HP 10b Business Calculator User manual

HP 10b Business Calculator User manual
Page 10 At a Glance
21 1: Getting Started
31 2: Business Percentages
35 3: Number Storage and Arithmetic
43 4: Picturing Financial Problems
51 5: Time Value of Money Calculations
75 6: Cash Flow Calculations
85 7: Statistical Calculations
95 8: Additional Examples
116 A: Assistance, Batteries, and Service
127 B: More About Calculations
133 Messages
136 Index
E] Pacino
Printed in Singapore 11/94 у i И РАСКАНО
(Р) 00010-90037 N
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O presos
19 HP-10B Business Calculator
Owners Manual
1. Interest conversion (page 71). 11. On, clear display,cancel
2. Time value of money (page 51). operation (page 21).
12. n through Zxy: statistical summation
registers (page 89).
13. Statistical functions (page 28).
14. Backspace (page 23).
3. Cash flows (page 75).
4. Store and recall (page 38).
5. Percent (page 31).
6. Clear all memory (page 23). 15. 3-key memory (page 37). Ky A CKARD
7. Separale two numbers (page 25). 16. Margin and markup (page 33).
8. Change sign (раде 22). 17. Accumulate statistical data Edition 6
9. Constant (page 35). (page 86 and 87). Part Number 00010-90037
10. Shift: activate yellow labeled 18. Amortization (page 66).
functions (page 24).
19. Annunciator line (page 24).
For warranty and regulatory information for this calculator, see pages 123
and 120.
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 and fitness for a
particular purpose. Hewlett-Packard Co. shall not be lable for any
crrors or for incidental or consequential damages in connection with the
furnishing, performance, or use of this manual or the keystroke programs
contained herein.
e Hewlett-Packard Co. 1988. All rights reserved. Reproduction,
adaptation, or translation of this manual is prohibited without prior
written permission of Hewlett-Packard Company, except as allowed under
the copyright laws.
The programs that control your calculator are copyrighted and all rights
are reserved, Reproduction, adaptation, or translation of those programs
without prior written permission of Hewlett-Packard Co. is also
Corvallis Division
1000 N.E. Circle Blvd.
Corvallis, OR 97330, U.S.A.
Printing History
Edition 1 October 1988
Edition 2 June 1989
Edition 3 June 1990
Edition 4 August 1992
Edition 6 November 1994
Welcome to the HP-10B
Your HP-10B reflects the superior quality and attention to detail in
engineering and manufacturing that have distinguished Hewlett-Packard
products for 50 years. Hewlett-Packard stands behind this calculator — we
offer expertise to support its use (sce inside the back cover) and world-
wide scrvice.
Hewlett-Packard Quality
Our calculators are made to excel and to be easy to use.
® This calculator is designed to withstand the drops, vibrations, pollu-
tants (smog, ozone), temperature extremes, and humidity variations
that it may encounter in everyday work life.
® The calculator and its manual have been designed and tested for case
of use. We added many examples to highlight the varied uses of the
calculator. Advanced materials and permanent, molded key lettering
provide a long keyboard life and a positive fecl to the keyboard.
m CMOS (low-power) electronics and a liquid-crystal display allow data
to be retained indefinitely and the batteries to last a long time.
m The microprocessor has been optimized for fast and reliable compu-
tations using 15 digits internally for precise results,
m Extensive research has created a design that has minimized the
adverse clfects of static electricity, a potential cause of malfunctions
and data loss in calculators.
Welcome to the HP-10B 3
Featu res
The features of the HP-10B and the manual reflect the needs and wishes
of many customers:
m A large 12-character display.
m An At-a-Glance section in the manual for quick reference.
m Applications to solve business and financial tasks:
= Time Value of Money. Loans, savings, Icases, and amortiza-
tion schedules.
» Interest Conversion. Nominal and effective rates.
= Cash Flows. Net present value and internal rate of return.
= Business Percentages. Percent change, markup, and margin
m Statistics. Mcan, standard deviation, correlation coefficient,
and linear regression forecasting, plus other statistical calcula-
® Enough memory to store an initial cash flow and 14 cash flow groups,
with up to 99 cash flows per group.
m Filtecn numbered storage registers.
mM Easy access to functions saves keystrokes and adds convenience.
® Auto-increment capability for amortization schedules.
wm Labels for amortization and cash (lows.
® Automatic constant.
m 3-key memory.
® Many examples are included in the manual so you can combine them
for your specific needs.
Welcome to the HP-10B
10 Ata Glance...
10 Basics
11 Percentages
12 Memory Keys
13 Time Value of Money (TVM)
14 TVM What if. ..
15 Amortization
16 Interest Rate Conversion
17 IRR/YR and NPV
19 Statistics
21 Getting Started
21 Power On and Off
21 Adjusting the Display Contrast
21 Simple Arithmetic Calculations
23 Understanding the Display and Keyboard
23 Cursor
23 Clearing the Calculator
23 Clearing Memory
24 Annunciators
24 Shift Key
25 INPUT Key
25 SWAP Key
25 Math Functions
26 Display Format of Numbers
27 Specifying Displayed Decimal Places
27 Scientific Notation
28 Displaying the Full Precision of Numbers
Time Value of Money Calculations
28 Interchanging the Period and Comma
28 Rounding Numbers
29 Messages
29 Picturing Memory
2 31 Business Percentages
31 Percent Key
31 Finding a Percent
32 Adding or Subtracting a Percent
32 Percent Change
33 Margin and Markup Calculations
33 Margin Calculations
34 Markup on Cost Calculations
34 Using Margin and Markup Together
3 35 Number Storage and Arithmetic
35 Using Stored Numbers in Calculations
35 Using Constants
37 Using the M Register
38 Using Numbered Registers
39 Doing Arithmetic Inside Registers
40 Doing Arithmetic
41 Power Operator
41 Using Parentheses in Calculations
4 43 Picturing Financial Problems
43 Howto Approach a Financial Problem
44 Signs of Cash Flows
45 Periods and Cash Flows
45 Simple and Compound Interest
45 Simple Interest
46 Compound Interest
47 Interest Rates
47 Two Types of Financial Problems
47 Recognizing a TVM Problem
49 Recognizing a Cash Flow Problem
6 Contents
51 Using the TVM Application
53 Clearing TVM
53 Begin and End Modes
53 Loan Calculations
58 Savings Calculations
62 Lease Calculations
66 Amortization
71 Interest Rate Conversions
71 Investments With Different Compounding Periods
73 Compounding and Payment Periods Differ
75 Cash Flow Calculations
75 How to Use the Cash Flow Application
77 NPV and IRR/YR: Discounting Cash Flows
77 Organizing Cash Flows
78 Entering Cash Flows
79 Viewing and Replacing Cash Flows
80 Calculating Net Present Value
83 Calculating Internal Rate of Return
84 Automatic Storage of IRR/YR and NPV
85 Statistical Calculations
85 Clearing Statistical Data
86 Entcring Statistical Data
86 One-Variable Statistics
86 Two-Variable Statistics and Weighted Mean
87 Correcting Statistical Data
87 Correcting One-Variable Dala
87 Correcting Two-Variable Data
88 Summary of Statistical Calculations
89 Mean, Standard Deviations, and Summation Statistics
91 Linear Regression and Estimation
94 Weighted Mean
Contents 7
8 95 Additional Examples
95 Business Applications
95 Setting a Sales Price
95 Forccasting Based on History
96 Cost of Not Taking a Cash Discount
97 » Loans and Mortgages
97 Simple Annual Interest
98 Continuous Compounding
99 Yicld of a Discounted (or Premium) Mortgage
101 Annual Percentage Rate for a Loan With Fees
102 Loan With a Partial (Odd) First Period
104 Automobile Loan
105 Canadian Mortgages
106 What if... TVM Calculations
107 Savings
107 Saving for College Costs
109 Gains That Go Untaxed Until Withdrawal
111 Value of a Taxable Retirement Account
112 Cash Flow Examples
112 Wrap-Around Mortgages
114 Net Future Value
A 116 Assistance, Batteries, and Service
116 Answers 10 Common Questions
117 Environmental Limits
118 Power and Batteries
118 Low Power Annuncialor
119 Installing Batteries
120 Determining if the Calculator Requires Service
121 Confirming Calculator Operation — the Sclf-Test
123 Limited One-Year Warranty
123 What Is Covered
123 What Is Not Covered
124 Consumer Transactions in the United Kingdom
124 [the Calculator Requires Service
124 Obtaining Service
125 Service Charge
8 Contents
125 Shipping Instructions
126 Warranty on Service
126 Service Agreements
126 Regulatory Information
127 More About Calculations
127 IRR/YR Calculations
127 Possible Outcomes of Calculating IRR/YR
128 Halting and Restarting IRR/YR
128 Entering a Guess for IRR/YR
129 Effect of Using E- to Correct Data
129 Range of Numbers
129 Equations
129 Margin and Markup Calculations
130 Time Value of Money (TVM)
130 Amortization
131 Interest Rate Conversions
131 Cash-Flow Calculations
132 Statistics
133 Messages
136 Index
At a Glance...
This section is designed for you if you're alrcady familiar with calculator
operation or financial concepts, You can usc it for quick reference. The
rest of the manual is filled with explanations and examples of the concepts
presented in this section,
—— оннЕЕЕЕ
Basics — At a Glance...
| EL |
Keys: Display: Description:
[С] 0.00 Turns calculator on.
E 0.00 Displays shift annuncia-
lor (—).
в 0.00 Discontinues shift.
123 [+] 12° Erases last character.
0.00 Clears display.
MiCL 7) 0.00 Clears statistics memory.
M[CLEAR ALL] 0.00 Clears all memory.
RC] Turns calculator off.
10 At a Glance...
Percentages — At a Glance...
Las — |]
- —
[PRC] Price.
MAR Margin,
Add 15% to $17.50.
Keys: Display: Description:
17.50 [+] 17.50 Enters number.
15 (%]) (=) 20.13 Adds 15 %.
Find the margin if the cost is $15.00 and selling price 1s $22.00).
15 15.00 Enters cost.
22 [PRC] 22.00 Enters pricc.
[MAR] 31.82 Calculates margin,
If the cost is $20.00 and the markup is 335¢, what is the selling price?
20 [CST] 20.00 Enters cost.
33 (MU) 33.00 Enters markup,
[PRC] 26.60 Calculates price.
А! д Glance... 11
Memory Keys — At a Glance. ..
Stores a constant operation.
Stores a value in the M register (memory location).
Recalls a value from the M register.
Adds a value to the number stored in the M register.
Stores a value in a numbered register.
Recalls a value from a numbered register.
Multiply 17, 22, and 25 by 7, storing “x 7” as à constant operation.
22 (=)
25 [=]
Display: Description:
7.00 Stores “X 7” as a constant
119.00 Multiplics 17 х 7.
154.00 Multiplies 22 x 7.
175.00 Multiplies 25 x 7.
Store 519 in register 2, then recall it.
519 M (STO) 2
[RCL] 2
519.00 Stores in register 2.
0.00 Clears display.
519.00 Recalls register 2.
12 At a Glance...
Time Value of Money (TVM) — At a Glance...
| Enter any four of the five values and solve for the filth.
A negative sign in the display represents money paid out;
money received is positive,
Number of payments.
Interest per year.
Present value.
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 (7/YR),
what is the monthly payment?
Set to End mode. Press M(BEG/END) if BEGIN annunciator is displayed.
12 BF/YR
360 (N)
Display: Description:
12.00 Sets payments per year.
360.00 Enters number of
10.00 Enters interest per year.
14,000.00 Enters present value.
0.00 Enters future value.
- 122.86 Calculates payment if
paid at end of period.
At a Glance... 13
TVM What if. ..— At a Glance. . .
| ОС;
O oO
% = =
100 [+7-]
— 100.00
| | It is not necessary to reenter TVM values for each example.
| Using the values you just entered (page 13), how much can
особо) you borrow if you want a payment of $100.00?
Enters new payment
amount. (Money paid out
is negative.)
Calculates amount you
can borrow.
How much can you borrow at a 9.5% interest rate?
9.5 [1/YR]
10 (1/YA)
14 Ata Glance...
- 122.86
Enters new interest rate.
Calculates new present
value for $100.00 pay-
ment and 9.5% interest.
Reenters original interest
Reenters original present
Calculates original
Amortize the 20th payment of the loan.
Amortizc the 1st through 12th loan payments.
1 (INPUT) 12
PEr 20- 20
PEr1- 12
= 1 ‚396.50
- 77.82
Amortization — At a Glance...
__liI After calculating a payment using Time Value of Moncey
cocoeo| (TVM), enter the periods to amortize, then press M[AMORT).
Using the previous TVM example (page 13), amortize a
single payment and then a range of payments.
Enters payment to
Displays payment to
Displays interest. (Moncy
paid out is negative.)
Displays principal.
Displays balance.
Enters range of payments
to amortize.
Displays range of periods
Displays interest. (Money
paid out is negative.)
Displays principal.
Displays balance.
At a Glance... 15
Interest Rate Conversion— At a Glance...
HNOM%]) Nominal interest percent.
B(EFF%) Effective interest percent.
M(P/YR] Periods per year.
| | To convert between nominal and effective interest rates,
coææsoo| enter the known rate and the number of periods per year,
= then solve for the unknown rate.
Find the annual effective interest rate of 10% nominal interest com-
pounded monthly.
10 BNOM%)
12 M(P/YR]
16 At a Glance...
Enters nominal rate.
Enters payments per
Calculates annual
effective interest.
IRR/YR and NPV — At a Glance...
4 COS с
H[P/YR Number of periods per year (default is 12).
[CF] Cash flows, up to 15 (*7” identifies the cash Flow number).
MÍN) Number of conscculive times cash flow “7” occurs.
B(RA/YR Internal rate of return per year.
BNPV) Net present value.
l you have an initial cash outflow ofl $- 40,000, followed by monthly cash
inflows ol $4,700, $7,000, $7,000, and $23,000, what is thc JRR/YR? What
is Lhe ZRR per month?
Keys: Display: Description:
BICLEAR ALL] 0.00 Clears all memory.
12 B(P/YR] 12.00 Sets payments per year.
40000 [+7] CFO Enters initial outflow.
- 40,000.00
4700 [СЕ] CF 1 Enters first cash flow.
7000 CF 2 Enters second cash flow.
2 (№) ne Enters number of con-
2.00 seculive Limes cash (low
At a Glance... 17
23000 [СЕЛ CF 3
B(iRR/YR] 15.96
(=) 12 [=] 1.33
Whal is the NPV if the discount rate 15 10%?
10 10.00
Ш (МУ) 622.85
18 At a Glance...
Enters third cash low.
Calculates IRR/YR.
Calculates IRR per
Enters //YR.
Calculates NPV.
Statistics — At a Glance. ..
ина ВС)!
С) в ол ев |
|0 вв в в CC)
1 сос)
M[CL 7)
number M[E-]
number] (INPUT) number?
number] (INPUT) number2 M(E-)
Bi: v] BSWAP]
H(Sx.Sy) (СУАР)
Bloxoy) H[SWAP)
y-value P(X) BSWAP]
x-value (Sm)
Clear statistical registers.
Enter one-variable statistical data.
Delete one-variablc statistical data.
Enter two-variable statistical data.
Delete two-variable statistical data.
Mean of x and y.
Mean of x weighted by y.
