, Estimation, and Regression Modes..................................................121
Weighted Mean .....................................................................................................124
Regression Models and Variables .............................................................................125
Probability Calculations ...........................................................................................126
Factorial ................................................................................................................126
Permutations...........................................................................................................126
Combinations.........................................................................................................127
Random Number and Seed......................................................................................127
Advanced Probability Distributions ............................................................................128
Normal Lower Tail Probability ..................................................................................129
Inverse of Normal Lower Tail Probability....................................................................130
Student's T Probability Lower Tail ..............................................................................131
3
Inverse of Student’s t Probability Lower Tail................................................................ 132
Conversions from Lower Tail .................................................................................... 133
13 Additional Examples .....................................................................................................137
Business Applications.............................................................................................. 137
Loans and Mortgages .............................................................................................139
Savings.................................................................................................................148
Cash Flow Examples............................................................................................... 152
14 Appendix A: Batteries and Answers to Common Questions ..................................................I
Power and Batteries..................................................................................................... I
Low Power Annunciator................................................................................................ I
Installing Batteries........................................................................................................ I
Determining if the Calculator Requires Service ................................................................II
Answers to Common Questions....................................................................................III
Environmental Limits................................................................................................... IV
15 Appendix B: More About Calculations.................................................................................I
IRR/YR Calculations..................................................................................................... I
Equations ................................................................................................................... I
16 Appendix C: Messages.......................................................................................................I
17 Warranty, Regulatory, and Contact Information .................................................................1
Replacing the Batteries................................................................................................ 1
HP Limited Hardware Warranty and Customer Care....................................................... 1
Limited Hardware Warranty Period .............................................................................. 1
General Terms ...........................................................................................................2
Exclusions.................................................................................................................. 2
Regulatory Information ................................................................................................ 3
Federal Communications Commission Notice................................................................. 3
Modifications............................................................................................................. 3
Declaration of Conformity for Products Marked with FCC Logo, United States Only ............ 4
Canadian Notice ....................................................................................................... 4
Avis Canadien ........................................................................................................... 4
European Union Regulatory Notice...............................................................................4
Japanese Notice ........................................................................................................ 5
Disposal of Waste Equipment by Users in Private Household in the European Union........... 5
Perchlorate Material - special handling may apply.......................................................... 6
Customer Care........................................................................................................... 6
Contact Information ....................................................................................................6
4
1 At a Glance...
This section is designed for you if you’re already familiar with calculator operation or financial concepts. You can use it for quick reference. The rest of the manual is filled with explanations and examples of the concepts presented in this section.

Basics of Key Functions

Table 1-1 Basics of key functions
Keys Display Description
=
] [blue]
\ [orange]
JGD|
M
\t
0.00 Turns calculator on.
0.00
0.00
12_ Erases last character.
0.00 Clears display.
0.00 Clears statistics
Displays shift
annunciator .
Displays shift
annunciator .
memory.
\N
]Oj
]OY
]OJ
]O:
\>
12 P _ Y r (message flashes, then
disappears)
BOND CLR (message flashes,
then disappears)
BR EV CLR (message flashes,
then disappears)
TVM CLR (message flashes, then
disappears)
CFLO CLR (message flashes, then
disappears)
Clears all memory.
Clears bond memory.
Clears break-even memory.
Clears tvm registers.
Clears cash flow memory.
Turns calculator off.

At a Glance...

1

Shift Keys

Most keys on the HP 10bII+ have three functions:
a primary function printed in white on the key.
a secondary function printed in orange on the bevel of the key.
a tertiary function printed in blue above the key on the keyboard (see Figure 1).
Figure 1
As an example, the functions associated with the equals key, 4, are illustrated in the text
as follows:
primary function (equals): 4
secondary function (display): \5
tertiary function (random): ]6

Boxed Key Functions

These special functions require subsequent key presses to operate. For example, the functions
associated with the clear key, M, include:
Table 1-2 Clearing functions
Keys Associated Function
Clear display.
M \N
Clear all memory.
]Oj
Clears bond memory.
At a Glance...2
Table 1-2 Clearing functions
Keys Associated Function
]OY
Clears break-even memory.
]OJ
Clears TVM memory.
]O:
Clears cash flow memory.
\t
Clears statistics memory.
For more information on the calculator’s keys and basic functions, refer to chapter 2, Getting Started.

Percentages

Table 1-3 Keys for percentage calculations
Keys Description
Percent
§ \¨
Percent change
À ¼ ® Ã
Add 15% to 17.50.
Table 1-4 Calculating the price
Keys Display Description
Jj7V:1 JV§4
Cost
Price
Margin
Markup
17.50 Enters number.
20.13 Adds 15%.
Find the margin if the cost is 15.00 and selling price is 22.00.
At a Glance...
3
Table 1-5 Finding the margin
Keys Display Description
JVÀ
15. 00 E n ter s cos t.
GG¼
22.00 Enters price.
®
31. 82 C al c u la t e s m arg i n.
If the cost is 20.00 and the markup is 33%, what is the selling price?
Table 1-6 Calculating the price
Keys Display Description
20.00 Enters cost.
G:À DDÃ
33.00 Enters markup.
¼
26.60 Calculates price.
For more information on percentages, refer to chapter 3, Business Percentages.

Memory Keys

Table 1-7 Memory keys
Keys Description
Stores a constant operation.
ª s
Stores a value in the M register (memory location).
p
Recalls a value from the M register.
m
Adds a value to the number stored in the M register.
\w
When followed by a number key, : to d, or 7 and : to d, stores a number in the display into a numbered data storage register. There are 20 storage registers, designated 0-
19. Pre ss
\w7 followed by : through d to access registers 10-19.
v
At a Glance...4
When followed by a number key, : to d, or 7 and : to d, recalls a number from
a storage register. Press
v7 followed by : through d to access registers 10-19.
Multiply 17, 22, and 25 by 7, storing ‘× 7’ as a constant operation.
Table 1-8 Storing ‘x 7’ as a constant
Keys Display Description
JjPjª
7.0 0 St ore s ‘ × 7’ as a
119.00 Multiplies 17 × 7.
4
154.00 Multiplies 22 × 7.
GG4
175.00 Multiplies 25 × 7.
GV4
Store 519 in register 2, then recall it.
Table 1-9 Storing and recalling
Keys Display Description
519.00 Stores 519 in register 2.
VJd\wG
0.00 Clears display.
M
519.0 0 Re c a lls reg i s te r 2.
vG
constant operation.
Store 1.25 into register 15, then add 3, and store the result in register 15.
Table 1-10 Storage register arithmetic
Keys Display Description
J7GV
\w7V
D\w17V
1. 25 In p ut s 1. 25 i nt o t he display.
Stores 1.25 in register 15 .
3.00 Adds 3 to 1.25 in register 15 stores the result in register 15.
0.00 Clears the display.
M v7V
4.25 Recalls register 15.
For more information on number storage and storage register arithmetic, refer to chapter 4, Number Storage and Storage Register Arithmetic.
At a Glance...
5

Time Value of Money (TVM)

Enter any four of the five values and solve for the fifth. A negative sign in the display represents money paid out, and money received is positive.
Table 1-11 Keys for TVM calculations
Keys Description
]OJ Ù \Ú Ò
Ï Ì É \¯ \Í
Clears TVM memory and the current P_YR is displayed.
Number of payments.
Multiplies a value by the number of payments per year and stores as N.
Interest per year.
Present value.
Payment.
Future value.
Begin or End mode.
Number of payments per year mode.
If you borrow 14,000 (PV) for 360 months (N) at 10% interest (I/YR), what is the monthly repayment?
Set to End mode. Press
Table 1-12 Calculating the monthly payment
Keys Display Description
]OJ
if BEGIN annunciator is displayed.
TVM CLR (message flashes, then
disappears)
12.00 Sets payments per year.
Clears TVM memory and displays the current P_YR.
JG\Í DS:Ù
360.00 Enters number of payments.
J:Ò
10.00 Enters interest per year.
JY:::Ï
14,000.00 Enters present value.
At a Glance...6
Table 1-12 Calculating the monthly payment
Keys Display Description
0.00 Enters future value.
Ì

TVM What if...

It is not necessary to reenter TVM values for each example. Using the values you just entered, how much can you borrow if you want a payment of 100.00?
Table 1-13 Calculating a new payment
Keys Display Description
J::yÌ
Ï
...how much can you borrow at a 9.5% interest rate?
-122.86 Calculates payment if paid at end of period.
-100.00 Enters new payment amount. (Money paid out is negative).
11,395.08 Calculates amount you can
borrow.
Table 1-14 Calculating a new interest rate
Keys Display Description
9.50 Enters new interest rate.
d7VÒ Ï
J:Ò JY:::Ï
11,892.67 Calculates new present
value for 100.00 payment and 9.5% interest.
10.00 Reenters original interest rate.
14,000.00 Reenters original present
value.
-122.86 Calculates original payment.
Ì
For more information on TVM concepts and problems, refer to chapter 5, Picturing Financial Problems, and chapter 6, Time Value of Money Calculations.
At a Glance...
7

Amortization

After calculating a payment using Time Value of Money (TVM), input the periods to amortize and press . Press once for periods 1-12, and once again for payments 13-
24. Press 4 to continually cycle through the principal, interest, and balance values (indicated by the PRIN, INT, and BAL annunciators respectively). Using the previous TVM example,
amortize a single payment and then a range of payments.
Amortize the 20th payment of the loan.
Table 1-15 Amortizing the 20th payment of the loan
Keys Display Description
G:Æ
20.00 Enters period to amortize.
20 – 20 Displays period to amortize.
-7.25 Displays principal.
4
-115. 61 D is pl ays in teres t. ( Mo ney
4
13,865.83 Displays the balance
4
Amortize the 1st through 24th loan payments.
Table 1-16 Amortization example
Keys Display Description
12_ Enters range of periods to
JÆJG
paid out is negative).
amount.
amortize.
1 – 12 Displays range of periods
(payments).
-77.82 Displays principal.
4 4 4
-1,396.5 0 Di sp lays i nt ere st. (M on ey paid out is negative).
13,922.18 Displays the balance
amount.
13 – 24 Displays range of periods.
\Ê 4
-85.96 Displays principal.
At a Glance...8
Table 1-16 Amortization example
Keys Display Description
4
-1,388.36 Displays interest.
4
For more information on amortization, refer to the section titled, Amortization in chapter 6, Time Value of Money Calculations.

Depreciation

Table 1-17 Depreciation keys
Keys Description
Expected useful life of the asset.
13,836.22 Displays the balance
amount.
Ù Ò
Declining balance factor entered as a percentage.
Depreciable cost of the asset at acquisition.
Ï É
Salvage value of the asset.
]{
Straight-line depreciation.
]x
Sum-of-the-years’-digits depreciation.
]u
Declining Balance depreciation.
A metalworking machine, purchased for 10,000.00, is to be depreciated over five years. Its salvage value is estimated at 500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first two years of the machine's life.
Table 1-18 Calculating the depreciation
Keys Display Description
10,000.00 Inputs cost of the item.
J::::Ï V::É
500.00 Inputs the salvage value of the item.
5.00 Inputs the useful life of the asset.
VÙ J]{
1,900.00 Depreciation of the asset in year
one.
At a Glance...
9
Table 1-18 Calculating the depreciation
Keys Display Description
\« G]{ \«
For more information on depreciation, refer to chapter 7, Depreciation.
7,600.00 Remaining depreciable value
after year one.
1,900.00 Depreciation of the asset in year
two.
5,700.00 Remaining depreciable value
after year two.