Sample standard deviation of x and y.
Population standard deviation of x and y.
Estimate of € and corrclation coefficient,
Estimate of y.
y-intercept and slope.
At a Glance... 19
Using the following data, find the mean of x and y, the sample standard
deviation of x and y, and the y-intercept and the slope of the linear regres-
sion forecast line. Then, use summation statistics to find n and Ey.
Ixdatal 2 | 4 | 6
| y-data | 50 | 90 | 160
Keys: Display: Description:
0.00 Clears statistics registers.
2 50 1.00 Enters first x,y pair.
4 90 2.00 Enters second x,y pair.
6 160 3.00 Enters third x,y pair.
4.00 Displays mean of x.
100.00 Displays mean of y.
2.00 Displays sample standard
deviation of x,
55.68 Displays sample standard
deviation of y.
- 10.00 Displays y-intercept of
regression line (predicted
ÿ value forx = 0),
27.50 Displays slope of regres-
sion line.
4 3.00 Displays n, number of
data points entered.
9 1,420.00 Displays Ex, sum of the
products of x- and
20 Ata Glance...
Getting Started
Power On and off
| "| To turn on your HP-10B, press (€) (the key above the “ON”
900965 label). To turn the calculator off, press the yellow shift key
AS (MM), then [C) (also written M(OFF)).
® 0000) Since the calculator has continuous memory, turning it off
? does not affect the information you've stored. To conserve
energy, the calculator turns itself off approximately 10 minutes after you
stop using it. The calculator's three alkaline batteries last approximately
one year, If you see the low-battery symbol (<3) in the display, replace
the batteries. Refer to appendix A for more information.
Adjusting the Display Contrast
To change the brightness of the display, hold down (C) and ргез$ (+) ог
Simple Arithmetic Calculations
Arithmetic Operators. The following examples demonstrate using the
arithmetic operators [+], [=], [x], and [=].
If you press more than one operator consccutively, for example [+] [=]
[x] [+], all are ignored except the last one.
1: Getting Started 21
If you make a typing mistake while entcring a number, press [e] to erase
the incorrect digits.
Keys: Display: Description:
24.71 (+) 62.47 [=] 87.18 Adds 24.71 and 62.47.
When a calculation has been completed (by pressing [=]), pressing a
number key starts a new calculation.
19 [x] 12.68 [=] 240.92 Calculates 19 x 12.68.
If you press an operator key after completing a calculation, the calculation
is continued.
115.5 (=) 356.42 Completes calculation of
240.92 + 115.5.
You can do chain calculations without using [=] after cach step.
6.9 [x] 5.35 [=] 36.92 Pressing [) displays
intermediate result (6.9 x
91 [=] 40.57 Completes calculation,
Chain calculations are interpreted in the order in which they are entered.
Calculate 4 + 9x3.
4 (+) 9 x] 13.00 Adds 4 + 9.
3 [=] 39.00 Multiplies 13 x 3.
Negative Numbers. Enter the number and press to change the
sign. Calculate -75 = 3.
Keys: Display: Description:
75 [+/-] -75_ Changes the sign of 75.
[=] 3 =) — 25.00 Calculates result.
22 1: Gotting Started
Understanding the Display and Keyboard
The cursor ( _ is visible when you are entering a number.
Clearing the Calculator
NL. ' When the cursor is on, [+] erases the last digit you entered.
205 oa Otherwise, (+) clears the display and cancels the calculation.
90009)! = * & 5
235555 While you are entering a number, pressing [C] clears it to
ООО) zero. Otherwise, [€) clears the display of its current contents
(e 0009
——— and cancels the current calculation.
Clearing Messages. When the HP-10B is displaying an crror mes-
sage, (+) or [C] clears the message and restores the original contents of the
display. Refer to “Messages,” on page 133 for a complete list of messages
and meanings.
Clearing Memory
Keys . Description
MICLEAR ALL) | Clears all memory. Does not reset modes.*
M[CLE Clears statistical memory.
* Modes on your HP-10B are number of payments per year (page 52 ), Begin and
End (page 53), and the display formats (page 26).
1: Getting Started 23
To clear all memory and reset calculator modes, press and hold down [C], | INPUT Key
then press and hold down both [N] and (£+]. When you release all three,
all memory is cleared. The ALL CLr message 1s displayed.
Annunciators are symbols in the display that indicate the status of the
Annunciator Status
_+ Shift is active; when a key is pressed, the function
labeled in yellow above the key, is executed
has been pressed, or two values have
been entered or returned (page 25).
PEND An arithmetic operator is pending ([+], for exam-
BEGIN | Begin mode is active (page 53).
= Battery power is low (page 118).
Shift Key
All of the HP-10B keys have a second or “shifted” function
printed in yellow above the key. The yellow shift key (BB) is
used to access these functions.
| |
i) cc) E a a =
206066 When you press ll, the shift annunciator (—2) is displayed
2000 14 indicate that the shifted functions are active. To turn the
— annunciator off, press NM again.
For example, press WM followed by [x?) (also shown M(x?)) to multiply a
number in the display by itself.
To perform consecutive shifted operations, hold down the shift key while
pressing the desired keys.
24 1: Getting Started
The [INPUT] key is used to separate two numbers when using
two-number functions or two-variable statistics.
| il
ша ОИ
9900| The : annunciator is displayed if INPUT] has been pressed. If
99000 a number is in the display, press [C] to erase the : annuncia-
9090000 | :
— tor and clear the display. If the cursor or an error message 1s
visible in the display, press (C) twice to erase the :
I —
Pressing W(SWAP) exchanges the following:
m The last two numbers that you entered; for instance, to change the
order of division or subtraction.
E The results of functions that return two values. The : annunciator
indicates that two results have been returned; press [SWAP] to see
the hidden result,
m The x- and y-values when using statistics.
Math Functions
| One-Number Functions. Math functions involving one
number use the number in the display.
1: Getting Started 25
Keys: Display: Description:
89.25 BE] 9.45 Calculates square root.
3.57 [+] 2.36 M(1/x) 0.42 1/2.36 15 calculated first.
[=] 3.99 Adds 3.57 and 1/2.36.
- Two-Number Functions. When a function requires two
|scocce numbers, the numbers are entered like this: number!
SS number2 followed by the operation. Pressing [INPUT] evalu-
lo 5050) ates the current expression and displays the : annunciator.
= 3559| For example, the following keystrokes calculate the percent
= change between 17 and 29.
Keys: Display: Description:
17 17.00 Enters number], displays
: annunciator.
29 29 Enters number2.
B(*CHG) 70.59 Calculates the percent
Display Format of Numbers
Mm |
O oca
© ce
When you turn on the HP-10B 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 à 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.
Regardless of the current display format, cach number is stored internally
as a signed, 12-digit number with a signed, three-digit exponent.
26 1: Getting Started
| Specifying Displayed Decimal Places
To specify the number of displayed decimal places:
1. Press MDISP).
2. Enter the number of digits (0 through 9) that you wish to appcar
after the decimal point.
Keys: Display: Description:
[С] 0.00 Clears display.
M(DISP] 3 0.000 Displays three decimal
45.6 [x] .1256 [=] 5.727
| [PERE 5.727360000 Displays nine decimal
M(DISP]) 2 5.73 Restores two decimal
places and rounds
number in display.
When a number is too large or too small to be displayed in DISP format,
it automatically displays in scientific notation,
Scientific Notation
Scientific notation is used to represent numbers that arc 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
1s 1.00E14, which means “onc times ten to the fourteenth
power” or “1.00 with the decimal point moved fourtecn
places to the right.” You can enter this number by pressing
1 mE) 14. The E stands for “cxponent of ten.”
Exponents can also be negative for very small numbers. The number
0.000000000004 15 displayed as 4.00E - 12, which means “four times ten to
the negative twellth power” or “4.0 with the decimal point moved 12
places to the left.” You can enter this number by pressing 4 M(E) (+/-) 12.
1: Getting Started 27
Displaying the Full Precision of Numbers
| |
o СЭС)
e oe
10 (+) 7 (=)
To set your calculator to display numbers as precisely as pos-
sible, press M(DISP) [) (trailing zcros are not displayed.) To
temporarily view all 12 digits of the number in the display
(regardless of the current display format setting), press
H(DISP) and hold (=). The number is displayed as long as you
continue holding (=). The decimal point is not shown.
Start with two decimal places (N(DISP) 2).
Display: Description:
1.43 Divides.
142857142857 Displays all 12 digits.
BOISP) [=]
Interchanging the Period and Comma
а а | не [а |
2 у J
= =
To switch betwcen the period and comma (United States and
International display) used as the decimal point and digit
separator, press M(-/).
For example, one million can be displayed as 1,000,000.00
or 1.000.000,00.
Rounding Numbers
| |
HO Cao;
The calculator stores and calculates using 12 digit numbers.
When 12 digit accuracy is not desirable, use (ВКО) 10 round
the number to the displayed format before using it in a calcu-
lation. Rounding numbers is useful when you want the actual
(dollars and cents) monthly payment.
28 1: Getting Started
Keys: Display: Description:
9.8/654321 9.87654321 Enters a number with
more than two non-zero
decimal places.
M(DISP) 2 9.88 Displays two decimal
H(OISP] (=] 987654321000 Displays all digits without
the decimal while you
press [=].
BAND] 9.88 Rounds to two decimal
places (specified by
pressing M[DISP) 2).
M(DISP]) |=] 988000000000 Shows rounded, stored
The HP-10B 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 [C] or [+]. Refer to “Messages” on page
133 for a list of meanings.
Picturing Memory
The available memory in the HP-10B consists of:
m Ten business application registers.
и А convenient M (memory) register.
® Fifteen registers for storing numbers, cash flows, and summary
1: Getting Started 29
As |
| R
General Storage R, Summation
and Cash Flows Statistics
. Ra
Numbered Memory Registers
You can picture each memory register as a separate box that has a name
and can hold onc number at a time. If you store a number in a register,
you write over the number that was previously stored there.
Notice that 7/YR and NOM% share the same register, and that MAR and
MU share the same register.
30 1: Getting Started
Business Percentages
Y ou can use the HP-10B to calculate simple percent, percent change,
Cost, price, margin, and markup.
Percent Key
!| The (%] key has two functions: finding a percent and 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.
Keys: Display: Description:
200 [x] 200.00 Enters 200.
25 0.25 Converts 25% to a
[=] 50.00 Multiplies 200 by 25%.
2: Business Percentages 31
Adding or Subtracting a Percent
You can add or subtract a percent in one calculation.
Example. Decrease 200 by 25%.
Keys: Display: Description:
200 (-] 200.00 Enters 200.
25 50.00 Multiplies 200 by 0.25.
[=] 150.00 Subtracts 50 from 200.
Example. 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?
Keys: Display: Description:
1250 [+] 7 87.50 Calculates loan interest.
(=) 1,337.50 Adds $87.50 and
$1,250.00 to show repay-
ment amount.
Percent Change
| |
3 then press M(4CHG).
Calculate the percent change between two numbers (n, and
M», expressed as a percent of ,) by entering ny (INPUT) n3,
Example. Calculate the percent change between 291.7 and 316.8.
Keys: Display: Description:
291.7 (INPUT 291.70 Enters n,.
316.8 J[%CHG] 8.60 Calculates percent
32 2: Business Percentages
Example. Calculate the percent change between (12x 5) and (65 + 18).
Keys: Display: Description:
12 (x] 5 [INPUT] 60.00 Calculates and enters ny.
65 [+) 18 [% СНС] 38.33 Calculates percent
Margin and Markup Calculations a
The HP-10B can calculate cost, selling price, margin, or markup.
Application Keys Description
Margin [CST], [PRC], Margin is markup expressed as
a percent of price.
Markup CST), [PRC], Markup calculations are
B{Mu] expressed as a percent of cost.
To sec any value used by the Margin and Markup application, press
and then the key you wish to sec. For example, to see the value stored as
CST), press . Margin and Markup share the same storage
register. For example, if you store 20 in [MAR], then press B(MU),
you will see 20.00 displayed.
Margin Calculations
Example. Kilowatt Electronics purchases televisions for $255. The tele-
visions are sold for $300. What 1s the margin?
Keys: Display: Description:
255 255.00 Stores cost in CST,
300 300.00 Stores sclling price in
15.00 Calculates margin.
2: Business Percontages 33
Markup on Cost Calculations
Example. The standard markup on costume jewelry at Kleiner's
Kosmetique 15 60%. They just received a shipment of chokers costing
$19.00 each. What is the retail price per choker?
19 (CST)
60 M(MU)
Stores cost.
Stores markup.
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?
15 BMY)
34 2: Business Percentages
Stores invoice cost.
Storcs markup.
Calculates the price on a
casc of soup.
Calculates margin.
Number Storage and Arithmetic
Using Stored Numbers in Calculations
Y ou can store numbers, for reuse, in scveral different ways:
® Use [K] (Constant) to store a number and its operator for repetitive
8 Use 3 Key Memory ([+=M], [RM], and (M+]) to store, recall, and sum
numbers with a single keystroke.
в Use and to store and recall the 15 numbered registers.
Using Constants
| Use [K] to store a number and arithmetic operator for repeti-
tive calculations. Once the constant operation is stored, enter
a number and press [=]. The stored operation is performed
| on the number in the display.
3: Number Storage and Arithmetic 35
Keys Operation )
number [K] (=) Stores “+ number" as constant.
[=] number (К) [=] | Stores “— number” as constant.
[x] number [K] [=] Stores “x number" as constant.
| & member (K) (=) Stores “+ number" as constant.
By) x value (К) >) Stores "y? "aluc” as constant,
| [+] number [K] [=] | Stores “+ number %" as constant.
[-) number (%] (K) [=] | Stores "— number %" as constant.
D) mumber (К) (=) | Stores “x number %'" as constant.
[+) mumber (%) [K] [=] | Stores “— mumber %” as constant.
Example. Calculate 5 + 2,6 + 2, and 7 + 2.
Keys: Display: Description:
5 [+] 2 (K] 2.00 Stores “+ 2" as constant.
[=] 7.00 Adds 5 + 2.
6 [=] 8.00 Adds 6 + 2.
7 [=] 9.00 Adds 7 + 2.
Example. Calculate 10 + 10%, 11 + 10%, and 25 + 10%.
Keys: Display: Description:
10 [+] 10 [%] [K] 1.00 Stores “+ 10%” as con-
(=) 11.00 Adds 10% to 10.
[=] 12.10 Adds 10% to 11.
25 [=) 27.50 Adds 10% to 25.
35 3: Number Storage and Arithmetic
Example. Calculate 2° and 4°.
Keys: Display: Description:
2 My") 3 (K] 3.00 Stores “y” as constant.
[=] 8.00 Calculates 2°,
4 (=) 64.00 Calculates 4°,
Using the M Register
| |! The (+>M], [RM], and keys perform memory opcrations
DOOGCC/| on a single storage register, called the M register. In most
900000 ‚ ©
Comeso|| cases, it is unnecessary to clear the M register, since [+M]
Io replaces the previous contents. However, you can clear the
DCC ein 3 Е :
0000) M register by pressing 0 [+M]. To add a series of numbers
= to the M register, use [+M) to store the first number and
to add subsequent numbers. To subtract the displaycd number from the
number in the M register, press followed by [M+].
EN Stores displayed number in the M register.
Recalls number from the M register.
Adds displayed number to the M register.
Example. Use the M register to add 17, 14.25, and 16.95. Then subtract
4.65 and recall the result.
Keys: Display: Description:
17 [+M] 17.00 Stores 17 in M register.
14.25 14.25 Adds 14.25 to M register.
16.95 16.95 Adds 16.95 to M register.
3: Number Storago and Arithmetic 37
4.65 - 4,65 Adds - 4.65 to M
43.55 Recalls contents of the
M register.
Using Numbered Registers
| || The W(STO] and keys access storage registers Ro
MODO | through Rs and R 4 through R 4. (Refer to “Picturing
[20000 Memory” on page 29.) The W[STO) key is used to copy the
lo HS displayed number to a designated register. The key is
| mmol used to copy a number from a register to the display.
© ово)
To store or recall a number in two steps:
1. Press (ЕТО) ог (ВС). (To cancel this step, press [¢] or [C).)
2. Enter the register number (0 through 9 for registers Ry through Ry
or [) 0 through [] 4 for registers R y through R 4).
In the following example, two storage registers are used. Calculate the
4756. 560.1 + 475.6
39.15 39.15
Keys: Display: Description:
475.6 MISTO] 1 475.60 Stores 475.60 (displayed
number) in Ry.
[:) 39.15 M(STO) 2 39.15 Stores 39.15 in Rs.
=] 12.15 Completes first
560.1 [+] [RCL] 1 475.60 Recalls R,.
=) 2 39.15 Recalls Ro.
[=] 26.45 Completes second
You can also use W[STO] and for application registers. For exam-
ple, W(STO) (1/YR) stores the number from the display in the [[/YR] regis-
ter. (RCL) copies the contents from to the display.
38 3: Number Storage and Arithmetic
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
Doing Arithmetic Inside Registers
You can do arithmetic inside storage registers Ry through Rg. The result
is stored in the register.
Keys New Number in Register
B(STO] [+] register number | Old contents + displayed number
H(STO) (F] register number | Old contents - displayed number
| [x] register number
B(STO) (=) register number
Old contents x displayed number
Old contents - displayed number
Example. Store 45.7 in Ra, multiply by 2.5, and store the result in Ra.
Keys: Display: Description:
45.7 BISTO) 3 45.70 Stores 45.7 in Ra.
2.5 H(STO) (x) 3 2.50 Multiplies 45.7 in R3 by
2.5 and stores result
3 114.25 Displays Rs.
3: Number Storage and Arithmetic 39
Doing Arithmetic
— Math functions operate on the number in the display.
Example. Calculate 1/4, then calculate Y 20 + 47.2 + 1.1%.
4 M(17:)
1.1 Ml?)
Calculates the reciprocal
of 4.
Calculates v/ 20.
Calculates V20 + 47.20.
Calculates 1.12.
Completes the calcula-
Example. Calculate natural logarithm (e**). Then calculate 790 + 4!
2.5 Pe”)
790 [+] 4 Mini
40 3: Number Storage and Arithmetic
Calculates e*>.
Calculates natural loga-
rithm of the result.
Calculates 4 factorial.
Completes calculation.
Power Operator
The power operator, B[y*], raises the preceding number (y-
value) to the power of the following number (x-value).
Example. Calculate 125° then find the cube root of 125.
Keys: Display:
125 8077 3 (=) 1,953,125.00
125 My) 3 M(1/x) (=) 5.00
Calculates 125°,
Calculates cube root of
125, which is the same as
Using Parentheses in Calculations
Use parentheses to postpone calculating an intermediate result until
you've entered more numbers. For example, suppose you want to
If you enter 30 (+) 85 [=], 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 sub-
tracted 12 from 85, use parentheses. Closing parentheses at the end of the
expression can be omitted. For example, entering “25 — (3 x (9 + 12 =”
is equivalent to “25 + (3 x (9 + 12)) =”.
3: Number Storage and Arithmetic 41
Keys: Display:
30 (=) M 85 (7) 85.00
12 M0] 73.00
[x] 0.41
9 [=] 3.70
42 3: Number Storage and Arithmetic
No calculation yet.
Calculates 85 = 12.
Calculates 30 = 73.
Multiplics the result by 9.
Picturing Financial Problems
How to Approach a Financial Problem
The financial vocabulary of the HP-10B is simplificd to apply to all finan-
cial fields. For example, your profession may use the term balance, bal-
loon payment, residual, matunty value, or remaining amount to designate a
valuc that the HP-10B knows as (future value).
The simplified terminology of the HP-10B 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.
4: Picturing Financial Problems 43
Up-arrows represent positive
The horizontal line represents
time. It 1s divided into regular
periods, 5,000.00
1 | 2 | 3 14
Down-arrows represent negative
Y - 9000.00 cash flows (money paid out).
Y - 6,000.00
- 7,000.00
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
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.
Signs of Cash Flows
In cash flow diagrams, money invested is shown as negative and money
withdrawn is shown as positive. Cash lowing 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.
A4 4: Picturing Financial Problems
Periods and Cash Flows
In addition to the sign convention (cash flowing out is ncgative, cash
flowing in is positive) on cash flow diagrams, there are several more
m 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.
m To solve a financial problem with the HP-10B, all cash flows must
occur at either the beginning or end of a period.
E If more than onc cash flow occurs at the same place on the cash flow
diagram, they arc 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).
w À 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 carns interest over
time. There are two types of interest: simple interest and compound
interest. The basis for Time Value of Money and cash flow calculations is
compound interest.
Simple Interest
In simple-interest contracts, interest 15 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 15 10% of 500). Simple interest calculations are donc using the [%) key
on your HP-10B. An example of a simple interest calculation is on page
4: Picturing Financlal Problems 45
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
onc compounding period. At the end of cach period the interest carned
on cach 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 15 1/,% of
The second month, the same proccss takes place on the new balance of
$1,005.00. The amount of interest paid at the end of the second month 15
1 /5% of $1,005.00, ог $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,
1 1,010.03
-1,005.00 4 1,025.26
The word compound in compound interest comes from the idea that
interest previously carned or owed is added to the principal. Thus, it can
earn more interest. The financial calculation capabilities on the HP-10B
are based on compound interest.
46 4: Picturing Financial Problems
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:
® As a periodic rate. This is the rate that is applied to your money from
period to period.
m As an annual nominal rate. This is the periodic rate multiplied by the
number of periods in a year.
m As an annual effective rate. This is an annual rate that considers com-
In the previous example of a $1,000.00 savings account, the periodic rate is
1/,% (per month), quoted as an annual nominal rate of 6% (1/2 x 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 arc on
pages 71 through 72.
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 and 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 arc five main keys used to solve a TVM problem.
4: Picturing Financial Problems 47
Number of periods or payments.
Annual percentage interest rate (usually the annual nomi-
nal rate).
Present value (the cash flow at the beginning of the time
Periodic payment.
38 5 6°
Future value (the cash flow at the end of the cash flow
diagram, in addition to any regular periodic payment).
You can calculate any value after entering the other four. 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. For example, following is a cash flow diagram, from the
borrower's perspective, for a 30-year, $75,000.00 mortgage, with a pay-
ment of $-684.07, at 10.5% annual interest, with a $5,000 balloon pay-
PV = 75,000.00
I/YR = 10.5%
N = 360 (30 x 12)
TTL TTL 8399 3
РМТ = - 684.07
1 2 3
FV = - 5,000.00 |
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.
48 A: Picturing Financial Problems
FV = 25 327.38
I/YYR = 8.00%
PMT = 0.00
1 2 3 4 5 66 . 57 58 59 60
N = 60
PV = -17,000.00
Time value of money calculations are described in the next chapter.
Recognizing a Cash Flow Problem
A financial problem that docs not have regular, uniform payments (some-
times called uneven cash flows) is a cash flow problem rather than a TVM
A cash flow diagram for an investment in a mutual fund follows. This is an
example of a problem that is solved using cither W(NPV) (Net Present
Value) or B(IRR/YR] (Internal Rate of Return per Year).
4: Picturing Financial Problems 49
444444445441 | Time Value of Money Calculations
5,000.00 Using the TVM Application
y - 6,000.00
The time value of money (TVM) application is used for com-
+ pound 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
Cash flow problems are described in chapter 6.
To use TVM, several prerequisites must be met:
m The amount of cach payment must be the same. If the payment
amounts vary, usc the procedures described in chapter 6, “Cash Flow
@ Payments must occur at regular intervals.
m The payment period must coincide with the interest compounding
period. (If it does not, convert the interest rate using the H(NOM%),
MEFF%), and M(P/YR) keys described on page 71.)
m There must be at least one positive and one negative cash flow.
50 4: Picturing Financial Problems 5: Time Value of Money Calculations 51
Key Stores or Calculates Cle aring TVM
The number of payments or compoundin
periods РОУ P J Press M[CLEAR ALL) to clear the TVM registers, This sets N, 7/YR, PY,
PMT, and FV to zero and bricfly displays the current value in P/YR.
The annual nominal interest rate.
The present value of future cash flows. PV is
usually an initial investment or loan amount and B egin and End Modes _
always occurs at the beginning of the first period.
PMT The amount of periodic payments. All payments
are equal, and none are skipped; payments can | | Before you start a TVM calculation, identify whether the
occur at the beginning or end of each period. (200000) [irst periodic payment occurs at the beginning or end of the
FUI The future value. FV is ekher a final cash flow or ONO first period. If the first payment occurs at the end of the first
"y compounded value of a serios of previous cash 0 0000) period, set your HP-10B to End mode; if it occurs at the
flows. FV occurs at the end of the last period. LEE beginning of the first period, set your calculator to Begin
B(P/YR Stores the number of periods per year. The default
Is 12. Reset only when you wish to change.
To switch between modes, press M[BEG/END). The BEGIN annunciator is
displayed when your calculator is in Begin mode. No annunciator 15
B(xP/YR] Optional shortcut for storing N: Number in display displayed when you are in End mode.
is multiplied by the value in P/YR and stores result | |
in N. Mortgages and loans typically use End mode. Leases and savings plans
typically use Begin mode.
HB (BEG/END] Switches between Begin and End mode. In Begin
mode, the BEGIN annunciator is displayed.
B{AMORT) Calculates an amortization table. В Ш Loan Calculations
To verify values, press (RCL) (N), (RCL) (i/YR), (РМ), [PMT), and | Example: A Car Loan. You arc financing a new car with a three year
[EV]. Pressing MGF/YA) recalls the total number of payments | loan at 10.5% annual nominal interest, compounded monthly. The price
in ycars and B(P/YR] shows you the number of payments per year, of the car is $7,250. Your down payment is $1,500.
Recalling these numbers does not change the content of the registers.
5 5 > 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.)
52 5: Time Value of Money Calculations 5: Time Value of Money Calculations 53
PV = 7,250 - 1,500
I/YR = 10.5%
P/YR = 12
РМТ = ?
End Mode
Set to End mode. Press WM(BEG/END] if BEGIN annunciator is displayed.
Keys: Display: Description:
12 MP/YR) 12.00 Sets periods per year.
3 (х) 12 (№ 36.00 Stores number of periods
in loan.
10.5 10.50 Stores annual nominal
interest rate.
7250 [-] 1500 5,750.00 Stores amount borrowed.
О [РУ] 0.00 Stores the amount left to
pay after 3 years.
- 186.89 Calculates the monthly
payment. The negative
sign indicates money paid
Part 2. At a pricc of $7,250.00, what interest rate is necessary to lower
your payment by $10.00, to — 176.89?
10 -176.89 Decreases payment from
- 186.89.
6.75 Calculates annual interest
rate for the reduced
54 5: Time Value of Money Calculations
Part 3. If interest 1s 10.5%, what is the maximum you can spend on the
car to lower your car payment to $175.00?
10.5 (1/YR 10.50 Stores original interest
175 +7] — 175,00 Stores desired payment,
[PV] 5,384.21 Calculates amount of
money to finance.
1500 [=] 6,884.21 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 $630.00. You can make a
$12,000 down payment, and annual interest rates are currently 11.5%. If
you obtain a 30 year mortgage, what is the maximum purchase price you
can afford?
I/YR = 11.5%
P/YR = 12
[= [= [= [==]
PMT = - 630.00
End Mode
Set to End mode, Press M(BEG/END) if BEGIN annunciator is displayed.
12 M(P/YR)
Display: Description:
Sets periods per year.
5: Time Value of Money Calculations 55
360.00 Stores the length of the | Set to End mode. Press M(BEG/END) if BEGIN annunciator is displayed.
mortgage (30 x 12). K Disnl Descripti
eys. 5 . .
0 [FV] 0.00 Pays mortgage off in 30 ye may евепрной
years. 12 MP/YR) 12.00 Sets periods per year.
11.5 |! 11.50 Stores interest rate. 25 M(xP/YA) 200.00 Stores length of mortgage
630 [+/-) (РМТ) — 630.00 Stores desired payment (25 x 12 = 300 months).
(money paid out is 0 0.00 Stores loan balance after
negative). 25 ycars.
63,617.64 Calculates the loan you | 79500 72.500.00 Stores original loan
can afford with a $630 balance.
payment, :
13.8 (1/YR] 13.80 Stores annual interest
12000 [=] 75,617.64 Adds $12,000 down rate.
ayment for the total
purchase price. - 861.65 Calculates monthly
Example: A Mortgage With a Balloon Payment. You've obtained .
a 25 ycar, $72,500 mortgage at 13.8% annual interest. You anticipate that Step 2. Since the payment is at the end of the month, the last payment
you will own the house for four years and then sell it, repaying the loan and the balloon payment occur at the samc time. The final payment is the
with a balloon payment. What will your balloon payment be? sum of PMT and FV.
Solve this problem using (wo steps: PV = 72,500.00
1. Calculate the loan payment using a 25 year term. A
2, Calculate the remaining balance after 4 years.
Step 1. First calculate the loan payment using a 25 year term. I/YR = 13.8%
№ = 4х 12
РМ = 72,500 PTR = 12
1 2 3 4
1/YR = 13.8% у
№ = 25 х 12
P/YR = 12
| as PMT = - 861.65
- > 299 200 End Mode
PMT = 7
End Mode
56 5: Time Value of Money Calculations 5: Time Value of Money Calculations 57
I Ji The value in PMT should always be rounded to two decimal
000800 fr : .
500000 places when calculating FV or PV to avoid small, accumula
icoooom| tive discrepancies between non-rounded numbers and actual
boooc ; .
== (dollars and cents) payments. If the display is not set to two
5 Sood) decimal places, press W(OISP) 2.
Keys: Display: Description:
HAND) -861.65 Rounds payment to two
decimal places, then
48 [№ 48.00 Stores 4 year term (12 x
4) that you expect to own
[FV] - 70,725.90 Calculates loan balance
after 4 years.
[=] - 71,587.55 Calculates total 48th
payment (PMT and FV)
10 pay off loan (money
paid out is negative).
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 53,000?
58 5: Time Value of Money Calculations
I/YR = 7.2%
N =?
P/YR = 1
PV = - 2,000.00
ER €
РМТ = 0
РУ = 3,000.00
Since this account has no regular payments (PMT = 0), the payment
mode (End or Begin) is irrelevant.
1 B(P/YA)
2000 (+7-)
12 P Yr
Displays a temporary
message and clears all
Sets P/YR to 1 since
interest 1s compounded
Stores amount paid out
for first deposit.