Interest Rate Conversion

To convert between nominal and effective interest rates, enter the known rate and the number of periods per year, then solve for the unknown rate.
Ta ble 1-19 Keys fo r int er est ra te co nv ersi o n
Keys Description
Nominal interest percent.
\Ó \Ð
Effective interest percent.
Periods per year.
Find the annual effective interest rate of 10% nominal interest compounded monthly.
Table 1-20 Calculating the interest rate
Keys Display Description
10.00 Enters nominal rate.
J:\Ó JG\Í
12.00 Enters payments per year.
For more information on interest rate conversions, refer to the section titled, Interest Rate Conversions in chapter 6, Time Value of Money Calculations.
10.47 Calculates annual effective interest.
At a Glance...10

Cash Flows, IRR/YR, NPV, and NFV

Table 1-21 Cash flows, IRR, NPV, and NFV keys
Keys Description
]O: \Í
¤
number1
Æ number 2 ¤
Clears cash flow memory.
Number of periods per year (default is
12). For annual cash flows, P/YR should be set to 1; for monthly cash flows, use the default setting, 12 .
Cash flows, up to 45. “J” identifies the cash flow number. When preceded by a
number, pressing amount.
Enter a cash flow amount, followed by
¤ enters a cash flow
Æ. Enter a number for the cash flow
count followed by flow amount and count simultaneously.
Opens editor for reviewing/editing
entered cash flows. Press
¤ to enter cash
1 or A to
\¥ \Á
\½ \½\«
scroll through the cash flows. Number of consecutive times cash flow
J” occurs. Internal rate of return per year.
Net present value.
Net future value.
At a Glance...
11
If you have an initial cash outflow of 40,000, followed by monthly cash inflows of 4,700, 7,000, 7,000, and 23,000, what is the IRR/YR? What is the IRR per month?
Table 1-22 Calculating the IRR/YR and IRR per month
Keys Display Description
]O:
JG\Í Y::::y¤
Yj::¤
j:::ÆG¤
GD:::¤
CFLO CLR
(message flashes, then
disappears)
12.00 Sets payments per year.
-40,000.00
(CF 0 flashes, then disappears)
4,700.00
(CF 1 flashes, then disappears)
2.00
(CFn 2 flashes, then disappears)
23,000.00
(CF 3 flashes, then disappears)
0 -40,000.00 Reviews entered cash flows
Clears cash flow memory.
Enters initial outflow.
Enters first cash flow.
Enters both the cash flow amount (7000.00) and count (2.00) simultaneously for second cash flow.
Enters third cash flow.
starting with the initial cash flow.
15 . 9 6 C a l c u l a t e s IRR/YR.
1. 3 3 C a l c u l a t e s IRR per month.
aJG4
What is the NPV and NFV if the discount rate is 10%?
Table 1-23 Calculating NPV and NFV
Keys Display Description
10.0 0 Ent er s I/YR.
J:Ò
622.85 Calculates NPV.
Press
1 to scroll through the
cash flow list to verify the cash flow number, the amounts, and
count for each entry. Press to exit.
M
At a Glance...12
Table 1-23 Calculating NPV and NFV
Keys Display Description
\½\«
643.88 Calculates NFV.
For more information on cash flows, refer to chapter 8, Cash Flow Calculations in the HP 10bII+ Financial Calculator User’s Guide.

Date and Calendar

Table 1-24 Keys used for dates and calendar functions
Keys Description
Enters dates in DD.MMYYYY or MM.DDYYYY formats. D.MY is the default. Numbers at the far right of a calculated date indicate days of the week. 1 is for Monday; 7 is for Sunday.
Toggles between 360-and 365-day (Actual) calendars.
]Å \Ç
Calculates the date and day, past or future, that is a given number of days from a given date. Based on your current setting, returned result is calculated using either 360-day or 365-day (Actual).
Calculates the number of days between two dates. Returned result is always calculated based on the 365-day calendar (Actual).
If the current date is February 28 2010, what is the date 52 days from now? Calculate the date using the 365-day calendar (actual) and the M.DY settings.
If 360 is displayed, press . If D.MY is displayed, press .
Table 1-25 Calculating the date
Keys Display Description
G7GgG:J:
2.28 Inputs the date in the selected format.
\Ç VG4
For more information on date and calendar functions, refer to chapter 9, Calendar Formats and Date Calculations.
4-21-2010 3 Inputs the number of days
and calculates the date along with the day of the week.
At a Glance...
13

Bonds

Bond calculations, primarily calculating bond price and yield, are performed by two keys,
and . These keys permit you to input data or return results. Pressing ]Û
only calculates a result. The other keys used in bond calculations only permit you to input the data required for the calculations.
Table 1-26 Bond calculation keys
Keys Description
]Oj ]Û ]Ô ]Ñ ]Î ]Ë
]È ]Å
Clears bond memory.
Calculates accrued interest only.
Yield% to maturity or yield% to call date for given price.
Price per 100.00 face value for a given yield.
Coupon rate stored as an annual %.
Call value. Default is set for a call price per
100.00 face value. A bond at maturity has a call value of 100% of its face value.
Date format. Toggle between day-month-year (dd.mmyyyy) or month-day-year (mm.ddyyyy).
Day count calendar. Toggle between Actual (365-day calendar) or 360 (30-day month/ 360-day year calendar).
Bond coupon (payment). Toggle between semiannual and annual payment schedules.
]¾ ]°
What price should you pay on April 28, 2010 for a 6.75% U.S. Treasury bond maturing on June 4, 2020, if you want a yield of 4.75%? Assume the bond is calculated on a semiannual coupon payment on an actual/actual basis.
If SEMI is not displayed, press
If D.MY is displayed, press to select M.DY format.
At a Glance...14
Settlement date. Displays the current settlement date.
Maturity date or call date. The call date must coincide with a coupon date. Displays the current maturity.
to select the semiannual coupon payment.
Table 1-27 Bond calculation
Keys Display Description
]Oj
Y7GgG:J: ]¾
S7:YG:G: ]°
S7jV]Î J::]Ë
Y7jV]Ô ]Ñ
BOND CLR (message
flashes, then disappears)
4-28-2010 3 Inputs the settlement date
6-4-2020 4 Inputs the maturity date.
6.75 Inputs CPN%.
100.00 Inputs call value. Optional,
4.75 Inputs Yield%.
115.89 Calculates the price.
Clears bond memory.
(mm.ddyyyy format).
as default is 100.
1]Û 4
For more information on bond calculations, refer to chapter 10, Bonds.
2.69 Displays the current value for accrued interest.
118.59 Returns the result for total price (value of price + value of accrued interest). The net price you should pay for the bond is 11 8 . 5 9 .
At a Glance...
15

Break-even

Table 1-28 Break-even keys
Keys Description
]OY
Clears break-even memory.
Stores the quantity of units required for a given profit or calculates it.
Stores the sales price per unit or calculates it.
]© ]¦
Stores variable cost per unit for manufacturing or calculates it.
Stores the fixed cost to develop and market or calculates it.
Stores the expected profit or calculates it.
]~
The sale price of an item is 300.00, the cost 250.00, and fixed cost 150,000.00. For a profit of 10,000.00, how many units would have to be sold?
Table 1-29 Calculating break-even
Keys Display Description
]OY
BR EV CLR (message flashes,
then disappears)
150,000.00 Inputs fixed cost.
Clears break-even memory.
JV::::] £
GV:]¦
250.00 Inputs variable cost per unit.
D::]©
300.00 Inputs price.
J::::]~
10,00 0.00 I nput s profi t.
For more information on break-even calculations, refer to chapter 11, Break-even.
3,200.00 Calculates the current value
for the unknown item, UNITS.
At a Glance...16

Statistical Calculations

Table 1-30 Statistics keys
Keys Description
\t
x-data
¡
x-data
Æ y-data ¡
x-data
x-data
Æ y-data \¢
\k \«
Clear statistical registers.
Enter one-variable statistical data.
Delete one-variable statistical data.
Enter two-variable statistical data.
Delete two-variable statistical data.
Opens editor for reviewing/ editing entered statistical data.
Means of x and y.
\T \« \h \« \e \«
y-data
\Z \«
\W \«
x-data
]L
Mean of x weighted by y. Also calculates b, intercept.
Sample standard deviations of x and y.
Population standard deviations of x and y.
Estimate of x and correlation coefficient.
Estimate of y and slope.
Permits selection of six regression models; linear is default.
At a Glance...
17
Using the following data, find the means of x and y, the sample standard deviations of x and
Σ
Σ
y, and the y-intercept and the slope of the linear regression forecast line. Then, use summation statistics to find xy.
x-data 2 4 6 y-data 50 90 160
Table 1-31 Statistics example
Keys Display Description
\t GÆV:¡ YÆd:¡ SÆJS:¡ v¡
\k \«
0.00 Clears statistics registers.
1.00 Enters first x,y pair.
2.00 Enters second x,y pair.
3.00 Enters third x,y pair.
1 2.00 Reviews entered statistical
data, starting with the initial
x-value. Press through and verify the
entered statistical data.
Press
M to exit.
4.00 Displays mean of x.
100.00 Displays mean of y.
1 to scroll
\h \« \T\« \W\« ]f
For more information on statistical calculations, refer to chapter 12, Statistical Calculations.
At a Glance...18
2.00 Displays sample standard deviation of x.
55.68 Displays sample standard deviation of y.
-10 .0 0 D is pl ays y-intercept of regression line.
27.50 Displays slope of regression line.
1,420.00
Displays xy, sum of the products of x- and y-values.

Probability

Table 1-32 Probability keys
Keys Description
]F ]o
F ]I
]o I ]<
]9 ]E
Calculates a cumulative normal probability given a Z-value.
Calculates a Z-value given a cumulative normal probability.
Calculates the cumulative Student’s T probability given degrees of freedom and a T-value.
Calculates a T-value given degrees of freedom and the cumulative Student’s T probability.
Calculates number of permutations of n items taken
r at a time.
Calculates number of combinations of n taken
r at a time.
Calculates factorial of n (where -253 < n <
253).
Enter .5 as a Z-value and calculate the cumulative probability of the Z-value and the Z-value from a given cumulative probability.
Table 1-33 Calculating the probability
Keys Display Description
\5V
7V]F
0.00000 Sets number display to five digits to the right of the decimal.
.69146 Calculates the cumulative
probability of the Z-value.
.94146 Adds .25.
17GV4 ]oF
For more information on probability, refer to the section titled, Probability in chapter 12, Statistical Calculations.
1.56717 Calculates the Z-value from the cumulative probability.
At a Glance...
19

Trigonometric Functions

θ
θ
θ
Table 1-34 Trigonometry keys
Keys Description
] c, R, or C
]o
c, R, or C
]r
c, R, or C
Calculates sine, cosine, and tangent.
Calculates inverse sine, inverse cosine, and inverse tangent.
Calculates hyperbolic sine, cosine and tangent.
]ro
Calculates inverse hyperbolic sine, cosine, and tangent.
c, R, or C ]3
Find Sin =.62 in degrees. If RAD is displayed, press ]3.
Table 1-35 Trigonometry example
Keys Display Description
Toggles between radians and degrees modes. Degrees is the default setting.
.62
Enters value of sine for
7SG ]oc
38.32
Calculates
.
.
At a Glance...20
Convert the results to radians using Pi.
Table 1-36 Converting to radians
Keys Display Description
P\;aJg
.67 Converts degrees to radians.
:4
For more information on trigonometric functions, refer to chapter 2, Getting Started.
At a Glance...
21
At a Glance...22
2 Getting Started

Power On and Off

To turn on your HP 10bII+, press =. To turn the calculator off, press the orange shift key,
\, then >. To change the brightness of the display, hold down = and then
simultaneously press 1 or A.
Since the calculator has continuous memory, turning it off does not affect the information you have stored. To conserve energy, the calculator turns itself off after five minutes of inactivity.
The calculator uses two CR2032 coin batteries. If you see the low-battery symbol ( ) in the display, replace the batteries. For more information, refer to the section titled, Installing Batteries in Appendix A.

Manual Conventions and Examples

In this manual, key symbols are used to indicate the key presses used in the example prob­lems. These symbols vary in appearance according to whether they indicate the primary, secondary, or tertiary functions required for the problem. For example, the functions associ-
ated with the equals key, 4, are illustrated in the text as follows:
primary function (equals): 4
secondary function (display): \5
tertiary function (random): ]6
Note the symbol for the primary function of the key, in this case, =, appears on each of the
key symbols depicted above. This repetition is intended to serve as a visual aid. By looking for the symbol of the primary function on the key, you can quickly locate the keys used for the secondary and tertiary functions on the calculator.

Displayed text

Text that appears in the display screen of the calculator is presented in BOLD CAPITAL letters throughout the manual.

Examples

Example problems appear throughout the manual to help illustrate concepts and demonstrate how applications work. Unless otherwise noted, these examples are calculated with CHAIN
set as the active operating mode. To view the current mode, press v]?. The
current mode, CHAIN or ALGEBRAIC, will flash, then disappear. To change the mode, press
] followed by ?.