Stores the amount you
wish to accumulate.
Stores annual interest
Calculates number of
years it takes to reach
5: Time Value of Money Calculations 59
Since the calculated value of N is between 5 and 6, 1t 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.
6 [N)
Sets [N] to 6 ycars.
Calculates amount you
can withdraw after 6
Example: An Individual Retirement Account. You opened an
individual retirement account on April 15, 1985, with a deposit of $2,000.
Thereafter, you deposit $80.00 to the account at the end of cach half-
month, The account pays 8.3% annual interest compounded semimonthly.
How much will be in the account on April 15, 2000?
FV = 7
I/YR = 8.3%
N = 360 (15 years x 24 half-months)
P/YR = 24
(Hall-month periods)
PV = -2,000.00
Set to End mode. Press M[BEG/END) if BEGIN annunciator is displayed.
Keys: Display: Description:
24 M(P/YR] 24.00 Sets number of periods
per year.
2000 [+/-) (PV) - 2,000.00 Stores initial deposit.
60 5: Time Value of Money Calculations
| 80 (57) (РМТ)
- 80.00 Stores regular semi-
monthly deposits.
8.3 8.30 Stores interest rate.
15 BxP/YR) 360.00 Stores number of
63,963.84 Calculates balance.
Example: An Annuity Account. You opt for an carly retirement
after a successful business carcer. You have accumulated a savings of
$400,000 that carns an average of 10% 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?
РМТ = ?
1 2 599 600
I/YR = 10% РУ = 0
№ = 600 (50 х 12)
у P/YR = 12
PV = - 400,000.00
Begin Mode
Set to Begin mode. Press W(BEG/END) if annunciator is not displayed.
Keys: Display: Description:
12 B[P/YR) 12.00 Sets payments per year.
400000 [+/-} -400,000.00 Stores your nest egg as
an outgoing deposit.
10 (1/YR) 10.00 Stores annual interest
rate vou expect to carn,
5: Time Value of Money Calculations 61
50 B[xP/YR) 600.00 Stores number of
0 0.00 Stores balance of account
alter 50 years.
3,328.68 Calculates amount that
you can withdraw at the
beginning of cach month.
Lease Calculations
A lcase 1s a loan of valuable property (like real estate, automobiles, or
equipment) for a specific amount of time, in exchange for regular pay-
ments. 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 TYM application keys can be used in lease calculations. There arc
lwo common lease calculations.
m Finding the Icase payment necessary to achieve à specified yield.
® Finding the present value (capitalized valuc) of a leasc.
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
14% annually, compounded monthly, what will the payments be? Calcu-
late the payments from your (the dealer's) point of view.
62 5: Time Value of Money Calculations
FV = 7,500.00
PMT = 7
Money received
by lessor is
1 2 35 36 positive.
I/YR = 14%
N = 36 Money paid out
P/YR = 12 by lessor is
Y negative.
PV = - 13,500.00
Begin Mode
Set to Begin mode. Press M[BEG/END) if annunciator is not displayed.
Keys: Display: Description:
12 M(P/YR) 12.00 Sets payments per year.
14 14.00 Stores desired annual
13500 -13,500.00 Stores lcasc price.
7500 7,500.00 Stores residual (buy out
36 (N) 36.00 Stores length of lease, in
PMT 289.19 Calculates monthly lease
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 Polc Barns, plans to lease a forklift for the warehouse. The lease is
wrilten for a term of 4 ycars 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.
5: Time Value of Money Calculations 63
If the annual interest rate 1s 18%, what is the capitalized value of the
Begin Mode
N =?
I/YR = 18%
N = 48
P/YR = 12
, | y
1 2 3 4 44 45 46 47 48
PMT = - 2,400.00
| } (48th payment due up front)
FV = -15,000.00
This solution requires four steps.
1. Calculate the present value of the 47 monthly payments:
(4 х 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 [J[BEG/END] if annunciator is not displayed.
Keys: Display: Description:
12 M(P/YR] 12.00 Sets payments per year.
47 [N] 47.00 Stores number of
2400 [+/-) [PMT - 2,400.00 Stores monthly payment,
64 5: Time Value of Money Calculations
0 0.00 Stores FV for step 1.
18 18.00 Stores interest rate.
(PV) 81,735.58 Calculates present value
of 47 monthly payments.
Step 2. Add the additional advance payment to PV. Store the answer.
Adds additional advance
=] 84,135.58 payment.
[+M] 84,135.58 Stores result in M
Step 3. Find the present value of the buy option.
48 [№ 48.00 Stores month when buy
option occurs.
0 0.00 Stores zero payment for
this step of solution.
15000 - 15,000.00 Stores value to discount.
[РУ] 7,340.43 Calculates present value
of last cash flow.
Step 4. Add the results of steps 2 and 3.
(+) [RM] [=]
Display: Description:
91,476.00 Calculates present
(capitalized) value of
lease. (Rounding
discrepancies are
explained on page 58.)
5: Time Value of Money Calculations 65
1 "| Amortization is the process of dividing a payment into the
200089 amount that applies to interest and the amount that applies
000000} à a 4 a
aca | to principal, Payments ncar the beginning of a loan
DOOOO| contribute more interest, and less principal, than payments
EEES) near the end of a loan.
HH el! | PRINCIPAL $ | 3
TS qi Prin
HT interest si NE
Cri HN
bpp HT HE
The B{AMORT] key on the HP-10B allows you to calculate.
® The amount applied to interest in a range of payments.
m The amount applied to principal in a range of payments.
m The /oan balance alter a specified number of payments are made.
66 5: Time Value of Money Calculations
The MAMORT) function assumes you have just calculated a payment or
you have stored the appropriate amortization values in 7/YR, PV, PMT,
and P/YR,
1/YR Annual nominal interest rate.
[PV] Starting balance.
[PMT] Payment amount (rounded to the display format).
BP/YR 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 [INPUT], then press MLAMORT). The HP-10B displays the
message PEr followed by the starting and ending payments that will bc
Hold [=] down to display the label of the value that you are about to view.
Press (=) to see interest (Int). Press [=] again to see the principal (Prin)
and again to sec the balance (DAL). Continue pressing [=] to cycle
through the same values again.
To amortize a range of payments, enter starting period number [INPUT]
ending period number, then press IH[AMORT]. The HP-10B displays the
message PEr followed by the starting and ending payments that will be
amortized. Then press [=] repeatedly to cycle through interest, principal,
and balance.
Press MLAMORT) 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.
If you store, recall, or perform any other calculations during amortization,
pressing [=] will no longer cycle through interest, principal, and balance.
To resume amortization with the same set of periods, press
5: Time Value of Money Calculations 67
Example: Amortizing a Range of Payments. Calculate the first Amortize the second year:
two years of the annual amortization schedule for a 30 year, $80,000
mortgage, at 9.75% annual interest with monthly payments. BAMORT PEr 13-24 Displays next range of
| o periods.
Set to End mode. Press M[BEG/END) if BEGIN annunciator is displayed. © Int Displays interest paid in
Keys: Display: Description: = 1,731.67 second ycar.
[=] Prin Displays principal paid in
12 M(P/YR) 12.00 Sets paymenis per year. -516.17 second year,
30 360.00 Stores total number of | (=) bAL Displays loan balance
payments. 79,015.41 after 24 payments.
9.75 9.75 Stores interest per year.
UNA) AA The amount paid toward interest and principal (7,731.67 + 516,17 =
80000 [PY] 80,000.00 Stores present valuc. 8,247.84) equals the total of 12 monthly payments (12 x 687.32 =
0 (EV) 0.00 Stores future value, 8,247.84). The remaining balance equals the initial mortgage less the
PR -687 32 Calculates monthly amount applied toward principal (80,000 - 468.42 - 516.17 = 79,015.41).
payment. More money is applied to principal during the second rather than the first
year, The succeeding years continue in the same fashion.
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, Example: Amortizing a Single Payment. Amortizc the 1st, 25th,
and 54th payments of a five year car lease. The lease amount is $14,250
1 (NFUTI2 12 Enters starting and and the interest rate is 11.5%. Payments are monthly and begin
Ш ending periods. immediately,
MAMORT) PEr1- 12 Displays range. Set to Begin mode, Press if annunciator is not displayed.
[=] int Displays label, then
-7,779.42 interest paid the first Keys: Display: Description:
year 12 M(P/YR) 12.00 Sets payments per year.
[=] Prin Displays label, then 5 MGP7VAI 60.00 . ber of
-468.42 principal paid the first Stores number ©
year. payments,
11.5 11.50 Stores interest per year,
5) DAL Displays label, then loan | 14250 [PY] 14,250.00 Stores present value,
79,531.58 balance after one year. — | 0 (FY) 0.00 Stores the future value.
The amount paid toward interest and principal (7,779.42 + 468.42 = ~310.42 Calculates monthly
8,247.84) equals the total of 12 monthly payments (12 x 687.32 = payment.
8,247.84). The remaining balance equals the initial mortgage, less the
amount applied toward principal (80,000 - 468.42 = 79,531.58).
68 5: Time Value of Money Calculations | 5: Time Value of Money Calculations 69
Amortize the 1st, 25th, and 54th payments.
54 [INPUT]
РЕГ 1 - 1
— 310.42
PEr 25- 25
- 90.21
PEr 54- 54
70 5: Time Value of Money Calculations
Enters first payment.
Displays amortized
payment period.
Displays interest.
Displays first principal
Displays loan balance
after one payment.
Enters payment to
Displays amortized
payment period.
Displays interest paid on
25th payment.
Displays principal paid
on 25th payment.
Displays balance after
25th payment.
Enters payment to
Displays amortized
payment period.
Displays interest paid on
54th payment.
Displays principal paid
on 54th payment.
Displays balance after
Sáth payment.
Interest Rate Conversions
| || The Interest Conversion application uses three keys:
ООС MNOM%) , Ш ЕРР%] , and M(P/YA) . They convert between
0000| nominal and annual effective interest rates. Nominal and
DEE | effective interest rates arc described on page 47.
O 0000
If you know an annual nominal interest rate and you wish to solve for the
corresponding annual eflective rate:
1. Enter the nominal rate and press (№М%).
2. Enter the number of compounding periods and press M(P/YR).
3. Calculate the effective rate by pressing (ЕРР%).
To calculate a nominal rate from a known effective rate:
1. Enter the cffective rate and press [J[EFF%).
2. Enter the number of compounding periods and press (Р/УА).
3. Calculate the nominal rate by pressing W(NOM%]).
In the TVM application, N(NOM%) and share the same register.
Interest conversions are used primarily for two types of problems:
m Comparing investments with different compounding periods.
m Solving TVM problems where the payment period and the interest
period differ.
Investments With Different Compounding Periods
Example: Comparing Investments. You arc considering opening a
savings account in onc of three banks. Which bank has the most favorable
interest rate?
5: Time Value of Money Calculations 71
First Bank
Second Bank
Third Bank
First Bank.
6.7 B(NOM%)
4 MP/YA)
Second Bank.
6.65 BNOM%]
12 MIP/YR)
Third Bank.
6.63 H[NOM%]
360 W[PLYR]
0.70% annual interest, compounded quarterly,
6.65% annual interest, compounded monthly.
6.63% annual interest, compounded 360 times per
Stores nominal rate.
Stores quarterly com-
pounding periods.
Calculates annual
effective rate.
Stores nominal rate.
Stores monthly com-
pounding periods.
Calculates annual
effective rate.
Stores nominal rate.
Stores compounding
Calculates annual
effective rate.
First Bank offers a slightly better deal since 6.87 is greater than 6.86 and
72 5: Time Value of Money Calculations
Compounding and Payment Periods Differ
assco| and the payment periods are the same, Some loan install
Soooo| ments or savings deposits and withdrawals do not coincide
9999| with the bank's compounding periods. If the payment period
95533 differs from the compounding period, adjust the interest rate
2777) to match the payment period before solving the problem.
— y The TVM application assumes that the compounding periods
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 W[NOM%). Enter the number of
compounding periods in a year and press J[P/YR). Solve for the
effective rate by pressing M[EFF%).
2. Enter the number of payment periods in a ycar and press M[P/YR].
Solve for the adjusted nominal rate by pressing W[NOM%]).
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.
Keys: Display: Description:
5 B(NOM%) 5.00 Stores nominal per-
cenlage rate.
365 M(P/YR) 365.00 Stores bank's compound-
ing periods per year.
BEFF%] 5.13 Calculates annual
effective rate.
12 (Р/УВ) 12.00 Stores monthly periods.
B(NOM%) 5.01 Calculates equivalent
nominal percentage rate
for monthly
Since NOM % and I/YR share the same register, this value is ready for use
in the rest of the problem.
5: Time Value of Money Calculations 73
Step 2. Calculate the future value.
Set to Begin mode. Press M(BEG/END] if annunciator is not displayed.
0 (РУ) 0.00
25 -25.00
7 B(xP/YR) 84.00
[FV] 2 519.61
74 5: Time Value of Money Calculations
Stores present value.
Stores payment,
Stores number of pay-
ments per year.
Calculates balance alter 7
Cash Flow Calculations
How to Use the Cash Flow Application
i| The cash flow application 15 used to solve problems where
овово cash flows occur over regular intervals but are of varying
coool amounts. You can also use cash flow calculations to solve
ВОС problems with regular, equal, periodic cash flows, but these
2099 situations arc handled more casıly using TVM.
In general, these are the steps for cash flow calculations on the HP-10B.
1. Organize your cash flows on paper —a cash flow diagram 1s uscful.
2. Clear the registers.
3. Enter the number of periods per year.
4. Enter the amount of the initial investment.
5. Enter the amount of the next cash flow.
6. If the amount entered in step 5 occurs more than once consecutively,
enter the number of times it occurs.
7. Repeat steps 5 and 6 for each cash [low and group.
8. To calculate net present value, enter the annual interest rate and
press (1/YR); then press [№У). Or, to calculate annual internal rate
of return, press ВА/УА).
Example: 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.
6: Cash Flow Calculations 75
12 M(P/YR)
5000 [+/-] (СЕ)
2000 [+/-] (CF)
4000 [+/-] (CFj)
E) 12 (5)
CF 1
CF 2
— 4,000.00
76 6: Cash Flow Calculations
Flows receivad
| are positive.
Flows paid out
are negative,
Clears all registers.
Stores periods per year,
Enters initial cash flow.
Displays cash flow group
number while you hold
down [CF].
Enters next cash [low.
Enters next cash flow.
Enters final cash flow.
Calculates annual
nominal yield,
Monthly yield.
NPV and IRR/YR: Discounting Cash Flows
Chapter 4 demonstrates the use of cash flow diagrams to clarify financial
problems. This section describes discounted cash flows. The NPV and
IRR /YR functions are frequently referred to as discounted cash flow
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 à series
of cash flows. The annual nominal interest rate must be known to
calculate NPV,
The internal rate of return (JRR/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 and IRR/YR calculations follow.
Organizing Cash Flows
The cash flow series is organized into an initial cash flow (CF 0) and
succeeding cash flow groups (up to 14 cash flows). CF 0 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 (lows of zero cach,
followed by a group of three $1,000 cash flows. The final group consists of
one $10,000 cash flow.