Getting Started

23

Basics of Key Functions

Table 2-1 Basics of key functions
Keys Display Description
=
][blue]
\[orange]
JGD| ]3
M \t
0.00 Turns calculator on.
0.00
0.00
12_ Erases last character.
RAD
(at the bottom of the display)
0.00 Clears display.
0.00 Clears statistics memory.
Displays shift annunciator .
Displays shift annunciator .
Toggles between radians and degrees. The item before the / is the alternate; the item after the / is the default setting. Except for the operating mode, annunciators in the display indicate alternate settings are active.
\N ]Oj ]OY ]OJ ]O: \>
12 P _Y r (message flashes, then
disappears)
BOND CLR (message flashes,
then disappears)
BR EV CLR (message flashes,
then disappears)
TVM CLR (message flashes, then
disappears)
CFLO CLR (message flashes, then
disappears)
Clears all memory.
Clears bond memory.
Clears break-even memory.
Clears tvm memory.
Clears cash flow memory.
Turns calculator off.
Getting Started24

Shift Keys

Most keys on the HP 10bII+ have three functions:
• a primary function printed in white on the key.
• a secondary function printed in orange on the bevel of the key.
• a tertiary function printed in blue above the key on the keyboard (see Figure 1).
Figure 1
When you press \ or ], a shift annunciator or is displayed to indicate that the shifted functions are active. For example, press \ followed by 2 to multiply a num­ber in the display by itself. To turn the shift annunciators off, press \ or ] again.

Boxed Key Functions

There are three shifted key functions on the calculator that are used to change the operation
of another key's function. These three tertiary functions, ]O, ]o and
]r, are bound by blue boxes to show that they operate differently. These special
functions require subsequent key presses to operate. For example, the functions associated
with the clear key, M, include:
Table 2-2 Clearing functions
Keys Associated Function
Clear display.
M \N \t ]Oj
Clear all memory.
Clear statistics memory.
Clears bond memory.
Getting Started
25
Table 2-2 Clearing functions
Keys Associated Function
]OY
Clears break-even memory.
]OJ
Clears TVM memory.
]O:
Clears cash flow memory.

Simple Arithmetic Calculations

Operating Modes

To change the operating mode, press the blue shift key, ] followed by ? to toggle
between Algebraic and Chain modes. A brief message is displayed indicating the selected operating mode.
To view the current mode, press v]?. The current mode will flash, then disappear.

Arithmetic Operators

The following examples demonstrate using the arithmetic operators 1, A, P, and
a.
If you press more than one operator consecutively, for example 1, A, 1, P
1, all are ignored except the last one.
If you make a typing mistake while entering a number, press | to erase the incorrect digits.
Table 2-3 Example displaying calculations using arithmetic operators
Keys Display Description
GY7jJ1SG7Yj4
When a calculation has been completed (by pressing new calculation.
4), pressing a number key starts a
87.18 Adds 24.71 and
62.47.
Table 2-4 Completing a calculation
Keys Display Description
240.92 Calculates 19 × 12.68.
JdPJG7Sg4
Getting Started26
If you press an operator key after completing a calculation, the calculation is continued.
Table 2-5 Continuing a calculation
Keys Display Description
1JJV7V4

Calculations in Chain Mode

Calculations in Chain mode are interpreted in the order in which they are entered. For example, entering the following numbers and operations as written from left to right,
356.42 Completes calculation of
240.92 + 115.5.
J1GPD4, returns 9. If you press an operator key, 1,A,P, or a, after 4, the calculation is continued using the currently displayed value.
You can do chain calculations without using 4 after each step.
Table 2-6 Chain calculations
Keys Display Description
S7dPV7DVa
36.92
Pressing a displays
intermediate result (6.9 × 5.35).
40.57 Completes calculation.
7dJ4
Without clearing, now calculate 4 + 9 × 3.
Table 2-7 Chain calculations
Keys Display
13.00 Adds 4 and 9.
Y1dP D4
39.00 Completes calculation.
In Chain mode, if you wish to override the left to right order of entry, use parentheses
\q and \n to prioritize operations.
Getting Started
27
For example, to calculate 1 + (2 x 3), you may enter the problem as written from left to right,
y
x
30
85 12()
----------------------
9×
with parentheses to prioritize the multiplication operation. When entered with parentheses, this expression returns a result of 7.

Calculations in Algebraic Mode

In Algebraic mode, multiplication and division have a higher priority than addition and
subtraction. For example, in Algebraic mode, pressing J1GPD4 returns a
result of 7.0 0 . In Chain mode, the same key presses return a result of 9.00 . In Algebraic mode, operations between two numbers have the following priority:
Highest priority: combinations and permutations, T probability calculations, % change, and
date calculations
Second priority: the power function ( )
Third priority: multiplication and division
Forth priority: addition and subtraction.
The calculator is limited to 12 pending operations. An operation is pending when it is waiting for the input of a number or the result of an operation of higher priority.

Using Parentheses in Calculations

Use parentheses to postpone calculating an intermediate result until you’ve entered more numbers. You can enter up to four open parentheses in each calculation. For example, suppose you want to calculate:
If you enter D:agVA, the calculator displays the intermediate result, 0.35.
This is because calculations without parentheses are performed from left to right as you enter them.
To delay the division until you’ve subtracted 12 from 85, use parentheses. Closing parentheses at the end of the expression can be omitted. For example, entering 25 ÷ (3 × (9 + 12 = is equivalent to 25 ÷ (3 × (9 + 12)) =.
If you type in a number, for example, 53, followed by the parenthesis symbol, the calculator considers this implicit multiplication.
Example
Table 2-8 Using parentheses in calculations
Keys Display Description
D:a\qgVA JG\n
Getting Started28
85.00 No calculation yet.
73.00 Calculates 85 - 12.
Table 2-8 Using parentheses in calculations
Keys Display Description
P
0.41 Calculates 30 ÷ 73.
d4
3.70 Multiplies the result by 9.

Negative Numbers

Enter the number and press y to change the sign.
Calculate -75 ÷ 3.
Table 2-9 Changing the sign of numbers
Keys Display Description
-75_ Changes the sign of 75.
jVy aD4
–25.00 Calculates result.
Understanding the Display and Keyboard Cursor
The blinking cursor ( _ ) is visible when you are entering a number.

Clearing the Calculator

Backspace

When the cursor is on, | erases the last digit you entered. Otherwise, | clears the
display and cancels the calculation.

Clear

M clears the current item on the display and replaces it with 0. If entry is in progress,
pressing M clears the current entry and replaces it with 0, but the current calculation continues. Otherwise, M clears the display of its current contents and cancels the current
calculation.

Clear Memory

]O followed by j,Y,J,: clears a selected memory type (register). Other
memory is left intact.
Getting Started
29
Table 2-10 Clear memory keys
Keys Description
]Oj
Clears bond memory.
]OY
Clears break-even memory.
]OJ
Clears TVM memory.
]O:
Clears cash flow memory.
\t
Clears statistics memory.

Clear All

\N all clears all memory in the calculator, with the exception of the payments per
year (P/Yr) setting. To clear all memory and reset calculator modes, press and hold down
=, then press and hold down both Ù and Ï. When you release all three, all
memory is cleared. The All Clear message is displayed.

Clearing Messages

When the HP 10bII+ is displaying an error message, |or M clears the message and
restores the original contents of the display.

Annunciators

Annunciators are symbols in the display that indicate the status of the calculator. For functions that toggle between settings, annunciators indicate alternate settings are active. For the defaults, no annunciators appear in the display. For example, when selecting a date format, the default setting is month-day-year (M.DY). When day-month-year (D.MY) is active, the D.MY in the display indicates it is the active setting. Table 2-11 lists all the annunciators that appear in the display screen.
Getting Started30
Table 2-11 Annunciators and status
Annunciator Status
,
INV Inverse mode is active for trigonometric or probability functions. RAD Radians mode is active. BEG Begin mode is active; payments are at the beginning of a
D.MY Day-month-year date format (DD.MMYYYY) is active. 360 360-day calendar is active. SEMI Semi-annual coupon payment schedule (bonds) is active. PEND An operation is waiting for another operand. INPUT
AMORT The amortization annunciator is lit, together with one of the
PER The range of periods for an amortization is displayed. PRIN The principal of an amortization is displayed.
A shift key has been pressed. When another key is pressed, the functions labeled in orange or blue are executed.
period.
The
Æ key has been pressed and a number stored.
Battery power is low.
following four annunciators:
INT The interest of an amortization is displayed. BAL The balance of an amortization is displayed.
CFLO The cash flow annunciator is lit, together with one of the
following two annunciators:
CF The cash flow number appears briefly, then the cash flow is
shown.
N The cash flow number appears briefly, then the number of
times the cash flow is repeated is shown.
STAT The statistics annunciator is lit, together with one of the following
two annunciators:
X The number of the data point, n, followed by an x-value is
shown, or, if STAT is not lit, indicates that the first of two results is displayed.
Y The number of the data point, n, followed by a y-value is
shown, or, if STAT is not lit, indicates that the second of two results is displayed.
ERROR The error annunciator is lit, together with one of the following
four annunciators:
TVM There is a TVM error (such as an invalid P/Yr), or, when
ERROR is not lit, a TVM calculation returned a second result.
FULL Available memory for cash flows or statistics is full, or the
pending operator memory is full.
STAT Incorrect data used in a statistics calculation or, when
ERROR is not lit, a statistical calculation has been performed.
Getting Started
31
Table 2-11 Annunciators and status
Annunciator Status
FUNC A math error has occurred (for example, division by zero).

Input Key

The Æ key is used to separate two numbers when using two-number functions or two­variable statistics. The Æ key can also be used to enter cash flows and cash flow counts,
ordered pairs, and evaluate any pending arithmetic operations, in which case the result is the
same as pressing 4.

Swap Key

Pressing exchanges the following:
The last two numbers that you entered; for instance, to change the order of division or subtraction.
The results of functions that return two values.
The « key toggles the item in the Æ register, or swaps the top two items in the
mathematical stack. This function is used to retrieve a secondary value returned during a calculation, as well as to swap two items during a calculation.

Statistics Keys

The statistics keys are used to access summary statistics from the statistics memory registers.
When you press ] followed by a statistics key, you can recall one of six summary statistics
with the next keystroke.
For example, press ] followed by the X key to recall the sum of the x-values entered.
Table 2-12 Statistics keys
Keys Description
]l ]i
Sum of the squares of the x­values.
Sum of the squares of the y­values.
]f
Sum of the products of the x- and y-values.
Number of data points entered.
][
Getting Started32
Table 2-12 Statistics keys
Keys Description
]U
Sum of the y-values.
]X
Sum of the x-values.

Time Value of Money (TVM), Cash Flows, Bond, and Break-even Keys

When entering data for TVM, cash flows, bond, depreciation and break-even calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations:
store data.
enter data for a variable that is used during calculations (input only).
calculate unknown variables based on stored data.
For more information on how these keys function, refer to the specific chapters which cover TVM problems, cash flows, and bond and break-even calculations.

Math Functions

One-Number Functions

Math functions involving one number use the number in the display. To execute one-number functions, with a number displayed, press the key or key combination corresponding to the operation you wish to execute. The result is displayed. See Table 2-14 for a list of one-number functions.
Before doing any trigonometric calculations, check whether the angle mode is set for degrees or radians (Rad). Degrees is the default setting. The RAD annunciator in the display indicates
radians is active. Press ]3 to toggle between the settings. You will need to change
the setting if the active mode is not what your problem requires.
Table 2-13 Example displaying one number functions
Keys Display Description
9.45 Calcula tes squa re root.
gd7GV\B D7Vj1G7DS\b
0.42 1/2.36 is calculated
first.
3.99 Adds 3.57 and 1/2.36.
4
Table 2-14 lists the one-number functions of the calculator.
Getting Started
33
Table 2-14 One-number functions
Keys Description
§ \} \b \B \2 \K \H \E ]
Divide a number by 100.
Rounds x to the number specified by the display format.
Calculates 1/x.
Calculates the square root of x.
Calculates the square of x.
Calculates natural exponent to the power of x.
Calculates natural log.
Calculates factorial of n (where -253 < n < 253). The Gamma function is used to calculate n! for non-integers or negative numbers.
Calculates sine, cosine, or tangent.
c, R, or C ]o
c, R, or C ]r
c, R, or C ]ro
c, R, or C ]F ]oF
Calculates inverse sine, cosine, or tangent.
Calculates hyperbolic sine, cosine, or tangent.
Calculates inverse hyperbolic sine, cosine, or tangent.
Calculates a cumulative normal probability given a Z-value.
Calculates a Z-value given a cumulative normal probability.
The random function]6, and Pi \; are special operators. They insert values
for Pi, or a random number in the range 0 < x <1, into calculations.
Getting Started34

Trigonometric and Hyperbolic Functions and Modes

Selecting Angle Format

The trigonometric angle format determines how numbers are interpreted when using trigonometry functions. The default format for angles on the 10bII+ is degrees. To change to
radians mode, press ]3. When radians mode is active, the RAD annunciator is
displayed.