6: Cash Flow Calculations 77
CF 3 = 10,000, №3 = 1
CF 2 = 1,000, N2 = 3
F 1
CF1=0 N1=6
CFO = -11,000
Whenever you enter à scries of cash flows, it is important to account for
every period on the cash flow diagram, even periods with cash flows of
Entering Cash Flows
The HP-10B can store an initial cash [low plus 14 additional cash flow
groups. Each cash flow group can have up to 99 cash flows. The cash flows
arc stored in registers Ro through Ro and R 5 through Ry. Enter cash
[lows using the following steps:
1. Press W[CLEAR ALL} to clear the registers.
2. Enter the number of periods per year and press M(P/YR].
3. Enter the amount of the initial investment, then press (CF). (The
de PP
7” stands for the cash flow “number,” 0 through 14.)
4. Enter the amount of the next cash flow and press [CFj].
5. If the amount entered in step 4 occurs more than once consecutively,
enter the number of times il occurs, and press M(Nj).
6. Repeal steps 4 and 5 for cach and BIN) until all cash flows
have been entered.
78 6: Cash Flow Calculations
Example. Enter the cash flows from the preceding diagram and calcu-
late the JRR/YR. Then calculate the effective interest rate, Assume there
are 12 periods per year.
Keys: Display: Description:
M(CLEAR ALL] 0.00 Clears all registers.
12 M(P/YR) 12.00 Sets to 12.
11000 [+/-) [СЕЛ CFO Enters initial cash flow.
- 11,000.00 Displays cash flow group
number for as long as
you hold down (CFj].
0 [CF] CF 1 Enters first cash flow
0.00 group amount.
6 (№ ni Enters number of
6.00 repetitions.
1000 (СЕ) CF 2 Enters second cash flow
1,000.00 group amount,
n2 Enters number of
3.00 repetitions,
10000 (CF1] CF 3 Enters final cash flow.
ВАЛУА) 21.22 Calculates annual
nominal yield.
Viewing and Replacing Cash Flows
To view a cash flow list press the following:
1. [RCL] 0 to see the initial cash flow.
2. [RCL] [CF]) to see the next flow.
3. EN) to sec the number of times the cash flow occurs.
Repeat steps 2 and 3 until all cash flows are reviewed.
You can also view cash flows individually by pressing [RCL), followed by a
register number. Register numbers coincide with cash flow numbers. For
example, press 4 to see cash flow 4, then [NJ] to see the
number of consecutive occurrences.
6: Cash Flow Calculations 79
To replace a cash flow, enter the new cash flow and press (СТО)
followed by the cash flow (register) number.
To replace the number of times a particular cash flow occurs, [RCL] the
cash flow whose number of occurrences will change. Then, enter the
number of times it occurs and press (№).
To replace both the cash flow and number of times it occurs, enter the
new cash flow, press N(STO) followed by the cash flow (register) number.
Then enter the number of times it occurs and press MÍN).
Since cash flows cannot be deleted or inserted, use [CLEAR ALL) to start
Calculating Net Present Value
The net present value (NPV) function is used to discount all cash [lows to
the front of the time line using an annual nominal interest rate that you
These steps describe how to calculate [NPV]:
1. Press J[CLEAR_ALLJ, store number of periods per year in P/YR.
2. Enter the cash flows using [CF]] and (NJ).
3. Store the annual nominal interest rate in //YR and press M(NPV).
Example: A Discounted Contract, Uneven Cash Flows. You
have an opportunity to purchase a contract with the following cash flows:
End Of Month Amount
$ 5,000.00
$ 5,000.00
10 $ 5,000.00
15 $ 7,500.00
25 $10,000.00
How much should you pay for the contract if you wish to yield a yearly
rate of 15% on your investment?
80 6: Cash Flow Calculations
I/YYR = 15%
12 B(P/YR]
0 [CF]]
0 (CF)
0 [СЕ]
4 (№
2 BN]
9 10
CF 1
CF 2
CF 3
CF 4
Clears registers.
Sels payments per year.
Enters initial cash flow of
zero. The cash flow
number is displayed as
long as you hold down
the [CF]) key.
Enters first cash flow.
Enters number of
Enters second cash flow.
Enters third cash flow.
Enters number of
Enters fourth cash flow.
Enters number of
6: Cash Flow Calculations Bi
0 CF5 Enters fifth cash flow.
4 №) nd Enters number of
4.00 Occurrences.
7500 [CF]) CF 6 Enters sixth cash flow.
0 [СЕ] CF 7 Enters seventh cash
0.00 flow,
9 BN] п? Enters number of
9.00 Occurrences.
10000 [CF]) CF8 Enters next cash flow.
The cash flows that describe your prospective investment are now in the
calculator. You can press 0, followed by [CF]) and
Now that you have entered the cash flows, store the interest rate and
calculate the net present value.
Keys: Display: Description:
15 15.00 Stores annual interest
BNP V 27,199.92 Calculates net present
value of stored cash
flows. (See rounding
example on page 58.)
This result shows that if you want a yield of 15% per year, you should pay
$27,199.92 for the contract. Notice that this amount is positive. The net
present value is simply the summed (or netted) value of a series of cash
flows when they are discounted to the front of the time linc.
82 6: Cash Flow Calculations
B(Nj), repeatedly to view the cash flows and number of times cach occurs.
NPV = 27,189.92
6,224.95 — ZZ
1% = 15% per year Dan
4,415.91 > Das Ä
4471.10 À
vtt 7,500.00
e" O
——— 5,000.00
i 3 5 7 9 11 13 15 17 19 21 23 25
Calculating internal Rate of Return
1. Press M[CLEAR ALL), store number of periods per year in P/YR.
2. Enter the cash flows using [CF]) and (Ni).
3. Press MIIRA/YR).
When you calculate IRR/YR, you get the annual nominal rate thal gives
an NPV of zero.
The following example uses the cash flows that were entered in the
previous example,
More than one JRR/YR can exist. If you get the no Solution message sce
Appendix B (page 127).
Example. If the seller of the contract in the previous example wants
$28,000 and you accept that price, what is your yield? This is an JRR/YR
calculation that requires a slight modification to the currently stored cash
6: Cash Flow Calculations 83
5,000 7,500
1 3 668 7 9 11 13 15 17 19 21 23 25
IRR/YR = ?
Кеуз: Display: Description:
28000 (*/-) M(STO) O -28,000.00 Changes initial cash How.
B(RR/YR] 12.49 Calculates annual nomi-
nal yicld.
More examples that use NPV and IRR/YR calculations arc given in
chapter 8, “Additional Examples.”
Statistical Calculations
Automatic Storage of IRR/YR and NPV
When you calculate NPV, the result is stored in PV for your convenience.
To recall that result, press [PV]. If you haven't changed the TVM
values from the last example using NPV (page 82), when you press
the result is 27,199.92.
When you calculate IRR/YR, the result is also stored in //YR. For the
previous example, press lo display the annualized yield 12.49.
84 6: Cash Flow Calculations
| |
С В 99 69 Г) ||
0) |
The and M(E-) keys are used to enter and delete data for
onc- and two-variable statistics. Summation data is accumu-
lated in registers Ry through Re. The register labels at the
lower right of the keys indicate what statistical data 15 stored
in each register. Once vou enter the data, you can usc the
statistical functions to calculate the following:
m Mcan and standard deviation.
mM Lincar regression statistics.
E Lincar estimation and forccasting,
® Weighted mean,
» Summation statistics: n, x, Ex”, Ey, 7, and Exy.
Clearing Statistical Data
Le... wd]
[5 300
Clear the statistical registers before entering new data so that
R, through R, arc zero when you begin, If you don’t clear the
registers, data currently stored in Rs through Rg is auto-
matically included in the summation calculations. To clear
the statistical registers, press . The display is also
7: Statistical Calculations 85
Entering Statistical Data
There is no limit to the number of values you can accumulate in the
statistical registers. *
One-Variable Statistics
To enter x data for one-variable statistics complete the following steps:
1. Clear the contents of R¿ through Ro by pressing M[CL E).
2. Enter the first value and press [£+). The HP-10B displays n, the
number of items accumulated.
3. Continue accumulating values by entering the numbers and pressing
[2+]. The n-value is incremented with cach entry.
Two-Variable Statistics and Weighted Mean
To enter x,y pairs of statistical data complete these steps:
1. Clear the contents of Ry through Rg by pressing С. 5).
2. Enter the first x-value and press (INPUT). The HP-10B displays the
x-value and the : annunciator appears in the display.
3. Enter the corresponding y-value and press (£+]. The HP-10B
displays n, the number of pairs of items accumulated.
4. Continue centering x,y pairs. The n-value is incremented with each
To enter data for calculating the weighted mean, enter each data valuc as
x, and its corresponding weight as y.
* If statistical data causes the value of à register to exceed =9.99999999999 x 10%, the
HP-10B displays a temporary overflow waming (OFLO).
86 7: Statistical Calculations
Correcting Statistical Data
Incorrect entries can be deleted using ME-]. If either value of an x.y pair
is incorrect, you must delete and reenter both values.
Correcting One-Variable Data
To delete and reenter statistical data:
1. Key in the x-value to be delcted.
2. Press [E-] to delete the value. The n-value is decreased by onc.
3. Enter the correct value using [£4].
Correcting Two-Variable Data
To delete and reenter x,y pairs of statistical data:
1. Key in the x-value, press and then key in the y-value.
2. Press M(E-) to delete the values. The n-value is decrcased by one.
3. Enter the correct x,y pair using (INPUT) and (+).
7: Statistical Calculations 87
Summary of Statistical Calculations
Some functions return two values. The : annunciator indicates that two
values have been returned. Press N[SWAP] to sec the hidden value.
MSWAF) to Display
Arithmetic mean (aver-
age) of the x-values.
Mean (average) of the
y-values if you entered
culated line.
| lated line.
Шу) Mean of the x-values
weighted by the y-values.
NSx.5>) Sample standard devia- | Sample standard devia- |
tion of the x-values.* tion of the y-values if you |
entered y-data.*
Eo x,0 y) Population standard devi- | Population standard devi-
ation of the x-values.* ation of the y-values if
you entered y-data.*
y-value Estimate of x for a given | Correlation coefficient.
Ш.) | value of y.
x-value | Estimate of y fora given | Slope (m) of calculated
(Sm) value of x. line.
0 M(P.m) y-intercept (b) of the cal- | Slope (m) of the calcu-
* The sample standard deviation assumes that the data is a sampling of a larger,
complete set of data. The population standard deviation assumes that the dala con:
stitutes the entire population.
t The correlation coefficient is à number in the range - 1 through +1 that measures
how closely the data fits the calculated line, A value of +1 indicates a perfect positive
correlation, and ~ 1 indicates a perfect negative correlation. A value close to zero
indicates the line is a poor fit.
7: Statistical Calculations
N Keys Description
4 (n) На Number of data points entered.
5 (Ex) Sum of the x-values.
6 (Ly) Sum of the y-values.
7 (Ex) Sum of the squares of the x-values.
8 (5) Sum of the squares of the y-values.
9 (59) Sum of the products of the x- and y-values.
Mean, Standard Deviations, and Summation
You can calculate the mean (xX), sample standard deviation
(S, ), and population standard deviation (0, ), and summation
statistics, n, Ex, and Iv? of x-data. For xy data, you can also
calculate the mean, sample standard deviation, and popula-
| tion standard deviation of the y-data and the summation
) statistics Ey, Ту”, and Ey.
Example 1. A yacht captain wants to determinc how long it takes to
change a sail. She randomly chooses six members of her crew, observes
them as they carry out the sail change, and records the number of minutes
required: 4.5, 4, 2, 3.25, 3.5, 3.75. Calculate the mean and sample standard
deviation of the times. Also, calculate the root mean square, using the
formula Y Xv? /n
Keys: Display: Description:
BCL 0.00 Clears statistical
7: Statistical Calculations 89
Example 2. The coach has four new players on the team with heights of
Enters first time.
Enters second time.
Enters third time.
Enters fourth time.
Enters fifth time.
Enters sixth time.
Calculates the mean.
Calculates the sample
standard deviation,
Displays E.
Displays m.
Calculates the root mean
The standard deviations calculated by B(Sx,57) and
W(Sx,Sy) B[SWAP] are the sample standard deviations. They
assume that the data is a sampling of a larger, complete set
ol data.
If the dala constitutes the entire population, the true popula-
tion standard deviations can be calculated by pressing
B(ox,0y) and Blox,cy) NSWAP).
193, 182, 177, and 185 centimeters and weights of 90, 81, 83, and 77 kilo-
grams. Find the mean and population standard deviation of both their
heights and weights, then sum the y-data.
BCL 2)
193 (INPUT) 90 2+] 1.00
182 81 [Z+] 2.00
90 7: Statistical Calculations
Clears statistical
Enters height and weight
of player 1.
Enters height and weight
of player 2.
| 177 (INPUT) 83 (+) — 3.00
185 [INPUT] 77 2+] — 4.00
EBEN 184.25
B(SWAP] 82.75
Eo x,0 y) 5.80
BISWAP] 4.71
6 331.00
Enters height and weight
of player 3.
Enters height and weight
of player 4.,
Calculates mean of
heights (x).
Displays mean of weights
Calculates population
standard deviation for
heights (x).
Displays population
standard deviation for
weights (y).
Displays the total of the
in three steps.
to display m (the slope of the line).
Linear Regression and Estimation
| Linear regression, is a statistical method for estimation and
| forecasting. It is used to find a straight line that best fits a set
| of xy data. There must be at least two different x,y pairs. The
| straight linc provides a relationship between the x- and
y-variables: y = mx + b, where m is the slope and b is the
Linear Regression. Calculate m, b, and r (the correlation coefficient),
1. Enter the x,y data using the instructions on page 86.
2. To display b (the y-intercept), press 0 N(P.m). Then press SWAP)
3. Press Bx) BSWAP) to display r, the correlation coefficient.
7: Statistical Calculations 91
Linear Estimation. The straight line calculated by lincar regression
can be used to estimate a y-value for a given x-valuc, or vice versa:
1. Enter the xy-data using the instructions on page 86.
2. Enter the known x-valuc or y-valuc.
w To cstimate x for the given y, enter the y-value, then press
в To estimate y for the given x, enter the x-value, then press
Example: Forecasting. Ali's Azalcas advertises on a local radio sta-
tion. For the past six weeks, the manager has kept records of the number
of minutes of advertising that were purchased, and the sales for that week.
Week Minutes of Advertising Sales
(x-values) (y-values)
Week 1 2 $1,400
Week 2 1 $ 920
Week 3 3 $1,100
Week 4 5 $2,265
Week 5 5 $2,890
Week 6 4 $2,200
What is the y-intercept, the slope, and the correlation coefficient?
92 7: Statistical Calculations
a ” R
a ”».
Sales in Dollars
m = 425.88
MT *
0 1 2 3 4 5 6 7 B
Minutes of Advertising
Keys: Display: Description:
BCL Z 0.00 Clears statistical
2 1400 1.00 Enters minutes and sales
for conseculive weeks.
1 INPUT) 920 2.00
3 1100 3.00
5 2265 [z+ 4.00
5 2890 5.00
4 (INPUT) 2200 6.00
о т) 376.25 Calculates y-intereepl
H(SWAP) 425.88 Displays slope.
Br) N(SWAP) 0.90 Calculates correlation
Estimate what the level of sales would be if the business purchased 7 or 8
minutes of advertising,
7: Statistical Calculations 93
7 MU.m)
8 Bm)
Estimates sales if 7
minutes of advertising
were purchased.