Trigonometric Functions

Table 2-15 Trigonometric functions
Keys Description
]c
Calculates sine, written as sin.
]R ]C ]oc
]oR ]oC
Example
Perform the following trigonometric calculations. If RAD is lit in the display, press ]3.
Table 2-16 Example using various trigonometric calculations
Calculates cosine, written as cos.
Calculates tangent, written as tan.
Calculates inverse sine, also written, arcsin, asin, or sin
Calculates inverse cosine, also written, arccos, acos, or cos
Calculates inverse tangent, also written, arctan, atan, or tan
-1
.
-1
.
-1
.
Keys Display Description
0.0000 Set display to four decimal places.
\5Y JV]c
0.2588
1. 7 3 21
J1S:]C
2.7321
4
69.5127 Displays inverse cosine of 0.35.
Displays sine of 15
Displays tangent of 60
Calculates 1 + tangent of 60
7DV]oR
o
.
o
.
Getting Started
o
.
35
Table 2-16 Example using various trigonometric calculations
π
π
π
A 4πr
2
=
π
Keys Display Description
A7SG]oR
51. 6839 D isp l ay s inv er s e co s ine o f 0. 62.
4
17.8288 Calculates arccos 0.35 - arccos 0.62.
\5G
17.83 Return display to default format.
Pi
Pressing \; displays the value of . Although the displayed value is appears in the
current display format, the 12 digit value is actually used for calculations. is often used during calculations in radians mode, as there are 2 radians in a circle.
Example
Find the surface area of a sphere with a radius of 4.5 centimeters. Use the formula:
Table 2-17 Example using Pi
Keys Display Description
YP\; PY7V\2 4

Hyperbolic Functions

Table 2-18 Hyperbolic and inverse hyperbolic functions
Keys Description
]rc ]rR ]rC ]roc
3.14
20.25
254.47 Calculates sphere surface area
Calculates hyperbolic sine, written as, sinh.
Calculates hyperbolic cosine, written as, cosh.
Calculates hyperbolic tangent, written as, tanh.
Calculates inverse hyperbolic sine, written as, arcsinh, asinh, or, sinh
Displays
Displays 4.5
in square centimeters.
.
2
.
-1
.
]roR ]roC
Getting Started36
Calculates inverse hyperbolic sine, also written, arccosh, acosh, or cosh
Calculates inverse hyperbolic tangent, also written, arctanh, atanh, or tanh
-1
.
-1
.
Example
y
x
Perform the following hyperbolic calculations.
Table 2-19 Example performing various hyperbolic calculations
Keys Display Description
\5Y
0.0000 Sets display to four decimal places.
J7GV]rc
1.6019 Display sinh 1.25.
17Vd]rC
0.5299 Displays tanh 0.59.
4
2.1318 Calculates sinh 1.25 + tanh 0.59.
]roR
1.3 89 9 C a lc u lat e s a c o sh 2.1318 .
\5G
1.39 Returns display to default format.

Two-Number Functions

When a function requires two numbers, other than for addition, subtraction, multiplication,
division, and the power function, ( ), you may key in the numbers as follows: number1 Æ number 2 followed by the operation. Pressing Æ evaluates the current expression and
displays the INPUT annunciator.

In-line Functions

For calculations involving \¨, \Ä, \Ç, ]9,
]<,]I, and ]oI, which require two numbers, you may also
key in the first number followed by the function keys, and then key in the second number
followed by 4 to return results. Throughout the manual, when examples are entered in this manner without using Æ, they are referred to as in-line functions. For example, the following keystrokes calculate the percent change between 17 and 29 using the
keys as an in-line function:
Getting Started
37
Table 2-20 Example calculating percent change as an in-line function
Keys Display Description
Jj\¨
17.0 0 E n te rs number1, displays the PEND annunciator indicating the calculator is awaiting instructions.
29_ Enters number 2.
Gd
4
Press M, and now calculate the same example using the Æ key to store the first number,
then key in the second number and perform the operation.
Table 2-21 Example calculating percent change using ‘INPUT’
Keys Display Description
JjÆ
70.59 Calculates the percent change.
17.0 0 E n te rs number1, and displays the INPUT annunciator indicating the number has been stored.
Gd\¨
Although the in-line function has fewer key strokes, performing this example using the Æ key permits you to store a value and then perform other calculations following Æwithout
using parentheses.
Table 2-22 Example displaying two-number functions with chain calculation
Keys Display Description
JjÆ
Gd1DD
1VYAgj
70.59 Enters number 2 and calculates the percent change.
17.0 0 E n t er s number1, and displays the INPUT annunciator.
87_ Enters and performs the chain
calculation. Results are stored and used in the next operation. The PEND annunciator and the blinking cursor indicate an operation is pending as the calculator awaits instructions.
Getting Started38
70.59 Calculates the percent change between 17 and the result of the chain operation (29).
The Table 2-23 below lists the two-number functions of the calculator.
20
20
Table 2-23 Two-number functions
Keys Description
1APa \Q \¨ ]9 ]< \Ç
\Ä ]I
Addition, subtraction, multiplication, division.
The power function.
% Change.
Combinations.
Permutations.
The date and day, past or future, that is a given number of days from a given date.
The number of days between two dates.
Calculates the cumulative Student’s t probability given degrees of freedom and a t­value.
Calculates a t-value given
]oI
Two-number functions may be performed in either CHAIN or ALGEBRAIC mode.
degrees of freedom and the cumulative Student’s t probability.

Arithmetic with One-and Two-number Functions

Math functions operate on the number in the display.

Example 1

Calculate 1/4, then calculate + 47.2 + 1.12.
Table 2-24 Calculating the expression
Keys Display Description
0.25 Calculates the reciprocal of 4.
Y\b G:\B
4.47
Calculates .
Getting Started
39
Table 2-24 Calculating the expression
20
y
x
Keys Display Description
1Yj7G1
51. 67
J7J\2
1. 21
4
52.88 Completes the calculation.
Example 2 Calculate natural logarithm (e
Table 2-25 Calculating the logarithm value
Keys Display Description
2.5
). Then calculate 790 + 4!
12.18
G7V\K \H
2.50 Calculates natural logarithm of
jd:1Y\E
24.00 Calculates 4 factorial.
Calculates + 47.20.
2
2.5
.
.
Calculates 1.1
Calculates e
the result.
4
814.00 Completes calculation.

Example 3

The power operator, , raises the preceding number (y-value) to the power of the following number (x -value).
3
Calculate 125
Table 2-26 Calculating the cube root
Keys Display Description
JGV\QD4 JGV\QD\b4
, then find the cube root of 125.
1/3
3
.
.
1,953,125.00
5.00 Calculates the cube root of
Calculates 125
125, or 125
Getting Started40

Last Answer

When a calculation is completed by pressing 4, or a calculation is completed during
another operation, the result is stored in a memory location that contains the last calculated result. This enables the last result of a calculation to be used during the next calculation.
To access the last calculated answer, press v4. Unlike the other stored memory
registers however, this register is automatically updated when you complete a calculation.

Example 1

Table 2-27 Using last answer
Keys Display Description
VAJ7GV4 D\Qv4 4

Example 2

Table 2-28 Using last answer with ‘INPUT’
Keys Display Description
V:Æ GG1JY\¨ S:Æ
3.75 Calculate 5-1.25
3.75 Recall last answer.
61. 5 5
50.00 Store 50 in the INPUT register.
-28.00 Calculate percent change.
60.00 Store 60 in the INPUT register.
Calculate 3
3.75
.
v4
36.00 Recalls last calculation, 22+14.
-40.00 Calculate percent change.

Display Format of Numbers

When you turn on the HP 10bII+ for the first time, numbers are displayed with two decimal places and a period as the decimal point. The display format controls how many digits appear in the display.
If the result of a calculation is a number containing more significant digits than can be displayed in the current display format, the number is rounded to fit the current display setting.
Getting Started
41
Regardless of the current display format, each number is stored internally as a signed, 12-digit number with a signed, three-digit exponent.

Specifying Displayed Decimal Places

To specify the number of displayed decimal places:
1. P r e s s \5 followed by :d for the desired decimal setting.
2. \5 followed by 7, v, or s changes the display mode. Pressing
\7 provides the best estimate and displays as many digits as required. v is
the value for 10, and s for 11.
Table 2-29 Example displaying the number of decimal places
Keys Display Description
\M
0.00 Clears display.
\5D
0.000 Displays three decimal places.
YV7SP
5.727
7JGVS4 \5d
5.727360000 Displays nine decimal places.
\5G
5.73 Restores two decimal places.
When a number is too large or too small to be displayed in DISP format, it automatically displays in scientific notation.

Displaying the Full Precision of Numbers

To set your calculator to display numbers as precisely as possible, press \57
(trailing zeros are not displayed.) To temporarily view all 12 digits of the number in the display (regardless of the current display format setting), press
is displayed as long as you continue holding 4. The decimal point is not shown.
Start with two decimal places
Getting Started42
\5G.
\5 and hold 4. The number
Table 2-30 Example displaying all digits
Keys Display Description
Jaj4
1. 4 3 D i v i d e s .
\54
142857142857 Displays all 12 digits.

Scientific Notation

Scientific notation is used to represent numbers that are too large or too small to fit in the display. For example, if you enter the number 10,000,000 x 10,000,000 =, the result is
1.0 0E 14, which means one times ten to the fourteenth power, or 1.00 with the decimal point
moved fourteen places to the right. You can enter this number by pressing J\
zJY. The E stands for exponent of ten.
Exponents can also be negative for very small numbers. The number 0.000000000004 is displayed as 4.00E–12, which means four times ten to the negative twelfth power, or 4.0 with the decimal point moved 12 places to the left. You can enter this number by pressing
Y\zyJG.

Interchanging the Period and Comma

To switch between the period and comma (United States and International display) used as
the decimal point and digit separator, press \8.
For example, one million can be displayed as 1,000,000.00 or 1.000.000,00.
Pressing
\8, toggles between these options.

Rounding Numbers

The calculator stores and calculates using 12-digit numbers. When 12 digit accuracy is not desirable, use
calculation. Rounding numbers is useful when you want the actual (dollars and cents) monthly payment.
\} to round the number to the displayed format before using it in a
Getting Started
43
Table 2-31 Example displaying rounding off numbers
Keys Display Description
d7gjSVYD
9.87654321_ Enters a number with more than two nonzero decimal places.
GJ \5G
9.88 Displays two decimal places.
\54
(while you press
4).
\}
987654321000 Displays all digits without the
decimal.
9.88 Rounds to two decimal places (specified by pressing
\5G).
988000000000 Shows rounded, stored number.
\54

Messages

The HP 10bII+ displays messages about the status of the calculator or informs you that you
have attempted an incorrect operation. To clear a message from the display, press M or
|. For a complete list of error messages, refer to Appendix C.
Getting Started44
3 Business Percentages

The Business Percentage Keys

When entering data for business percentage calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations:
store data.
enter known data for variables used during calculations.
calculate unknown variables based on stored data.
You can use the 10bII+ to calculate simple percent, percent change, cost, price, margin, and markup.

Percent key

The § key has two functions:
Finding a percent
Adding or subtracting a percent

Finding a Percent

The § key divides a number by 100 unless it is preceded by an addition or subtraction
sign.
Example Find 25% of 200.
Table 3-1 Finding a percent
Keys Display Description
200.00 Enters 200.
G::P GV§
0.25 Converts 25% to a decimal.
4
50.00 Multiplies 200 by 25%.

Adding or Subtracting a Percent

You can add or subtract a percent in one calculation.
Example 1 Decrease 200 by 25%.

Business Percentages

45
Table 3-2 Subtracting a percent in a calculation
Keys Display Description
G::A
200.00 Enters 200.
GV§
50.00 Multiplies 200 by 0.25 and subtracts 50 from 200.
150.00 Completes the calculation.
4
Example 2 You borrow 1,250 from a relative, and you agree to repay the loan in a year with 7% simple
interest. How much money will you owe?
Table 3-3 Adding a percent in a calculation
Keys Display Description
JGV:1j§ 4

Percent Change

1,337.50 Calculates loan interest, 87.50
and adds 87.50 and 1250.00 to show the repayment amount.
Calculate the percent change between two numbers. Example 1
Calculate the percent change between 291.7 and 316.8 using the in-line feature.
Table 3-4 Calculating the percent change
Keys Display Description
291.70 Enters number1.
GdJ7j\¨ DJS7g4
8.60 Calculates percent change.
Example 2
Calculate the percent change between (12 × 5) and (65 + 18) using Æ.
Table 3-5 Calculating the percent change between two numbers
Keys Display Description
JGPVÆ
60.00 Calculates and enters number1. Note the INPUT annunciator.
SV1Jg\¨
38.33 Calculates percent change.
For more information on in-line features, refer to chapter 2, Getting Started.
Business Percentages46

Margin and Markup Calculations

The 10bII+ can calculate cost, selling price, margin, or markup.
Table 3-6 Keys for margin and markup
Application Keys Description
Margin
À, ¼, ®
Markup
À, ¼, Ã
To see any value used by the margin and markup application, press v and then the key you wish to see. For example, to see the value stored as À, press .
Margin is markup expressed as a percent of price.
Markup calculations are expressed as a percent of cost.