Estimates sales if 8
minutes were purchased.
How many minutes of advertising should Ali’s buy to attain salcs of
3000 г)
Weighted Mean
The following procedure calculates the weighted mean of data points x,
Ma, +»
+X, occurring with weights y,, V2,- - -
Estimates minutes of
advertising required for
$3,000 in sales.
1. Use [INPUT] and [2+] to enter xy pairs. The y-values arc the weights
of the x-
2. Ргс55
Example. A survey of 266 one-bedroom rental apartments reveals that
54 of them rent for $200 per month, 32 for $205, 88 for $210, and 92 for
$216. What is the average monthly rent?
Keys: Display:
BCL: 0.00
200 (INPUT) 54 [+] 1.00
205 (INPUT) 32 (#+] 2.00
210 88 3.00
216 [INPUT] 92 [2+] 4.00
ИУ] 209.44
94 7: Statistical Calculations
Clears statistics memory.
Enters first rent and its
Enters second rent and
its weight.
Enters third rent and its
Enters fourth rent and its
Calculates weighted
Additional Examples
Business Applications
Setting a Sales Price
Onc method for setting the per unit sales price is to determine the cost of
production per unit, and then multiply by the desired rate of return. For
this method to be accurate, you must identify all costs associated with the
The following cquation calculates unit price based on total cost and rate
of return;
Example. To produce 2,000 units, your cost is $40,000. You want a 20%
rate of return, What price should you charge per unit?
Keys: Display: Description:
40000 40,000.00 Enters cost.
2000 [x] 20.00 Calculates unit cost.
MO 1 (+) 00 20 (= Calculates unit sales
100 [=] 24.00 price.
Forecasting Based on History
Onc method of forecasting sales, manufacturing rates, or expenses 15
reviewing historical trends. Once you have historical data, the data are fit
Lo a curve that has time on the x-axis and quantity on the y-axis.
8: Additional Examples 95
Example. Given the following sales data, what arc the sales estimates
for years six and scven?
Year Sales $
1 10,000
2 11,210
3 13,060
4 16,075
5 20,590
Keys: Display: Description:
a 0.00 Clears statistics registers.
1 10000 1.00 Enters first year and
sales for that year.
2 [INPUT] 11210 2.00 Enters second year's
3 13060 3.00 Conlinucs data entry.
4 16075 4.00
5 20590 5.00
6 B[5,m] 22,000.50 Estimates sales for year
7 [9m] 24,605.00 Estimates sales for ycar
Cost of Not Taking a Cash Discount
A cash discount gives a buyer a reduction in price if the payment is made
within a specified time period, For example, “2/10, NET /30” means that
the buyer can deduct 2 percent if payment is made within 10 days. If pay-
ment is not made within 10 days, the full amount must be paid by the 30th
You can use the equation shown below to calculate the cost of failing to
take the cash discount. The cost 1s calculated as an annual interest rate
charged for delaying payment.
96 8: Additional Examples
DISC% x 360 x 100
DISC 15 the discount percent if the payment is made carly. TOTAL
DAYS is the total number of days until the bill must be paid. DISC DAYS
is the number of days for which the discount is available.
Example. You receive a bill with the credit terms 2/10, NET /30. What
is the cost of not taking the cash discount?
Keys: Display: Description:
2 [x] 360 [x] 100 [=] 72,000.00 Calculates numerator in
ШО №00 100 (-) 2 Parentheses force order
HD) 98.00 of calculation.
[) BJ 30 (-) 10 [=] 36.73 Calculates, as an annual
percentage rate, cost of
not taking discount.
Loans and Mortgages
Simple Annual interest
Example. Your good friend needs a loan to start his latest enterprise
and has requested that you lend him $450 for 60 days. You lend him the
money at 10% simple annual interest, to be calculated on a 365-day basis.
How much interest will he owe you in 60 days, and what is the total
amount owed?
This equation is used for calculating simple annual interest using a 365
day year:
8: Additional Examples 97
Keys: Display: Description:
450 [+M)[x) 10 0.10 Stores interest.
[x] 60 [=] 365 [=] 7.40 Calculates interest owed.
[RM] (=) 457.40 Calculates total owed.
Continuous Compounding
The cquation for calculating an effective rate for continuous compounding
EFF % = (e(WOM® +100) _ 1) x 100
To solve a continuous compounding problem complete these steps:
1. Compute the annual effective rate using the above equation,
2. Either use this effective rate in your calculations with an annual
period (P/YR = 1) or convert this rate so that it applics to your pay-
ment period. In the following example, P/YR = 12 so you have to
calculate a new NOM% using the interest rate conversion applica-
tion with P/YR equal to 12.
Example. You currently have $4,572.80 in an account at Dream World
Investments that earns 18% annual interest compounded continuously. At
the end of cach month, you deposit $250.00 in the account. What will the
balance be after 15 years?
Keys: Display: Description:
18 0.18 Divides nominal rate by
Ble] 1.20 Raiscs e to 0.18 power.
(=) 1 [x] 100 [=] 19.72 Calculates annual
effective rate.
W(EFF%) 19.72 Stores cffective rate.
12 MP/YR) 12.00 Sets payments per year.
98 8: Additional Examples
18.14 Calculates annual nomi-
nal rate for a monthly
payment period.
Set to End Mode. Press W[BÉG/END] if BEGIN annunciator is displayed.
15 MxP/YR) 180.00 Stores number of
250 - 250.00 Stores regular payment.
4572.8 [+/-] -4,572.80 Stores current balance as
a negative value (like an
initial investment).
297,640.27 Calculates account bal-
ance after 15 years of
payments with 18%
interest compounded
Yield of a Discounted (or Premium) Mortgage
The annual yield of a mortgage bought at a discount or premium can be
calculated given the original mortgage amount (PV), interest rate (I/YR),
periodic payment (PMT), balloon payment amount (FV), and the price
paid for the mortgage (new РИ).
Remember the cash flow sign convention: money paid oul is negalive;
moncy received is posilive,
Example. An investor wishes to purchase a $100,000 mortgage taken out
at 9% for 20 years. Since the mortgage was issucd, 42 monthly payments
have been made. The loan is to be paid in full (a balloon payment) at the
end of its fifth year. What is the yicld to the purchaser if the price of the
mortgage is $79,000?
Step 1. Calculate PMT, Make sure FV = 0.
Set to End Mode. Press W(BEG/END] if BEGIN annunciator is displayed.
B: Additional Examples 99
Keys: Display: Description:
12 M(P/YR] 12.00 Sets payments per year.
9 9.00 Stores interest rate.
20 H[xP/YR] 240.00 Stores number of
100000 - 100,000.00 Stores original amount of
0 (FV] 0.00 Enters amount left to pay
after 20 ycars.
[PMT] 899.73 Calculates regular
Step 2. Enter the new value for N indicating when the balloon occurs,
then find FY, the amount of the balloon,
Keys: Display: Description:
BRAND) 899.73 Rounds payment to two
decimal places lor
5 M(xP/YR) 60.00 Stores number of pay-
ments until balloon.
[FV] 88,706.74 Calculates balloon
payment (add to final
Step 3. Enter actual, current values for N and PV; then find the new
I/YR for the discounted mortgage with balloon.
Keys: Display: Description:
[RCL] [N) [=] 42 [N] 18.00 Stores remaining number
of payments.
79000 (+/-) - 79,000.00 Stores price of mortgage.
20.72 Calculates the return on
this discounted mortgage.
100 85: Additional Examples
| Annual Percentage Rate for a Loan With Fees
The annual percentage rate, APR, incorporates fees usually charged when
a mortgage is issued, which cffectively raises the interest rate. The actual
amount received by the borrower (the PV) is reduced, while the periodic
payments remain the same. The APR can be calculated given the term of
the mortgage (N periods), the annual interest rate (//YR), the mortgage
amount (new PV), and the amount of the fee.
Remember the cash flow sign convention: money paid out is negative,
moncy received is positive.
Example: APR for a Loan With Fees. A borrower is charged two
points for the issuance of a mortgage. (One point is equal to 1% of the
mortgage amount.) If the mortgage amount 15 $60,000 for 30 years and the
annual interest rate is 11.5% with monthly payments what APR is the bor-
rower paying?
Set to End Mode. Press [lI[BEG/END] if BEGIN annunciator is displayed.
Keys: Display: Description:
12 M(P/YR) 12.00 Sets payments per ycar.
11.5 11.50 Stores interest rate.
30 H[xP/YR] 360.00 Stores length of
60000 [PY] 60,000.00 Stores original amount of
0 0.00 The loan will be com-
pletely paid off in 30
-594.17 Calculates paymenl.
[RCL] 60,000.00 Recalls loan amount.
[=] 2 58,800.00 Subtracts points.
УВ 11.76 Calculates APR, con-
sidering fecs.
8: Additional Examples 101
Example: Interest-Only Loan With Fee. A $1,000,000, 10-year,
12% (annual interest) interest-only loan has an origination fee of three
points. What is the yield to the lender? Assume that monthly payments of
interest are made.
Set to End mode. Press M[BEG/END) if BEGIN annunciator is displayed.
Keys: Display: Description:
12 M(P/YA] 12.00 Sets payments per year.
12 12.00 Stores interest rate.
10 MxP/YR] 120.00 Stores length of
1000000 1,000,000.00 Stores original amount of
[*+/-) -1,000,000.00 Enters amount due at
end of term. Payments
are interest only so entire
loan amount is due.
PMT - 10,000.00 Calculates interest-only
[PV] 1,000,000.00 Recalls loan amount.
[=] 3 970,000.00 Subtracts points.
1/ УВ. 12.53 Calculates APR.
Loan With a Partial (Odd) First Period
TVM calculations apply to financial transactions where each payment
period is the same length, However, situations exist where the first pay-
ment period is not the same length as the remaining periods. This first
period is sometimes called an odd or partial first period.
If interest is applied to an odd first period, it is usually calculated as sim-
ple interest. So using the HP-10B to do a payment calculation with an odd
first period is a two step process:
102 8: Additional Examples
1. Calculate the amount of simple interest that accrues during the frac-
tional first period and add it to the loan amount. This is the new PY.
You must be able to calculate the length of the odd first period as a
fraction of the whole period. (For example, a 15-day odd first
period would be 0.5 periods assuming a whole period to be a 30-day
2. Calculate the payment using the new PV, with N equal to the
number of full periods. Use Begin mode if the number of days until
the first payment is less than 30; otherwise use End mode.
Example. A 36-month loan for $4,500 has an annual rate of 15%. If the
first monthly payment is made in 46 days, what is the monthly payment
amount assuming 30-day months?
The odd first period in this example is 16 days.
Set to End mode. Press JJ[BEG/END] if BEGIN annunciator is displayed.
Keys: Display: Description:
12 MP/YR) 12.00 Sets payments per year.
15 15.00 Stores interest rate.
[+] 12 [x] 1.25 Calculates periodic
interest rate.
16 [=] 30 [x] 0.67 Multiplies by fraction of a
4500 BISWAP) (%] (=) 30.00 Calculates amount of
simple interest owed for
odd period.
4500 4,530.00 Adds this simple interest
to present value.
36 (N) 36.00 Stores term of loan.
O [FV] 0.00 Enters amount left to pay
alter 36 payments.
- 157.03 Calculates payment
8: Additional Examples 103
Automobile Loan
Example. You are buying a new $14,000.00 sedan. Your down payment
is $1,500 and you are going to finance the remaining $12,500. The car
dealer is offering two choices for financing;
m A 3-year loan with an annual interest rate of 3.5%.
E A 3-year loan with an annual interest rate of 9.5% and a $1,000.00
With which choice do you pay less for the car?
Set to End mode. Press W(BEG/ENO) if BEGIN annunciator is displayed.
Calculate the first option:
Keys: Display: Description:
12 M(P/YR) 12.00 Sets payments per year.
36 [N] Stores known values.
0 [FV] 0.00
3.5 [I/YR] 3.50 Stores first interest rate.
PMT - 366.28 Calculates payment.
[x] [N] [=] -13,185.94 Calculates total interest
and principal.
Calculate the second option:
Keys: Display: Description:
11500 11,500.00 Stores loan amount with
9.5 9.50 Stores second interest
PMT - 368.38 Calculates payment.
[x] [N] (=) —13,261.64 Calculates total interest
and principal.
The first option costs slightly less.
104 8: Additional Examples
| Canadian Mortgages
In Canadian mortgages, the compounding and payment periods are not
the same. Interest is compounded semi-annually while payments are
made monthly. To use the TVM application in the HP-10B, you need to
calculate a Canadian mortgage factor (which is an adjusted interest rate)
to store in 7/YR.
For additional information on interest rate conversions, sce the section
“Interest Rate Conversions” in chapter 5.
Example. What 15 the monthly payment required to fully amortize a
30-year, $30,000 Canadian mortgage if the annual interest rate is 12%?
Keys: Display: Description:
12 M[NOM%| Stores known nominal
2 M(P/YR)] 2.00 percentage and number
of compounding periods.
B(EFF%] 12.36 Calculates annual
effective rate.
12 B(P/YR] 12.00 Sets payments per year.
B(NOM%) 11.71 Calculates Canadian
mortgage factor (adjusted
interest rate).
30000 Stores other known
0 (FV) values for mortgage.
30 MxP7YR) 360.00
PMT -301.92 Calculates monthly
payment for Canadian
8: Additional Examples 105
What if ... TVM Calculations
One of the most valuable aspects of the HP-10B’s TVM application is the
case with which it handles the question “what if ,..” in financial calcula-
tions, For example, onc of the most popular “what if...” questions is,
“What if the interest rate changes to ...? How will that affect my pay-
ment?” To answer this question, once you have calculated a payment
based on one interest rate, all you need to do is enter the new interest rate
and recalculate PMT,
Some of the examples carlier in this manual have included some bricf
encounters with “what if …” questions, but a more complete example
Example. You are about to sign on the dotted line for a 30-year,
$735,000 mortgage, on a vacation home. The annual interest rate is 11.2%.
Part 1. What will your payments be at the end of the month?
Set to End mode. Press M[BEG/END) if BEGIN annunciator is displayed.
Keys: Display: Description:
12 M(P/YR] 12.00 Sets payments per year.
735000 Stores known values.
30 MxP/YR)
0 [EV) 0.00
-7,110.88 Calculates payment.
Part 2. Your company’s regular payroll is generated every other Friday.
The bank agrees to automatically draw payments of $3,555.00 out of each
paycheck (approximately half of what a monthly payment would be) and
adjust the payment period accordingly (26 compounding periods per
year). What would be the new term of the loan?
3565 (*/-) ~ 3,555.00 Enters new payment,
26 B(P/YR] 26.00 Sets payments per year
for every two weeks.
106 8: Additional Examples
514.82 Calculates number of
biweekly payments.
B(xP/YR) 19.80 Displays years required
to pay off loan.
Part 3. What if you had monthly payments as in part 1, but chose a
15-year term? What would your new payment be? What would be the
total interest paid on the contract?
Keys: Display: Description:
12 M(P/YR) 12.00 Sets payments per year.
15 B(xP/YR] 180.00 Stores new term.
PMT - 8,446.53 Calculates payment for
shorter term.
[x] [N] -1,520,374.70 Calculates total paid.
[=] - 785,374.70 Displays total interest
paid on contract.
Saving for College Costs
Supposc you start saving now to accommedate a futurc series of cash
outflows. An example of this is saving money for college. To determine
how much you need to save each period, you must know when you'll need
the money, how much you'll need, and at what interest rate you can invest
your deposits.
Example. Your oldest daughter will attend college in 12 years and you
are starting a fund for her education. She will need $15,000 at the begin-
ning of each year for four years. The fund earns 9% annual interest, com-
pounded monthly, and you plan to make monthly deposits, starting at the
end of the current month. The deposits cease when she begins college.
How much do you need to deposit each month?
8: Additional Examples 107
This problem is solved in two steps. First calculate the amount you'll need
when she starts college. Start with an interest rate conversion because of
the monthly compounding.
А $15,000 A
I/YYR = 9%
Year 1 Year 2 Year 3 Year 4
Keys: Display: Description:
9 BNOM%] 9.00 Stores annual nominal
12 M(P/YR) 12.00 Stores number of com-
pounding periods used
wilh this nominal rate.
B(EFF%] 0.38 Calculates annual
effective rate.
When compounding occurs only once per year, the effective rate and the
nominal rate are the same.
(/УВ) 9,38
Stores effective rate as
annual rate.
Set to Begin mode. Press JI[BEG/END] if BEGIN annunciator is not
1 MP/YR) 1.00 Sets 1 payment per year.
15000 (РМТ) 15,000.00 Stores annual withdrawal.
4 (N] 4,00 Stores number of with-
108 8: Additional Examples
0 0.00 Stores balance at end of
four years.
(PV) -52,713.28 Calculates amount
required when your
daughter starts college.
Then use that PV as the FV on the following cash flow diagram, and cal-
culate the PMT.
FV from
142 | 143 | 144
РМТ = ?
Set to End mode. Press M(BEG/END] if BEGIN annunciator is displayed.
[+/-) [РУ] 52,713.28 Stores amount you need.
0 0.00 Stores amount you arc
starting with.
12 M(P/YR) 12.00 Sets payments per year.
144 [N] 144.00 Stores number of
9 9.00 Stores interest rate.
-204,54 Calculates monthly
deposit required.
Gains That Go Untaxed Until Withdrawal
You can use the TVM application to calculate the future value of a tax-
free or tax-deferred account. (Current tax laws and your income deter-
minc whether both interest and principal arc tax-free. You can solve for
either case.)
8: Additional Examples 109
The purchasing power of that future value depends upon the inflation rate
and the duration of the account.
Example. You arc considering opening a tax-deferred account with a
dividend rate of 8.175%. Il you invest $2,000 at the beginning of cach year
for 35 years, how much will be in the account at retirement? How much
will you have paid into the account? How much interest will you have you
carncd? If your post-retirement tax rate is 15%, what will the alter-tax
future value of the account be? Assume that only the interest 15 taxed
(assume the principal was taxed before deposit). What is the purchasing
power of that amount, in today’s dollars, assuming an 8% inflation ratc?
Set to Begin mode. Press W(BEG/END] if BEGIN annunciator is not
Keys: Display: Description:
1 BIP/YA) 1.00 Scts 1 payment per year.
35 [N] Stores number of periods
8.175 and interest rate.
0 0.00 Stores amount you start
2000 [+/-] - 2,000.00 Stores amount of annual
[FV] 387,640.45 Calculates amount in
account at retirement,
[x] Calculates amount you
(ВСС) [№ |] -70,000.00 have paid into account by
[FV] (=] 317,640.45 Calculates interest
account has carned by
[>] 15 [%] [=] 47,646.07 Calculates taxes at 15%
of interest.
+4] [FV] [=] 339,994.39
Calculates after-tax FV.
110 8: Additional Examples
339,994.39 Stores after-tax future
valuc in FV,
8 0 [PMT] [PV] -22,995.36 Calculates present-value
purchasing power of
after-tax FV, assuming an
8% inflation rate.
Value of a Taxable Retirement Account
This problem uses the TVM application to calculate the future value of a
taxable retirement account that receives regular, annual payments begin-
ning today (Begin mode). The annual tax on the interest is paid out of the
account. (Assume the deposits have been taxed already.)
Example. Il you invest $3,000 cach year for 35 ycars, with dividends
taxed as ordinary income, how much will you have in the account al retire-
ment? Assume an annual dividend rate of 8.175%, a tax rate of 28%, and
that payments begin today. What is the purchasing power ol that amount
in today’s dollars, assuming 8% inflation?
Set to Begin mode. Press M[BEG/END) if BEGIN annunciator is nol
Keys: Display: Description:
1 B(P/YRA) 1.00 Sets 1 payment per year.
35 (N] 35.00 Stores number of pay-
ment periods until
8.175 [-] 28 [%] [=] 5.89 Calculates interest rate
diminished by tax rate.
I/YR 5.89 Stores adjusted interest
0 0.00 Stores amount you arc
starting with.
3000 [PMT] - 3,000.00 Stores amount of annual
8: Additional Examples 111
[FV] 345,505.61
Calculates amount in
account at retirement.
8 [1/YR] O ~23,368.11 Calculates present-value
purchasing power of FV,
assuming an 8% inflation
— —
Cash Flow Examples
Wrap-Around Mortgages
A wrap-around mortgage is a combination of refinancing a mortgage and
borrowing against real estate equity. Usually the two unknown quantitics
in the wrapped mortgage are the new payment and the rate of return to
the lender. To arrive at a solution, you need to use both the TVM and the
cash flow applications.
Example. You have 82 monthly payments of $754 left on your 8% mort-
gage, leaving a remaining balance of $47,510.22. You would like to wrap
that mortgage and borrow an additional $35,000 for another investment.
You find a lender who is willing to “wrap” an $82,510.22 mortgage al
9,5% for 15 years. What are your new payments and what return 1s the
lender getting on this wrap-around mortgage?
The payment calculation is a straightforward TVM payment calculation
using the new amount as the PV,
Set to End mode. Press [J(BEG/END] ¡f BEGIN annunciator is displayed.
Keys: Display: Description:
BICLEAR_ALL] 0.00 Clears all registers.
12 MP/YR) 12.00 Sets payments per year.
82510.22 82,510.22 Stores loan amount on
which your new payment
is calculated.
112 8: Additional Examples
19.5 [1/YR) 9.50 Stores interest rate.
0 [FV] 0.00 Stores final balance.
15 B(xP/YR] 180.00 Stores number of
monthly payments you
will make.
(РМТ) - 861.59 Calculates your new
Then, to calculate the lender's return, enter cash flows that represent the
complete picture of the wrap-around mortgage from the lender’s point of
1 2 3 4 82 83 84 180
eee eed)
When you group the above cash flows, you'll find that:
CF, = 47,510.22 - 82,510.22 = -35,000.00
CF, = 861.59 - 754,00 = 107,59
N, = 82
CF, = 861.59
N, = 180 - 82 = 98
8: Additional Examples 113
35000 (F7) (CFD
(RCL) EMT) (4) 5)
754 [CF])
82 MÍN)
(RCL] (PMT) (*/-) (CFI)
180 =) 82 MINT
Net Future Value
Enters $35,000 for loan
Enters nct payment for
first 82 months.
Enters number of times
payment occurs.
Enters net payment for
next 98 months.
Enters number of times
payment occurs,
Calculates annual return.
The net future value can be calculated by using the TVM keys to slide the
net present value (NPV) forward on the cash flow diagram.
Example: Value of a Fund. You have made the following deposits
over the past two years into a money market fund earning 8.8%. What is
the current balance of the account?
1,2,3,4,5,6,7.8,9.10,11.1213,14 15.16,17,18.19 20,21,22 23 24
1/YR = 8.8%
114 8: Additional Examples
Current Date
12 M(P/YR]
12000 [CF])
0 [CF]}
2 a6)
3000 (37) (СЕЛ
3 MN)
0 [CF] 9 MINI)
7500 (+/-) (CFI)
0 (CF)) 3 MINI)
2000 [+/-} [CF]
8.8 (I/YR]
- 12,000.00
= 7.500. 00
| Set to End mode. Press B(BEG/END] if BEGIN annunciator is displayed.
Clears all registers.
Sets payments per year.
Enters initial cash flow.
Enters amount in
group 1.
Enters number of times
payment occurs.
Enters amount in group
Enters number of times
payment occurs.
Enters number of times
payment occurs.
Enters cash [low group 4.
Enters number of times
payment occurs.
Enters cash flow group 6.
Stores annual interest
Calculates net present
value (NPV), automati-
cally stored as PY,
Stores known values.
Calculates net future
8: Additional Examples 115
Assistance, Batteries, and Service
We at Hewlett-Packard are committed to providing you with ongoing
support. You can obtain answers to questions about using your calculator
from our Calculator Support department.
Please read “Answers to Common Questions” before contacting us, Our
experience has shown that many of our customers have similar questions
about our products. If you don’t find an answer to your question, you can
contact us using the address or phone number listed on the inside back
Answers to Common Questions
Q: Im not sure if the calculator is malfunctioning or if I'm doing some-
thing incorrectly. How can I determine if the calculator is operating prop-
A: The diagnostic sell-test is described on page 121,
Q: My numbers contain commas instcad of periods as decimal points.
How do I restore the periods?
A: Press M7) (page 28).
Q: How do I change the number of decimal places that the HP-10B
A: Press N(DISP) and the number of decimal places that you want
(page 27).
Q: What does an “E” in a number (for example, 2.51E — 13) mcan?
116 A: Assistance, Battorios, and Service
A: Exponent of ten (for example, 2.51 x 10°), Refer to “Scientific and
Engineering Notation” on page 27.
Q: Why do I get a wrong answer or the no Solution message when using
A: Be surc to enter a value for four of the five TVM values before you
solve for the fifth, even if one of the values is zero, (Don’t [orget to store a
zero for [FV] if you completely pay off a loan.) Clearing all the registers
(NICLEAR ALL)) before entering your known values accomplishes the
same thing. Check to see that the calculator is in the appropriate payment
mode (Begin or End mode) and that P/YR is sct correctly.
Q: How can I change the sign of a number in a list of cash flows?
A: You must replace the cash flow entry. “Viewing and Replacing Cash
Flows” is discussed on page 79.
Q: What does PEND in the display mean?
A: An arithmetic operation is pending (in progress).
Q: What does : in the display mean?
A: The [INPUT] key has been pressed, or two values have been returned
(page 25).
Q: Why is 7RR/YR larger than I expected?
A: This is IRR per year. To sce a periodic IRR, divide 7RR/YR by P/YR.
Environmental Limits
To maintain product reliability, you should avoid getting the calculator
wet and observe the following temperature and humidity limits:
m Operating temperature: 0° Lo 45°C (32° to 113°F).
wm Storage temperature: = 20° to 65°C (— 4° to 149°F).
= Operating and storage humidity: 90% relative humidity at 40°C
(104°F) maximum.
A: Assistance, Battarios, and Servico — 117
Noise Declaration. In thc operator position under normal operation
(per ISO 7779): LpA < 70dB.
Power and Batteries
The calculator is powered by three button cell batteries, Expected battery
life depends on how the calculator is used and the chemical content of the
Use only fresh button-cell batteries. Do not use rechargeable batteries.
Low Power Annunciator
When the low battery annunciator (1) comes on, you should replace
the battcries as soon as possible.
If the battery annunciator is on and the display dims, you may lose data.
The ALL CLr message is displayed if data is lost due to low power.
Battery Specifications
Your HP calculator requires three 1.5-volt, button-cell batteries. We
reccommend using either alkaline or silver-oxide (ype batteries. Do not nse
rechargeable batteries. Usc batteries from the following list, or usc another
manufacturer's cquivalent.
Alkaline Silver Oxide o
Panasonic SR44 W or SP357
Evercady 357
Varta V357
Toshiba LR44
Panasonic LR44
Evercady A76
Duracell LR44
Varta VI3GA
Kodak KA76
118 A: Assistance, Batteries, and Service
Installing Batteries
1. Havc three fresh button-cell batteries at hand. Only touch batteries
by their edges. Wipe cach battery with a lint-free cloth to remove
dirt and oil.
2. Make sure the calculator is off. You will lose memory if the bat-
teries are removed when the calculator is on. Do not press [C) again
until the entire procedure for changing batterics is completed.
3. Hold the calculator as shown. To remove the battery-compartment
door, press down and outward on it until it slides off (away from the
4. Turn the calculator over and shake the batteries out.
Do not mutilate, puncture, or dispose of batteries in
fire. The batteries can burst or explode, releasing
hazardous chemicals.
5. Hold the calculator as shown and stack the batteries in the battery
compartment. Orient the batteries according to the diagram inside
the battery compartment. Be sure the raised and flat ends match the
A: Assistance, Battarles, and Service 119
6. Slide the tab of the battery-compartment door back into the slot in
the calculator case.
Determining if the Calculator Requires
Use these guidelines to determine if the calculator requires service. If
these procedures confirm that the calculator is not functioning properly,
read the section “If the Calculator Requires Service” on page 124.
= The calculator won't turn on (nothing is in the display):
1. Reset the calculator. Hold down the [C] key and press at
the same time. It may be necessary to repeat the reset keys-
trokes several times.
2. Erase memory. Press and hold down [C], then press and hold
down both [N) and [24]. Memory is cleared and the ALL CLr
message is displayed when you release all three keys.
3. If the calculator fails to respond alter steps 1 or 2, replace the
batteries (page 119).
4. If the calculator fails to respond after step 3, remove the
batteries (page 119) and lightly press a coin against both calcu-
lator battery contacts. Put the batteries back in and turn on the
calculator. It should display ALL CLr.
If steps 1 through 4 fail to restore calculator operation, it requires
120 A: Assistance, Batteries, and Service
| в The calculator doesn’t respond to keystrokes (nothing
happens when you press the keys):
1. Reset the calculator (see step 1 above).
2. Erase memory (sec step 2 above).
3. If the calculator fails to respond after steps 1 and 2, remove the
batteries (page 119) and lightly press a coin against both calcu-
lator battery contacts. Put the batteries back in and turn on the
calculator. It should display ALL Cr.
If steps 1 through 3 fail to restore calculator function, the calculator
requires service.
u The calculator responds to keystrokes but you suspect
that it is malfunctioning:
1. Do the self-test (described below). If the calculator fails the self
test, it requires service.
2. If the calculator passes the self-test, it is likely that you've made
a mistake in operating the calculator. Try rereading portions of
the manual, and check “Answers to Common Questions” on
page 116.
3. Contact the Calculator Support department. The address and
phone number arc listed on the inside back cover.
Confirming Calculator Operation — the Self-
If the display can be turned on, but it appears that the calculator 1s not
operating properly, you can do a diagnostic self-test. To run the self-test:
1. First, hold down the [C] key, then press at the same time.
2. Press any key four times, and watch the display as various patterns
are displayed. After pressing the key four times, the calculator
displays the copyright message COPr. HP 1987 momentarily, and
then the message 01. This indicates the calculator is ready for the
key Lest.