Margin Calculations

Example Kilowatt Electronics purchases televisions for 255. The televisions are sold for 300. What is
the margin?
Table 3-7 Calculating the margin
Keys Display Description
255.00 Stores cost in CST.
GVVÀ D::¼
300.00 Stores selling price in PRC.
®
15. 00 Ca l cu lat es m a rg i n.

Markup on Cost Calculations

Example The standard markup on costume jewelry at Kleiner’s Kosmetique is 60%. They just received
a shipment of chokers costing 19.00 each. What is the retail price per choker?
Table 3-8 Calculating the retail price
Keys Display Description
19.0 0 St or es co st.
JdÀ S:Ã
60.00 Stores markup.
Business Percentages
47
Table 3-8 Calculating the retail price
Keys Display Description
¼
30.40 Calculates retail price.

Using Margin and Markup Together

Example A food cooperative buys cases of canned soup with an invoice cost of 9.60 per case. If the
co-op routinely uses a 15% markup, for what price should it sell a case of soup? What is the margin?
Table 3-9 Calculating the margin
Keys Display Description
9.60 Stores i nvoic e cost.
d7SÀ JVÃ
15. 00 St or es m a rk up .
¼
11.04 Calculates the price on a case of soup.
13 . 0 4 C a l c u l a t e s margin.
®
Business Percentages48
4 Number Storage and Storage Register Arithmetic

Using Stored Numbers in Calculations

You can store numbers for reuse in several different ways:
•Use ª (Constant) to store a number and its operator for repetitive operations.
•Use 3 Key Memory ( keystroke.
•Use

Using Constants

Use ª to store a number and arithmetic operator for repetitive calculations. Once the constant operation is stored, enter a number and press 4. The stored operation is
performed on the number in the display.
Example 1 Calculate 5 + 2, 6 + 2, and 7 + 2.
Table 4-1 Storing ‘+2’ as constant
Keys Display Description
\w and v to store to, and recall from, the 20 numbered registers.
s, p, and m) to store, recall, and sum numbers with a single
2.00 Stores + 2 as constant.
V1Gª 4 S4 j4
7.00 Adds 5 + 2.
8.00 Adds 6 + 2.
9.00 Adds 7 + 2.

Number Storage and Storage Register Arithmetic

49
Example 2 Calculate 10 + 10%, 11 + 10%, and 25 + 10%.
Table 4-2 Storing ‘+ 10%’ as a constant
Keys Display Description
J:1J:§ª
1. 0 0 S t o r e s + 10% as a constant.
4
11.0 0 Adds 10% to 10.
4
12.10 A dds 10% t o 11.
GV4
27.50 Adds 10% to 25.
Example 3 Calculate 23 and 43.
Table 4-3 Storing ‘y
Keys Display Description
3
’ as a constant
3.00
G\QDª 4
8.00
Stores
Calculates 2
3
y
as constant.
3
.
Y4
64.00
Calculates 4
3
.
Number Storage and Storage Register Arithmetic50
Example 4 Calculate the percent change between 55 and 32 and store it as a constant. Then calculate
the percent change between 50 and 32, and 45 and 32.
Table 4-4 Calculating percent change
Keys Display Description
VV\¨DGª
32.00 Stores % change 32 as constant.
4 V:4 YV4
All of the other two-number functions on the calculator may be used with ª in the same
manner as shown in example 4. For a complete list of two-number functions, refer to the section titled, Two -Number Functions in chapter 2.

Using the M Register

The s, p, and m keys perform memory operations on a single storage register, called the M register. In most cases, it is unnecessary to clear the M register, since s
-41.82 Calculates the % change between 55 and 32.
-36.00 Calculates the % change between 50 and 32.
-28.89 Calculates the % change between 45 and 32.
replaces the previous contents. However, you can clear the M register by pressing :s. To add a series of numbers to the M register, use s to store the first number and m to
add subsequent numbers. To subtract the displayed number from the number in the M register,
press y followed by m.
Table 4-5 Keys for performing memory operations
Keys Description
Stores displayed number in the M register.
s p
Recalls number from the M register.
m
Adds displayed number to the M register.
Number Storage and Storage Register Arithmetic
51
Example
475.6
39.15
----------------
and
560.1 475.6+
39.15
---------------------------------------
Use the M register to add 17, 14.25, and 16.95. Then subtract 4.65 and recall the result.
Table 4-6 Calculating basic arithmetic operations using M register
Keys Display Description
Jjs
17.00 S to re s 17 in M re gi st er.
JY7GVm
14.2 5 A dds 14 . 25 to M r eg i s te r.
JS7dVm
16.95 Adds 16.95 to M register.
Y7SVym
-4.65 Adds -4.65 to M register.
p

Using Numbered Registers

The \w and v keys access the 20 user registers, designated 0-19. The
43.55 Recalls contents of the M register.
\w key is used to copy the displayed number to a designated register. The v key
is used to copy a number from a register to the display. To store or recall a number in two steps:
•Press \w or v. To cancel this step, press | or M.
•Press
\w followed by a number key, : to d, or 7 and : to d, to store a
number in the display into a numbered data storage register. Press
\w7 followed by
: through d to access registers 10-19.
•Press
Example In the following example, two storage registers are used. Set the calculator for CHAIN mode
(]?) and calculate the following:
v followed by a number key, : to d, or 7 and : to d, to recall a
number from a storage register. Press 10 -19.
v7 followed by : through d to access registers
Number Storage and Storage Register Arithmetic52
Table 4-7 Calculating the expression using two storage registers
Keys Display Description
YjV7S \w7Y
aDd7JV \wG
4 VS:7J1
v7Y
avG 4
475.60 Stores 475.60 (displayed number) in R
39.15 Stores 39.15 in R
12.15 Completes first calculation.
1,035.70 Recalls R
NOTE: If the calculator is set for
Algebraic mode, press 4 at the
end of this step.
39.15 Recalls R
26.45 Completes second calculation.
.
14
.
2
.
14
.
2
With the exception of the statistics registers, you can also use \w and v for application registers. For example, \wÒ stores the number from the display in the
Ò register. vÒ copies the contents from Ò to the display.
In most cases, it is unnecessary to clear a storage register since storing a number replaces the previous contents. However, you can clear a single register by storing 0 in it. To clear all the
registers at once, press \N.

Doing Arithmetic Inside Registers

You can do arithmetic inside storage registers R0 through R19. The result is stored in the register.
Table 4-8 Keys for performing arithmetic inside registers
Keys New Number in Register
\w1 register number \wA register number
Old contents + displayed number.
Old contents - displayed number.
\wP register number
Old contents × displayed number.
Number Storage and Storage Register Arithmetic
53
Table 4-8 Keys for performing arithmetic inside registers
Keys New Number in Register
\wa register number
Example 1 Store 45.7 in R3, multiply by 2.5, and store the result in R3.
Table 4-9 Calculating and storing the result in the storage register
Keys Display Description
Old contents ÷ displayed number.
45.70 Stores 45.7 in R
YV7j \wD
G7V
2.50 Multiplies 45.7 in R
\wPD vD
114 . 2 5 D i s p l a y s R
.
3
by 2.5 and
3
stores result (114.25) in R
.
3
.
3
Example 2 Store 1.25 into register 15, then add 3, and store the result in register 15.
Table 4-10 Storage register arithmetic
Keys Display Description
1. 25 Inp u ts 1. 25 i n to t h e di s p lay.
J7GV \w7V
1. 25 St o re s 1.25 in R
D\w17V
3.00 Adds 3 to 1.25 in R stores the result R
0.00 Clears the display.
M v7V
4.25 Recalls R
.
15
.
15
and
15
.
15
Number Storage and Storage Register Arithmetic54
5 Picturing Financial Problems

How to approach a Financial Problem

The financial vocabulary of the HP 10bII+ is simplified to apply to all financial fields. For example, your profession may use the term balance, balloon payment, residual, maturity
value, or remaining amount to designate a value that the HP 10bII+ knows as É (future
value). The simplified terminology of the HP 10bII+ is based on cash flow diagrams. Cash flow
diagrams are pictures of financial problems that show cash flows over time. Drawing a cash flow diagram is the first step to solving a financial problem.
The following cash flow diagram represents investments in a mutual fund. The original investment was 7,000.00, followed by investments of 5,000.00 and 6,000.00 at the end of
the third and sixth months. At the end of the 11th month, 5,000.00 was withdrawn. At the end of the 16th month, 16,567.20 was withdrawn.
Figure 2 Cash flow diagram
Any cash flow example can be represented by a cash flow diagram. As you draw a cash flow diagram, identify what is known and unknown about the transaction.
Time is represented by a horizontal line divided into regular time periods. Cash flows are placed on the horizontal line when they occur. Where no arrows are drawn, no cash flows occur.

Picturing Financial Problems

55

Signs of Cash Flows

In cash flow diagrams, money invested is shown as negative and money withdrawn is shown as positive. Cash flowing out is negative, cash flowing in is positive.
For example, from the lender’s perspective, cash flows to customers for loans are represented as negative. Likewise, when a lender receives money from customers, cash flows are represented as positive. In contrast, from the borrower’s perspective, cash borrowed is positive while cash paid back is negative.

Periods and Cash Flows

In addition to the sign convention (cash flowing out is negative, cash flowing in is positive) on cash flow diagrams, there are several more considerations:
The time line is divided into equal time intervals. The most common period is a month, but days, quarters, and annual periods are also common. The period is normally defined in a contract and must be known before you can begin calculating.
To solve a financial problem with the HP 10bII+, all cash flows must occur at either the beginning or end of a period.
If more than one cash flow occurs at the same place on the cash flow diagram, they are added together or netted. For example, a negative cash flow of -250.00 and a positive cash flow of 750.00 occurring at the same time on the cash flow diagram are entered as a 500.00 cash flow (750 - 250 = 500).
A valid financial transaction must have at least one positive and one negative cash flow.

Simple and Compound Interest

Financial calculations are based on the fact that money earns interest over time. There are two types of interest:
Simple interest
•Compound interest
The basis for Time Value of Money and cash flow calculations is compound interest.

Simple Interest

In simple-interest contracts, interest is a percent of the original principal. The interest and principal are due at the end of the contract. For example, say you loan 500 to a friend for a year, and you want to be repaid with 10% simple interest. At the end of the year, your friend
owes you 550.00 (50 is 10% of 500). Simple interest calculations are done using the key on your HP 10bII+. An example of a simple interest calculation can be found in chapter
6 under the section titled, Interest Rate Conversions.
§
Picturing Financial Problems56

Compound Interest

A compound-interest contract is like a series of simple-interest contracts that are connected. The length of each simple-interest contract is equal to one compounding period. At the end of each period the interest earned on each simple-interest contract is added to the principal. For example, if you deposit 1,000.00 in a savings account that pays 6% annual interest, compounded monthly, your earnings for the first month look like a simple-interest contract
written for 1 month at 1/2% (6% ÷ 12). At the end of the first month the balance of the account is 1,005.00 (5 is 1/2% of 1,000).
The second month, the same process takes place on the new balance of 1,005.00. The amount of interest paid at the end of the second month is 1/2% of 1,005.00, or 5.03. The
compounding process continues for the third, fourth, and fifth months. The intermediate results in this illustration are rounded to dollars and cents.
Figure 3 Annual interest compounded monthly
The word compound in compound interest comes from the idea that interest previously earned or owed is added to the principal. Thus, it can earn more interest. The financial calculation capabilities of the HP 10bII+ are based on compound interest.

Interest Rates

When you approach a financial problem, it is important to recognize that the interest rate or rate of return can be described in at least three different ways:
Picturing Financial Problems
57
As a periodic rate. This is the rate that is applied to your money from period to period.
As an annual nominal rate. This is the periodic rate multiplied by the number of periods in a year.
As an annual effective rate. This is an annual rate that considers compounding.
In the previous example of a 1,000.00 savings account, the periodic rate is 1/2% (per month), quoted as an annual nominal rate of 6% (1/2 × 12). This same periodic rate could be quoted
as an annual effective rate, which considers compounding. The balance after 12 months of compounding is 1,061.68, which means the annual effective interest rate is 6.168%.
Examples of converting between nominal and annual effective rates can be found in the section titled, Interest Rate Conversions in the next chapter.

Two Types of Financial Problems

The financial problems in this manual use compound interest unless specifically stated as simple interest calculations. Financial problems are divided into two groups:
•TVM problems
Cash flow problems

Recognizing a TVM Problem

If uniform cash flows occur between the first and last periods on the cash flow diagram, the financial problem is a TVM (time value of money) problem. There are five main keys used to solve a TVM problem.
Table 5-1 Keys for solving a TVM problem
Keys Description
Number of periods or payments
Ù Ò Ï
Annual percentage interest rate (usually the annual nominal rate)
Present value (the cash flow at the beginning of the time line)
Periodic payment
Ì É
You can calculate any value after entering the other four values. Cash flow diagrams for loans, mortgages, leases, savings accounts, or any contract with regular cash flows of the same amount are normally treated as TVM problems.
Future value (the cash flow at the end of the cash flow diagram, in addition to any regular periodic payment).
For example, following is a cash flow diagram, from the borrower’s perspective, for a 30-year, 150,000.00 mortgage, with a payment of 1,041.40, at 7.5% annual interest, with a 10,000 balloon payment.
Picturing Financial Problems58
Figure 4 Cash flow diagram (Borrower’s perspective)
One of the values for PV, PMT, FV can be zero. For example, following is a cash flow diagram (from the saver’s perspective) for a savings account with a single deposit and a single withdrawal five years later. Interest compounds monthly. In this example, PMT is zero.
Figure 5 Cash flow diagram (Saving perspective)
Time value of money calculations are described in the next chapter titled, Time Value of Money Calculations.

Recognizing a Cash Flow Problem

A financial problem that does not have regular, uniform payments (sometimes called uneven cash flows) is a cash flow problem rather than a TVM problem.
Picturing Financial Problems
59
The following is a cash flow diagram for an investment in a mutual fund. This is an example
of a problem that is solved using either (Net Present Value) or
(Internal Rate of Return per Year).
Figure 6 Cash flow diagram (Investment in a mutual fund)
Cash flow problems are described in chapter 8 titled, Cash Flow Calculations.
Picturing Financial Problems60
6 Time Value of Money Calculations

Using the TVM Application

The time value of money (TVM) application is used for compound interest calculations that involve regular, uniform cash flows – called payments. Once the values are entered you can vary one value at a time, without entering all the values again.
To use TVM, several prerequisites must be met:
The amount of each payment must be the same. If the payment amounts vary, use the procedures described in chapter 8 titled, Cash Flow Calculations.
Payments must occur at regular intervals.
The payment period must coincide with the interest compounding period. If it does not, convert the
interest rate using the section titled, Interest Rate Conversions.
There must be at least one positive and one negative cash flow.
\Ó, \Ð, and keys described below in the

The TVM Keys

When entering data for TVM calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations:
store data.
enter known data for variables used during calculations.
calculate unknown variables based on stored data.
Table 6-1 Keys for performing TVM calculations
Keys Stores or Calculates
Number of payments or compounding periods.
Ù Ò
Annual nominal interest rate.
Ï Ì É \Í \Ú
Present value of future cash flows. PV is usually an initial investment or loan amount and always occurs at the beginning of the first period.
Amount of periodic payments. All payments are equal, and none are skipped; payments can occur at the beginning or end of each period.
Future value. FV is either a final cash flow or compounded value of a series of previous cash flows. FV occurs at the end of the last period.
Stores the number of periods per year. The default is 12. Reset only when you wish to change it.
Optional shortcut for storing N: number in display is multiplied by the value in P/YR and the result is stored in N.

Time Value of Money Calculations

61
Table 6-1 Keys for performing TVM calculations
Keys Stores or Calculates
Switches between Begin and End mode. In Begin mode, the BEGIN annunciator is displayed.
Calculates an amortization table.
To verify values, press , , , , and . Pressing v\Ú recalls the total number of payments in years and v\Í
shows you the number of payments per year. Recalling these numbers does not change the content of the registers.

Begin and End Modes

Before you start a TVM calculation, identify whether the first periodic payment occurs at the beginning or end of the first period. If the first payment occurs at the end of the first period, set your HP 10bII+ to End mode; if it occurs at the beginning of the first period, set your calculator to Begin mode.
To switch between modes, press . The BEGIN annunciator is displayed when your
calculator is in Begin mode. No annunciator is displayed when you are in End mode. Mortgages and loans typically use End mode. Leases and savings plans typically use Begin
mode.

Loan Calculations

Example: A Car Loan You are financing a new car with a three year loan at 10.5% annual nominal interest,
compounded monthly. The price of the car is 14,500. Your down payment is 1,500.
Part 1
What are your monthly payments at 10.5% interest? (Assume your payments start one month after the purchase or at the end of the first period.)
Time Value of Money Calculations62
Figure 7 Cash flow diagram (Calculate PMT)
Set to End mode. Press if BEGIN annunciator is displayed.
Table 6-2 Calculating the monthly payment
Keys Display Description
JG\Í
12.00 Sets periods per year (optional, as 12 is the default).
36.00 Stores number of periods in loan.
DPJGÙ J:7VÒ
10.50 Stores annual nominal interest rate.
JYV::A
13,000.00 Stores amount borrowed.
JV::Ï :É Ì
Part 2
At a price of 14,500, what interest rate is necessary to lower your payment by 50.00, to
372.53?
0.00 Stores the amount left to pay after 3 years.
-422.53 Calculates the monthly payment. The negative sign indicates money paid out.
Time Value of Money Calculations
63
Table 6-3 Calculating the interest rate
Keys Display Description
1V:Ì
-372.53 Decreases payment from 422.53.
Ò
Part 3
If interest is 10.5%, what is the maximum you can spend on the car to lower your car payment to 375.00?
Table 6-4 Calculating the amount
Keys Display Description
2.03 Calculates annual interest rate for the reduced payment.
10.50 Stores original interest rate.
J:7VÒ DjVyÌ
-375.00 Stores desired payment.
Ï 1JV::4
11,537.59 Calculates amount of money to
finance.
13,037.59 Adds the down payment to the
amount financed for total price of the car.
Example: A Home Mortgage You decide that the maximum monthly mortgage payment you can afford is 930.00. You can
make a 12,000 down payment, and annual interest rates are currently 7.5%. If you obtain a 30 year mortgage, what is the maximum purchase price you can afford?
Figure 8 Cash flow diagram (Calculate PV)
Time Value of Money Calculations64
Set to End mode. Press if BEGIN annunciator is displayed.
Table 6-5 Calculating the maximum purchase price
Keys Display Description
JG\Í
12.00 Sets periods per year.
D:\Ú
360.00 Stores the length of the mortgage (30 × 12).
0.00 Pays mortgage off in 30 years.
:É j7VÒ
7.50 Stores interest rate.
dD:yÌ Ï 1JG:::4
Example: A Mortgage With a Balloon Payment You’ve obtained a 25 year, 172,500 mortgage at 8.8% annual interest. You anticipate that
you will own the house for four years and then sell it, repaying the loan with a balloon payment. What will your balloon payment be?
-930.00 Stores desired payment (money paid out is negative).
133,006.39 Calculates the loan you can
afford with a 930 payment.
145,006.39 Adds 12,000 down payment
for the total purchase price.
Solve this problem using two steps:
1. Calculate the loan payment using a 25 year term.
2. Calculate the remaining balance after 4 years.
Step 1
First calculate the loan payment using a 25 year term.
Time Value of Money Calculations
65
Figure 9 Cash flow diagram (Calculate PMT)
Set to End mode. Press if BEGIN annunciator is displayed.
Table 6-6 Calculating the monthly payment
Keys Display Description
JG\Í
12.00 Sets periods per year.
GV\Ú :É
300.00 Stores length of mortgage (25 × 12 = 3 00 m ont hs) .
0.00 Stores loan balance after 25 years.
172,500.00 Stores original loan balance.
JjGV::Ï g7gÒ
8.80 Stores annual interest rate.
Ì
-1,424.06 Calculates the monthly payment.
Step 2
Since the payment is at the end of the month, the past payment and the balloon payment occur at the same time. The final payment is the sum of PMT and FV.
Time Value of Money Calculations66
Figure 10 Cash flow diagram (Calculate FV)
The value in PMT should always be rounded to two decimal places when calculating FV or PV to avoid small, accumulative discrepancies between non-rounded numbers and actual (dollars and cents) payments. If the display is not set to two decimal places, press
\5G.
Table 6-7 Calculating the final amount
Keys Display Description
\}Ì YgÙ É 1vÌ4
-1,424.06 Rounds payment to two decimal places, then stores.
48.00 Stores four year term (12 × 4) that you expect to own house.
-163,388.39 Calculates loan balance after four years.
-164 ,812. 45
Calculates the total 48 payment (PMT and FV) to pay off the loan (money paid out is negative).
th

Savings Calculations

Example: A Savings Account If you deposit 2,000 in a savings account that pays 7.2% annual interest compounded
annually, and make no other deposits to the account, how long will it take for the account to grow to 3,000?
Time Value of Money Calculations
67
Figure 11 Cash flow diagram (Calculate the number of years)
Since this account has no regular payments (PMT = 0), the payment mode (End or Begin) is irrelevant.
Table 6-8 Calculating the number of years
Keys Display Description
]OJ
0.00 Clears TVM memory.
J\Í G:::yÏ D:::É
1. 0 0 S e t s P/YR to 1 since interest is compounded annually.
-2,000.00 Stores amount paid out for the first deposit.
3,000.00 Stores the amount you wish to
accumulate.
7.20 Stores annual interest rate.
j7GÒ Ù
Since the calculated value of N is between 5 and 6, it will take six years of annual compounding to achieve a balance of at least 3,000. Calculate the actual balance at the end of six years.
5.83 Calculates the number of years it takes to reach 3,000.
Time Value of Money Calculations68
Table 6-9 Calculating the balance after six years
Keys Display Description
6.00 Sets n to 6 years.
É
Example: An Individual Retirement Account You opened an individual retirement account on April 14, 1995, with a deposit of 2,000.
80.00 is deducted from your paycheck and you are paid twice a month. The account pays
6.3% annual interest compounded semimonthly. How much will be in the account on April 14, 2010?
3,035.28 Calculates the amount you can
withdraw after six years.
Figure 12 Cash flow diagram (Calculate FV)
Set to End mode. Press if BEGIN annunciator is displayed.
Table 6-10 Calculating the balance amount
Keys Display Description
24.00 Sets number of periods per year.
GY\Í G:::yÏ
-2,000.00 Stores initial deposit.
g:yÌ
-80.00 Stores regular semimonthly deposits.
Time Value of Money Calculations
69
Table 6-10 Calculating the balance amount
Keys Display Description
S7DÒ
6.30 Stores interest rate.
JV\Ú
360.00 Stores the number of deposits.
É
52,975.60 Calculates the balance amount.
Example: An Annuity Account You opt for an early retirement after a successful business career. You have accumulated a
savings of 400,000 that earns an average of 7% annual interest, compounded monthly. What annuity (repetitive, uniform, withdrawal of funds) will you receive at the beginning of each month if you wish that savings account to support you for the next 50 years?
Figure 13 Cash flow diagram (Calculate the amount)
Set to Begin mode. Press if BEGIN annunciator is not displayed.
Table 6-11 Calculating the amount at the beginning of each month
Keys Display Description
12.00 Sets payments per year.
JG\Í Y:::::yÏ jÒ
-400,000.00 Stores your nest egg as an outgoing deposit.
7.00 Stores annual interest rate you expect to earn.
600.00 Stores number of withdrawals.
V:\Ú :É Ì
0.00 Stores balance of account after 50 years.
2,392.80 Calculates the amount that you
can withdraw at the beginning of each month.
Time Value of Money Calculations70

Lease Calculations

A lease is a loan of valuable property (like real estate, automobiles, or equipment) for a specific amount of time, in exchange for regular payments. Some leases are written as purchase agreements, with an option to buy at the end of the lease (sometimes for as little as
1.00). The defined future value (FV) of the property at the end of a lease is sometimes called the residual value or buy out value.
All five TVM application keys can be used in lease calculations. There are two common lease calculations.
Finding the lease payment necessary to achieve a specified yield.
Finding the present value (capitalized value) of a lease.
The first payment on a lease usually occurs at the beginning of the first period. Thus, most lease calculations use Begin mode.
Example: Calculating a Lease Payment A customer wishes to lease a 13,500 car for three years. The lease includes an option to buy
the car for 7,500 at the end of the lease. The first monthly payment is due the day the customer drives the car off the lot. If you want to yield 10% annually, compounded monthly, what will the payments be? Calculate the payments from your (the dealer’s) point of view.
Figure 14 Cash flow diagram (Calculate the monthly lease payment)
Set to Begin mode. Press if BEGIN annunciator is not displayed.
Time Value of Money Calculations
71
Table 6-12 Calculating the monthly lease payment
Keys Display Description
JG\Í
12.00 Sets payments per year.
J:Ò
10.00 Stores desired annual yield.
JDV::yÏ
-13,500.00 Stores lease price.
jV::É
7,500.00 Stores residual (buy out value).
DSÙ
36.00 Stores length of lease, in months.
Ì
Notice that even if the customer chooses not to buy the car, the lessor still includes a cash flow coming in at the end of the lease equal to the residual value of the car. Whether the customer buys the car or it is sold on the open market, the lessor expects to recover 7,500.
Example: Lease With Advance Payments Your company, Quick-Kit Pole Barns, plans to lease a forklift for the warehouse. The lease is
written for a term of four years with monthly payments of 2,400. Payments are due at the beginning of the month with the first and last payments due at the onset of the lease. You have an option to buy the forklift for 15,000 at the end of the leasing period.
253.99 Calculates the monthly lease payment.
If the annual interest rate is 9%, what is the capitalized value of the lease?
Figure 15 Cash flow diagram (Calculate PV of the lease)
Time Value of Money Calculations72
This solution requires four steps:
1. Calculate the present value of the 47 monthly payments: (4 × 12) - 1 = 47.
2. Add the value of the additional advance payment.
3. Find the present value of the buy option.
4. Sum the values calculated in steps 2 and 3.
Step 1
Find the present value of the monthly payments.
Set to Begin mode. Press if BEGIN annunciator is not displayed.
Table 6-13 Calculating the present value
Keys Display Description
JG\Í
12.00 Sets payments per year.
YjÙ
47.00 Stores number of payments.
GY::yÌ
-2,400.00 Stores monthly payment.
0.00 Stores FV for Step 1.
9.00 Stores interest rate.
Ï
Step 2
Add the additional advance payment to PV. Store the answer.
Table 6-14 Adding the advance payment
Keys Display Description
1vÌy4
95,477.55 Calculates the present value of
47 monthly payments.
97,877.55 Adds additional advance.
payment
s
97,877.55 Stores result in M register.
Step 3
Find the present value of the buy option.
Table 6-15 Calculating the present value of the last cash flow
Keys Display Description
48.00 Stores month when buy option
YgÙ
occurs.
Time Value of Money Calculations
73
Table 6-15 Calculating the present value of the last cash flow
Keys Display Description
0.00 Stores zero payment for this step of solution.
-15,000.00 Stores value to discount.
JV:::yÉ Ï
Step 4
Add the results of ’Step 2’ and ’Step 3’.
Table 6-16 Calculating the present value of lease
Keys Display Description
108,356.77 Calculates the present (capitalized)
1p4

Amortization

Amortization is the process of dividing a payment into the amount that applies to interest and the amount that applies to principal. Payments near the beginning of a loan contribute more interest, and less principal, than payments near the end of a loan.
10,479.21 Calculates the present value of
last cash flow.
value of lease. (Rounding discrepancies are explained on page 67.)
Figure 16 Graph
Time Value of Money Calculations74
The AMORT key on the HP 10bII+ allows you to calculate.
The amount applied to interest in a range of payments.
The amount applied to principal in a range of payments.
•The loan balance after a specified number of payments are made.
The function assumes you have just calculated a payment or you have stored the
appropriate amortization values in I/YR, PV, FV, PMT, and P/YR.
Table 6-17 Keys for storing the amortization values
Keys Description
Ò
Annual nominal interest rate.
Ï
Starting balance.
É
Ending balance.
Ì
Payment amount (rounded to the display format).
Number of payments per year.
The numbers displayed for interest, principal, and balance are rounded to the current display setting.

To Amortize

To amortize a single payment, enter the period number and press . The HP 10bII+
displays the annunciator PER followed by the starting and ending payments that will be amortized.
4 to see interest (INT). Press 4 again to see the principal (PRIN) and again to see
Press
the balance (BAL). Continue pressing 4 to cycle through the same values again.
To amortize a range of payments, enter starting period number
then press
and ending payments that will be amortized. Then press interest, principal, and balance.
Press \Ê again to move to the next set of periods. This auto-increment feature saves
you the keystrokes of entering the new starting and ending periods.
. The HP 10bII+ displays the annunciator PER followed by the starting
Æ ending period number,
4 repeatedly to cycle through
Time Value of Money Calculations
75
If you store, recall, or perform any other calculations during amortization, pressing 4 will
no longer cycle through interest, principal, and balance. To resume amortization with the
same set of periods, press v\Ê.
Example: Amortizing a Range of Payments Calculate the first two years of the annual amortization schedule for a 30 year, 180,000
mortgage, at 7.75% annual interest with monthly payments.
Set to End mode. Press if BEGIN annunciator is displayed.
Table 6-18 Calculating the monthly payment
Keys Display Description
JG\Í
12.00 Sets payments per year.
D:\Ú
360.00 Stores total number of payments.
j7jVÒ
7. 75 S t or es i n t er est p er y e ar.
Jg::::Ï
180,000.00 Stores present value.
0.00 Stores future value.
Ì
-1,289.54 Calculates the monthly payment.
If you already know the mortgage payment, you can enter and store it just like you store the other four values. Next, amortize the first year.
Table 6-19 Calculating the loan balance after a year
Keys Display Description
JÆJG
12_ Enters starting and ending
periods.
Time Value of Money Calculations76
\Ê 4
4
4
1– 12 Displays the PER and AMORT
annunciators and range.
-1,579.84 Displays the PRIN annunciator and the principal paid in the first year.
-13,894. 67 D is pl ays th e INT annunciator and the interest paid in the first year.
178,420 .16 D is p la ys the BAL annunciator
and the loan balance after one year.
The amount paid toward interest and principal (13,894.67 + 1,579.84 = 15,474.51) equals the total of 12 monthly payments (12 × 1,289.54 = 15,474.51). The remaining balance equals the initial mortgage, less the amount applied toward principal (180,000 - 1,579.84 = 178 ,42 0 .16 ) .
Amortize the second year:
Table 6-20 Calculating the remaining balance
Keys Display Description
JDÆGY
13 – 24 Displays PER and the next range of
periods.
\Ê 4 4 4
The amount paid toward interest and principal (13,767.79 + 1,706.69 = 15,474.51) equals the total of 12 monthly payments (12 × 1,289.54 = 15,474.51). The remaining balance equals the initial mortgage less the amount applied toward principal (180,000 - 1,579.84 - 1,706.69 = 176,713.49). More money is applied to principal during the second year rather than the first year. The succeeding years continue in the same fashion.
Example: Amortizing a Single Payment Amortize the 1st, 25th, and 54th payments of a five year car lease. The lease amount is 14,250
and the interest rate is 11.5%. Payments are monthly and begin immediately.
-1,70 6. 69 D is pl ay s PRIN and the principal paid in the second year.
-13,767.79 D is pl ay s INT and the interest paid in the second year.
176 ,713 . 49 D is p l ay s BAL and the loan balance
after 24 payments.
Set to Begin mode. Press
Table 6-21 Calculating the monthly payment
Keys Display Description
if BEGIN annunciator is not displayed.
12.00 Sets payments per year.
JG\Í V\Ú
60.00 Stores number of payments.
JJ7VÒ
11.50 Stores interest per year.
JYGV:Ï
14,250.00 Stores present value.
0.00 Stores future value.
Time Value of Money Calculations
77
Table 6-21 Calculating the monthly payment
Keys Display Description
Ì
-310.42 Calculates the monthly payment.
Amortize the 1st, 25th, and 54th payments
Table 6-22 Calculating the amount
Keys Display Description
1.00 Enters first payment.
1 – 1 Displays PER and the amortized payment
-310.42 Displays PRIN and the first principal
4
0.00 Displays INT and the interest.
4
13 ,9 3 9. 5 8 D i s p l a y s BAL and the loan balance after
4
25.00 Enters payment to amortize.
GVÆ
period.
payment.
one payment.
\Ê 4
4 4 VYÆ
\Ê 4
4 4
25 – 25 Displays PER and the amortized payment
period.
-220.21 Displays PRIN and the principal paid on
th
the 25
-90.21 Displays INT and the interest paid on the 25
9,193. 28 Di spl ays BAL and the balance after the
25
54.00 Enters payment to amortize.
54 – 54 Displays PER and the amortized payment
period.
-290.37 Displays PRIN and the principal paid on the 54
-20.05 Displays INT and the interest paid on the 54
1, 801. 57 D i sp l a ys BAL and the balance after the
54
payment.
th
payment.
th
payment.
th
payment.
th
payment.
th
payment.
Time Value of Money Calculations78

Interest Rate Conversions

The Interest Conversion application uses three keys: , , and
. They convert between nominal and annual effective interest rates.
If you know an annual nominal interest rate and you wish to solve for the corresponding annual effective rate:
1. Enter the nominal rate and press .
2. Enter the number of compounding periods and press .
3. Calculate the effective rate by pressing .
To calculate a nominal rate from a known effective rate:
1. Enter the effective rate and press .
2. Enter the number of compounding periods and press .
3. Calculate the nominal rate by pressing .
In the TVM application, and Ò share the same memory.
Interest conversions are used primarily for two types of problems:
Comparing investments with different compounding periods.
Solving TVM problems where the payment period and the interest period differ.

Investments With Different Compounding Periods

Example: Comparing Investments You are considering opening a savings account in one of three banks. Which bank has the
most favorable interest rate?
First Bank 6.70% annual interest, compounded quarterly Second Bank 6.65% annual interest, compounded monthly Third Bank 6.63% annual interest, compounded 360 times per year
First Bank
Table 6-23 Calculating the interest rate (First bank)
Keys Display Description
6.70 Stores nominal rate.
S7j\Ó Y\Í
4.00 Stores quarterly compounding periods.
Time Value of Money Calculations
79
Table 6-23 Calculating the interest rate (First bank)
Keys Display Description
6.87 Calculates the annual effective rate.
Second Bank
Table 6-24 Calculating the interest rate (Second bank)
Keys Display Description
6.65 Stores nominal rate.
S7SV\Ó
12.00 Stores monthly compounding
JG\Í
6.86 Calculates the annual effective rate.
Third Bank
Table 6-25 Calculating the interest rate (Third bank)
Keys Display Description
6.63 Stores nominal rate.
S7SD\Ó
periods.
DS:\Í
360.00 Stores compounding periods.
6.85 Calculates the annual effective rate.
First Bank offers a slightly better deal since 6.87 is greater than 6.86 and 6.85.

Compounding and Payment Periods Differ

The TVM application assumes that the compounding periods and the payment periods are the same. Some loan installments or savings deposits and withdrawals do not coincide with the bank’s compounding periods. If the payment period differs from the compounding period, adjust the interest rate to match the payment period before solving the problem.
To adjust an interest rate when the compounding period differs from the payment period complete the following steps:
1. Enter the nominal rate and press
in a year and press . Solve for the effective rate by pressing .
. Enter the number of compounding periods
2. Enter the number of payment periods in a year and press . Solve for the adjusted nominal rate by pressing .
Time Value of Money Calculations80
Example: Monthly Payments, Daily Compounding Starting today, you make monthly deposits of 25 to an account paying 5% interest,
compounded daily (using a 365 day year). What will the balance be in seven years?
Step 1 Calculate the equivalent rate with monthly compounding.
Table 6-26 Calculating the equivalent nominal percentage rate
Keys Display Description
V\Ó
5.00 Stores nominal percentage rate.
DSV\Í
365.00 Stores bank’s compounding periods per year.
5.13 Calculates annual effective rate.
\Ð JG\Í
12.0 0 S to re s mo nth ly p er io ds.
Since NOM% and I/YR share the same memory, this value is ready for use in the rest of the problem.
Step 2 Calculate the future value.
Set to Begin mode. Press if BEGIN annunciator is not displayed.
5.01 Calculates the equivalent nominal percentage rate for monthly compounding.
Table 6-27 Calculating the future value
Keys Display Description
0.00 Stores present value
:Ï GVyÌ
-25.00 Stores payment
j\Ú
84.00 Stores total number of payments
É
2,519.61 Calculates the balance after 7
years.
Time Value of Money Calculations
81

Resetting the TVM Keys

Press ]OJ to clear the TVM registers. This sets N, I/YR, PV, PMT, and FV to zero
and briefly displays TVM CLR, followed by the current value in P/Yr.
Time Value of Money Calculations82
7Depreciation
On the 10bII+, depreciation calculations are performed using the functions printed in blue on the keyboard located under the blue bracket titled, DEPRECIATION. Depreciation calculations
are based on data entered into the Time Value of Money (TVM) keys: Ï, É, Ò, and
Ù.
Table 7-1 Depreciation keys
TVM Key Description
]OJ
Ù
Ï
É
]{
]x
]u
Ò
Clear TVM memory. Since the TVM and depreciation applications share the same memory, clearing TVM resets depreciation also.
The expected useful life of the asset in years.
The depreciable cost of the asset at acquisition.
The salvage value of the asset at the end of its useful life.
Straight line is a method of calculating depreciation presuming an asset loses a certain percentage of its value annually at an amount evenly distributed throughout its useful life.
Sum-of-the-years' digits is an accelerated depreciation method. In SOYD, the depreciation in year y is (Life-y +1)/SOY of the asset,
where SOY is the sum-of-the-years for the asset, or, for an asset with a 5-year life, 5+4+3+2+1=15.
Declining balance is an accelerated depreciation method that presumes an asset will lose the majority of its value during the first few years of its useful life.
The declining balance factor as a percentage. This is used for declining balance method.
With the calculated depreciation displayed, press display the remaining depreciable value at the end of the given year.
to

The Depreciation Keys

When entering data for depreciation calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations:
store data.
enter known data for variables used during calculations.
calculate unknown variables based on stored data.

Depreciation

83
To perform a depreciation calculation:
1. Enter the original cost of the asset, using Ï.
2. Enter the salvage value of the asset, using FV. If the salvage value is zero, press
:É.
3. Enter the expected useful life of the asset (in years), followed by Ù.
4. If the declining-balance method is being used, enter the declining-balance factor (as a
percentage), followed by Ò. For example, 1-1/4 times the straight-line rate — 125
percent declining-balance — would be entered as 125.
5. Key in the number of the year for which depreciation is to be calculated followed by the desired depreciation method:
]{ for depreciation using the straight-line method.
]u for depreciation using the sum-of-the-years digits method.
]x for depreciation using the declining-balance method.
]{, ]u, and ]x each place the amount of depreciation in the display,
and the TVM and X annunciators are displayed. Press to display the remaining depreciable value (the book value less the salvage value). After pressing to
display the remaining depreciable value, note the X annunciator changes to Y.

Example 1

A metalworking machine, purchased for 10,000.00, is to be depreciated over five years. Its salvage value is estimated at 500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first two years of the machine's life. See Table 7-2.
Table 7-2 Depreciation example using SL
Keys Display Description
]OJ
TVM CLR (message flashes
then disappears)
Clears TVM registers.
J::::Ï
V::É
Depreciation84
10,00 0.00 En te rs 10,000.00 for the depreciable cost
of the item in the selected format.
500.00 Enters 500.00 for the salvage value of the item in the selected format.
Table 7-2 Depreciation example using SL
Keys Display Description
J]{
G]{
5.00 Inputs 5 for the expected useful life of the asset in the selected format.
1,900.00 Enters the year for which depreciation is
to be calculated and calculates the depreciation of the asset in year one. TVM and X are displayed.
7,600.00 Displays remaining depreciable value
after year one. X changes to Y in the display.
1,900.00 Enters the year for which depreciation is
to be calculated and calculates the depreciation of the asset in year two.
5,700.00 Displays remaining depreciable value
after year two.

Example 2

A machine was purchased for 4,000 and is to be depreciated over four years with a 1,000 salvage value. Using the sum-of-the-year's digit method, what is the depreciation during the machine's first year and third years? What is the remaining depreciable value?
Table 7-3 Depreciation example using SOYD
Keys Display Description
]OJ
Y:::Ï
TVM CLR (message flashes
then disappears)
4,000.00 Enters the depreciable cost of the asset at
4.00 Enters the expected useful life of the asset.
Clears TVM registers.
acquisition.
J:::É
1,000.00 Enters the salvage value.
J]x
1,200.00 Calculates the depreciation for the first year.
D]x
600.00 Calculates the depreciation for the third year.
300.00 Displays the remaining depreciable value.
Depreciation
85

Example 3

A machine was purchased for 5,000 and is to be depreciated over seven years with no salvage value. Using the double declining balance method, what is the depreciation for the first three years of the machine's life? What is the remaining depreciable value?
Table 7-4 Depreciation example using Declining Balance
Keys Display Description
]OJ V:::Ï jÙ G::Ò :É J]u G]u D]u \«
TVM CLR (message flashes
then disappears)
5,000.00 Enters the depreciable cost of the asset at
7.00 Enters the expected useful life of the asset.
200.00 Enters the double declining balance factor as a
0.00 Enters the salvage value.
1,428.57 Calculates the depreciation for the first year.
1,020.41 Calculates the depreciation for the second year.
728.86 Calculates the depreciation for the third year.
1,822.16 Displays the remaining depreciable value.
Clears TVM registers.
acquisition.
percentage.

Resetting the TVM Keys

To clear the TVM registers and reset the TVM and depreciation functions to their default
values, press ]O, followed by J. The messages, TVM CLR and 12 P _ yr appear
briefly to indicate the TVM registers have been reset.
Depreciation86
8 Cash Flow Calculations

How to Use the Cash Flow Application

The cash flow application is used to solve problems where cash flows occur over regular intervals. Problems with regular, equal, periodic cash flows are handled more easily using the TVM keys. To operate the cash flow system, cash flow amounts and repeat values are keyed in either individually or together. In the following chapter, the term repeat value is used to describe the number of times a cash flow occurs. Terms such as cash flow count, number of occurrences, or cash flow group are also used to describe the repeat value.
If a new cash flow is entered, the calculator auto-increments the current cash flow count by 1. A value of 1 is automatically entered for a repeat value. To enter a repeat value for the current
cash flow entry, enter a value using . To enter the cash flow and a repeat value together, enter the cash flow value followed by Æ, then enter the repeat value followed by
¤.
In general, use the following steps for cash flow calculations on the HP 10bII+:
1. Organize your cash flows on paper. A cash flow diagram is useful.
2. Clear the cash flow memory.
3. Enter the number of periods per year.
4. Enter the amount of the initial investment (CF The CF0 value may have a repeated value. To enter the cash flow amount and repeat
value simultaneously, enter a cash flow amount, followed by Æ, then enter a number
for the repeat value followed by
5. Unless the cash flow and repeat value have already been entered as described in step 4
using Æ and ¤, as an alternative, enter the repeat value using .
6. Repeat steps 4 and 5 for each cash flow and repeat value.
7. To calculate net present value and net future value, you must first enter a value for the annual interest rate and press
¤.
Ò; then press \½. With NPV calculated, press
) using ¤ to enter the cash flow value.
0
to display Net Future Value.
8. To calculate IRR, press .

Cash Flow Calculations

87
Table 8-1 Cash Flow Keys
Key Description
]O:
Clears cash flow memory.
number1
number1
number 2 ¤
number 2
¤
Æ
Number of periods per year (default is 12). For annual cash flows, P/YR should be set to 1; for monthly cash flows, use the default setting, 12.
Cash flows, up to 45. J identifies the cash flow number. When preceded by a
number, pressing
Enter a cash flow amount, followed by Æ. Enter a number for the repeat
value followed by simultaneously. An alternative for entering repeat value for cash flow J .
¤ enters a cash flow amount.
¤. This enters cash flow amount and repeat value
Opens editor for reviewing or editing entered cash flows. Press 1 or
A to scroll through the cash flow data.
Internal rate of return per year.
Net present value.
\½\«
Net future value.
]X
With cash flow editor open, displays total of cash flows.
]U
With cash flow editor open, displays total number of cash flows.

Clearing the Cash Flow Memory

It is always a good idea to clear the cash flow memory before beginning. To clear cash flows,
use ]O:. A brief message appears, CFLO CLR, to indicate the cash flow memory
has been reset. On the 10bII+, there is always space reserved for up to 15 cash flows. In addition, up to 30
additional cash flows may be stored in memory shared with the statistics memory, as shown in Figure 1 below.
Cash Flow Calculations88
Figure 1
As illustrated in Figure 1, if no more than 15 data points are stored in the statistics memory, you may store up to 45 cash flows with the shared memory space.
If more than 15 data points are stored in the statistics memory, the total memory available for storing cash flows is reduced. For example, in Figure 2, there are 25 data points stored, and the amount of available shared memory has therefore decreased by 10 slots.
Figure 2
If data storage in the calculator memory resembles Figure 2, and you have a cash flow calculation requiring more than 35 data points, clearing unneeded statistical information will free up more space for information. When available memory is reached (see Figure 3), the FULL annunciator indicates there is not enough space to continue saving data. If you attempt to enter another cash flow at this point, the ERROR annunciator is displayed. In this case, no additional cash flow data can be entered until some data in the statistics memory is removed and the shared memory is once again available.
Figure 3
Example 1: A Short Term Investment The following cash flow diagram represents an investment in stock over three months.
Purchases were made at the beginning of each month, and the stock was sold at the end of the third month. Calculate the annual internal rate of return and the monthly rate of return.
Cash Flow Calculations
89

Calculating Internal Rate of Return

1. P r e s s ]O:, and store the desired number of periods per year in P/YR.
2. Enter the cash flows using Æ and ¤.
3. Press .
Figure 4 Cash flow diagram (Investments in stock)
Table 8-2 Example 1: a short term investment
Keys Display Description
]O:
CFLO CLR
(message flashes, then
disappears)
12.00 Set payments per year.
Clears cash flow memory.
JG\Í V:::y¤
G:::y¤
-5,000.00
(CF 0 flashes, then
disappears)
-2,000.00
(CF 1 flashes, then
disappears)
Enters initial cash flow. Note the CFLO and CF annunciators.
Enters first cash flow. Note the CFLO and CF annunciators.
Cash Flow Calculations90
Table 8-2 Example 1: a short term investment
Keys Display Description
Y:::y¤
JJjSV7Gd¤
-4,000.00
(CF 2 flashes, then
disappears)
11 , 7 6 5 . 2 9
(CF 3 flashes, then
disappears)
38.98 Calculates annual nominal yield.
Enters second cash flow. Note the CFLO and CF annunciators.
Enters third cash flow. Note the CFLO and CF annunciators.
\Á aJG
3.25 Monthly yield.

NPV and IRR/YR: Discounting Cash Flows

Chapter 5 titled, Picturing Financial Problems demonstrates the use of cash flow diagrams to clarify financial problems. This section describes discounted cash flows. The NPV, NFV and IRR/YR functions are frequently referred to as discounted cash flow functions.
When a cash flow is discounted, you calculate its present value. When multiple cash flows are discounted, you calculate the present values and add them together.
The net present value (NPV) function finds the present value of a series of cash flows. The annual nominal interest rate must be known to calculate NPV.
The net future value (NFV) function finds the value of the cash flows at the time of the last cash flow, discounting the earlier cash flows by the value set for the annual nominal interest rate.
The internal rate of return (IRR/YR) function calculates the annual nominal interest rate that is required to give a net present value of zero.
The utility of these two financial tools becomes clear after working a few examples. The next two sections describe organizing and entering your cash flows. Examples of NPV, NFV, and IRR/YR calculations follow.

Organizing Cash Flows

The cash flow series is organized into an initial cash flow (CF0) and succeeding cash flow groups (up to 44 cash flows). CF0 occurs at the beginning of the first period. A cash flow group consists of a cash flow amount and the number of times it repeats.
For example, in the following cash flow diagram, the initial cash flow is -11,000. The next group of cash flows consists of six flows of zero each, followed by a group of three 1,000 cash flows. The final group consists of one 10,000 cash flow.
Cash Flow Calculations
91
Figure 5 Initial cash flow and cash flow groups
Whenever you enter a series of cash flows, it is important to account for every period on the cash flow diagram, even periods with cash flows of zero.
Example Enter the cash flows from the preceding diagram and calculate the IRR/YR. Assume there are
12 periods per year.
Table 8-3 Example calculating IRR and effective interest rate
Keys Display Description
]O:
JG\Í JJ:::y¤
S\¥
Cash Flow Calculations92
CFLO CLR
(message flashes, then
disappears)
12.00 Set payments per year.
-11,000.00
(CF 0 flashes, then
disappears)
0.00
(CF 1 flashes, then
disappears)
6.00
(CFn 1 flashes, then
disappears)
Clears cash flow memory.
Enters initial cash flow. Displays cash flow group number and amount. Note the CFLO and CF annunciators.
Enters first cash flow group amount. Note the CF annunciator.
Enters number of repetitions. Note the CFLO and N annunciators.
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