A: Assistance, Battaries, and Service 121
3. Starting at the upper left corner ([N]) and moving from left to right,
press each key in the top row, Then, moving left to right, press each
key in the second row, third row, etc., until you've pressed each key.
m If you press the keys in the proper order, and they arc function-
ing properly, the calculator displays two-digit numbers. (The
calculator is counting the keys using hexadecimal basc.)
m If you press a key out of order, or if a key isn’t functioning
properly, the next keystroke displays 10 - FAIL, followed by a
onc-digit number. If you received the message because you
pressed a key out of order, you should reset the calculator (hold
down (C] and press [PV]) and start the self-test over. If you
pressed the keys in order, but got this message, the calculator
requires service.
4. When the keyboard test has been completed, the calculator displays
a message:
m The calculator displays 10 - Good if it passed the sel[-test.
® The calculator displays 10 - FAIL, followed by a one-digit hexa-
decimal number 1 through F, if it failed the self-test. If the cal-
culator failed the self-test, it requires service (page 124).
Include a copy of the fail message with the calculator when you
ship it for service,
5. If the calculator failed the self-test, rerun the test to verify the
6. To exit the self-test, reset the calculator (hold down [€] and press
To start a continuous self-test (like the one performed at the factory),
hold down [С] (еп press [EV]. This test displays various patterns and the
copyright message, then automatically repeats. The test continues until
you press (CJ.
122 A: Assistance, Battaries, and Service
Limited One-Year Warranty
What Is Covered
The calculator (except for the batteries, or damage caused by the bat-
terics) is warranted by Hewlett-Packard against defects in materials and
workmanship for one year from the date of original purchase. If you sell
your unit or give it as a gift, the warranty is automatically transferred to
the new owner and remains in cffect for the original one-year period.
During thc warranty period, we will repair or, at our option, replace at no
charge a product that proves to be defective, provided you return the
product, shipping prepaid, to a Hewlett-Packard service center, (Replace-
ment may bc with a newer model of equivalent or better functionality.)
This warranty gives you specilic legal rights, and you may also have other
rights that vary from state to state, province to province, or country to
What Is Not Covered
Batteries, and damage caused by the batteries, are not covered by the
Hewlett-Packard warranty. Check with the battery manufacturer about bat-
tery and battery leakage warranties.
This warranty does not apply if the product has been damaged by accident
or misuse or as the result of service or modification by other than an
authorized Hewlett-Packard service center.
No other express warranty is given, The repair or replacement of a
product is your exclusive remedy. ANY OTHER IMPLIED WAR-
Some states, provinces, or countries do not allow limitations on how long
an implied warranty lasts, so the above limitation may not apply to you.
vinces, or countries do not allow the exclusion or limitation of incidental
or consequential damages, so the above limitation or exclusion may not
apply to you.
A: Assistance, Battarios, and Service 123
Products are sold on the basis of specifications applicable at the time of
manufacture. Hewlett-Packard shall have no obligation to modily or
update products, once sold.
Consumer Transactions in the United Kingdom
This warranty shall not apply to consumer transactions and shall not affect
the statutory rights of à consumer. In relation to such transactions, the
rights and obligations of Seller and Buyer shall be determined by statute.
If the Calculator Requires Service
Hewlett-Packard maintains service centers in many countries. These
centers will repair a calculator, or replace it with the same model or one
of equal or greater value, whether it is under warranty or not. There is a
service charge for service after the warranty period. Calculators normally
are serviced and reshipped within five working days.
Obtaining Service
a In the United States: Send the calculator to the Corvallis Service
Center listed on the inside of the back cover.
в In Europe: Contact your Hewlett-Packard sales office or dealer, or
Hewlett-Packard’s European headquarters for the location of the
nearest service center. Do not ship the calculator for service without
first contacting a Hewlett-Packard office.
Hewlett-Packard S.A.
150, Route du Nant-d'Avril
P.O. Box CH 1217 Mcyrin 2
Geneva, Switzerland
Telephone: (022) 780 81 11
124 A: Assistance, Battaries, and Service
m In other countries: Contact your Hewlett-Packard sales office or
dealer or write to the Corvallis Service Center (listed on the inside of
the back cover) for the location of other service centers, If local
service is unavailable, you can ship the calculator to the Corvallis
Service Center for repair.
All shipping, reimportation arrangements, and customs costs are your
Service Charge
There is a standard repair charge for out-of-warranty service. The
Corvallis Service Center (listed on the inside of the back cover) can tell
you how much this charge 15. The full charge 15 subject to the customer's
local sales or valuc-added tax wherever applicable.
Calculator products damaged by accident or misuse are not covered by
the fixed service charges. In these cases, charges are individually deter-
mined based on time and material.
Shipping Instructions
If your calculator requires service, ship it to the nearest authorized service
center or collection point.
m Include your return address and description of the problem.
m Include proof of purchase date if the warranty has not expired.
m Include a purchase order, check, or credit card number plus expira-
tion date (VISA or MasterCard) to cover the standard repair charge.
= Ship the calculator in adequate protective packaging to prevent dam-
age. Such damage is not covered by the warranty, so we recommend
that you insure the shipment.
m Pay the shipping charges for delivery to the Corvallis Service Center,
whether or not the calculator is under warranty.
A: Assistance, Batteries, and Service 125
Warranty on Service
Service 1s warranted against defects in materials and workmanship for 90
days from the date of service.
Service Agreements
In the U.S, a support agreement is available for repair and service. Reler
Lo the form in the front of the manual, For additional information, contact
the Corvallis Service Center (sec the inside of the back cover).
Regulatory Information
U.S.A. The HP-10B generates and uses radio frequency encrgy and may
interfere with radio and television reception. The calculator complies with
the limits for a Class B computing device as specified in Subpart J of Part
15 of FCC Rules, which provide reasonable protection against such
interference in a residential installation. In the unlikely event that there is
interference to radio or television reception (which can be determined by
turning the HP-10B ofl and on or by removing the batteries), try the
m Reorienting the receiving antenna.
® Relocating the calculator with respect to the receiver.
For more information, consult your dealer, an experienced
radio/television technician, or the following booklet, prepared by the
Federal Communications Commission: How to Identify and Resolve
Radio-TV Interference Problems. This booklet is available from the U.S.
Government Printing Office, Washington, D.C. 20402, Stock Number
004-000-00345-4, At the first printing of this manual, the telephone
number was (202) 783-3238.
West Germany. The HP-10B complics with VFG 1046/84, VDE
0871B, and similar noninterference standards. If vou use equipment that is
not authorized by Hewlett-Packard, that system configuration has to com-
ply with the requirements of Paragraph 2 of the German Federal Gazetie,
Order (VFG) 1046/84, dated December 14, 1984,
126 A: Assistance, Battaries, and Service
More About Calculations
IRR/YR Calculations
The calculator determines JRR/YR for a set of cash flows using
mathematical formulas that “scarch” for the answer. The process finds a
solution by estimating an answer and then using that estimate to do
another calculation — this is called an iterative process.
In most cases, the calculator finds the desired answer, since there is usu-
ally only one solution to the calculation, However, calculating JRR/YR for
certain sets of cash flows is more complex. There may be more than one
(or no) mathematical solution to the problem. In these cases, the calcula-
tor displays a message to help you interpret what has happened.
Possible Outcomes of Calculating IRR/YR
These are the possible outcomes of an IRR /YR calculation:
m Case 1. The calculator displays a positive answer. This is the only
positive answer. However, one or more negative answers may exist.
m Case 2. The calculator finds a negative answer but a single positive
answer also exists, It displays: POS Irr ALSO. To see the negative
answer, press [+] to clear the message. To search for the positive
answer, you must input a guess. (Refer to “Entering a Guess for
IRR /YR,” below). There might also be additional negative answers.
= Case 3. The calculator displays a negative answer and no message.
This is the only answer.
m Case 4. The calculator displays the message: Error - Soin, This
indicates that the calculation is very complex. It might involve more
than one positive or negative answer, or there may be no solution, To
continue the calculation, you must store a guess (see below).
B: More About Calculations 127
= Case 5. The calculator displays: no Solution, There is no answer.
This situation might be the result of an error, such as a mistake in
keying in the cash flows. A common mistake that results in this mes-
sage 1s putting the wrong sign on a cash flow. A valid cash-flow series
for an /RR/YR calculation must have at least onc positive and one
negative cash flow.
Halting and Restarting IRR/YR
The scarch for /RR/YR may take a relatively long time. You can halt the
calculation at any time by pressing the [C] key. The message IntErruPtEd
is displayed, Pressing (+) now displays the current estimate for JRR/YR.
You can resume the calculation by:
m Pressing B(RR/YR] while the current estimate is displayed in
the calculator hne. This continues the calculation from where it left
s Storing a guess for 7RR/YR, discussed below.
Entering a Guess for IRR/YR
To enter a guess, key in an estimate of 7RR/YR and then press
B(RR/YR]. You can enter a guess for JRR/YR at these times:
m Before beginning the calculation. A fairly accurate guess can reduce
the time required to calculate an answer and reduce the chance of the
calculator solving for an undesirable negative solution.
m After you've interrupted the calculation.
m Alter the calculator has halted the calculation due to any of the
aforementioned cases. However, for cases 3 and 5, no other solutions
will be found.
When calculating JRR/YR using a guess, the calculation halts when it
finds an answer. However, there may be additional positive or negative
answers, or no true solution at all. You can continue searching for another
solution by halting the calculation and entering a different guess.
Onc way to obtain a good guess for 7RR/YR is to calculate the NPV for
various interest rates. Since /RR/YR is the interest rate at which NPV
equals zero, the best estimate of JRR/YR is the interest rate that yields
the value for NPV closest to zero.
128 B: More About Calculations
Effect of Using >— to Correct Data
The HP-10B stores the statistical numbers in an “accumulated” fashion. It
doesn’t store every number that you enter, but rather it performs inter-
mediate calculations when you press the key. The ME--) key performs
the opposite intermediate calculations to effectively remove a number or
pair of numbers from the stored results.
When correcting statistical data, M[E-) docs not delete rounding errors
that may occur during the intermediate calculations done by [E+]. Thus,
subsequent results for corrected data may be different than for data that
was entered originally without having to use M(E-). However, the
difference will not be serious unless the incorrect data has a very large
magnitude compared with the correct valucs; in this case, you may want to
clear the statistical registers and re-enter the data,
Range of Numbers
The largest positive and negative numbers available on the calculator are
+9.99999999999 x 10*”; the smallest positive and negative numbers avail-
able are +1 x 10-7, Underflow displays a zero. Refer to the message
OFLO in “Messages” following this appendix,
Margin and Markup Calculations
MAR = | Jo Mu = | | xo
B: More About Calculations 129
Time Value of Money (TVM)
Payment Mode Factor: $ = 0 for End mode; 1 for Begin mode.
> . I/YR
1% = PyR
: 97 N°
i Yo
1 - |1 + — =
0 = РИ + |1 + Хх | PMT x | 9
100 1%
i% |
+ РИ Xx | + 100
LINT = accumulated interest
LPRN = accumulated principal
i = periodic interest rate
BAL 1s initially PV rounded to the current display setting.
РМТ is mitially PMT rounded to the current display setting.
7 P/YR x 100
130 B: More About Calculations
| For each payment amortized:
INT" = BAL Xi (INT is rounded to the current display setting;
INT” = 0 for period 0 in Begin mode.) —
INT = INT” (with sign of PMT)
ENT neu = ENT + INT
EPRN e = EPRN oy + PRN
interest Rate Conversions
|], _NOM% "
100 x P /YR
\ ’
EFF 9% = - 1| х 100
Cash-Flow Calculations
19 = periodic interest rate
j = the group number of the cash flow,
CF; = amount of the cash flow for group j.
n; = number of times the cash flow occurs for group j.
К = the group number of the last group of cash Mows.
Nj = 2 mn = total number of cash [lows prior to group j.
о -
1 - |1 + = |
NPV = CF, + №} СЁ) | > 1%]
= + X х |1 + —
’ # 1% 100
“ я
When NPV = 0, the solution for i% is the periodic internal rate of return.
B: More About Calculations 131
132 B: More About Calculations
Press [C] or [+] to clear a message from the display.
(All Clear). Memory has been erased (page 23).
(Balance). Balance in an amortization schedule (page 67).
(Cash Flow j). Cash flow number (page 78).
COPr. HP 1987
(Copyright HP 1987). Copyright is displayed during self-test.
Error - Func
(Error - Function).
E Attempt Lo divide by zero.
® Attempt Lo calculate n! with n< 0 or na noninteger.
mu Attempt to calculate the logarithm of zero or a negative number,
m Attempt to calculate 0° or 0 raised to a negative power.
® Attempt to raise a negative number to a noninteger power.
mM Attempt to calculate the square root of a negative number.
Error - Full
(Error - Full). Attempt to calculate an expression with more than five
pending operations or attempt to enter more than 15 cash [low groups.
Error - Int
(Error - Interest), Periodic interest percent is < - 100%.
Error - n
(Error - n). Attempt to solve for //YR with N < 0.999909 or > 1E10.
Messagos 133
Error-P Yr
(Error - Payments per Year). Attempt to solve for P/YR, or storc a
number in P/YR that is outside the legal range (1 to 999) or is not an
Error - PEr
(Error - Period). Attempt (o enter a value in N; that is outside the legal
range (1 to 99) or is not an integer.
Error - Soln
(Error - Solution). A solution for 7RR/YR or 7/YR may or may not exist,
If you arc attempting to solve I/YR, you may be able to perform the calcu-
lation using 7RR/YR. If you are attempting an JRR/YR calculation, rcler
to page 127.
Error - StAt (Error - Statistics).
mM Attempt to calculate Y, À, Or r with x-data only (all y-values cqual to
m Altempt to calculate x, y, r, or m, with all x- values equal.
® Attempt to calculate with n equal to zero.
E Allempl to calculate S,, бу, r, orm with n <1, or when a divi-
sion by zero or square root of a negative number occurrred in a statis-
tics calculation. Also, attempt to calculate X', with Ly = 0.
(Interest). Interest in an amortization schedule (page 67).
(Interrupted). An /RR/YR, 1/YR, or amortization calculation was inter-
rupted by pressing (C).
n <i>
(Nj). Number of times a cash flow of the same amount occurs consecu-
ively (page 78).
no Solution
(No Solution). No solution exists for values entered (page 127).
134 Messages
(Overflow). The magnitude of a result is too large for the calculator to
handle. Message is displayed for a moment, then the overflow result is
returned (+ 9,99999999999E 499). The overflow message is also displayed
if an intermediate TYVM or cashflow calculation results in an overflow
condition. In this casc, the message remains in the display.
PEr <P1> - <P?>
(Periods starting - ending). Displays beginning and ending paymenis for an
amortization schedule (page 67).
(Positive Internal Rate of Return Also). An IRR/YR calculation pro-
duced a negative solution, A positive solution also exists (page 127).
(Principal). Principal in an amortization schedule (page 67).
(Running). A calculation is in process.
(Underflow). An intermediate result in TVM is too small for the HP-10B
LO process.
<nnn> P Yr
(nnn Payments per Year). Temporary message showing number of pay-
ments per year. Displaycd for a moment when you press M[CLEAR ALL).
10 - FAIL n
(HP-10B Fail). The self-test failed; n 15 the fail code (page 121).
10 - Good
(HP-10B Good). The self-test is complete (page 121).
Messages 135
Special Characters
136 Index
[+M], 35, 37
_ 4,24
A, 21, 24, 118
:, 24
Accumulative discrepancies, 58
Add percent, 31
Adjusted interest rate, 73
Advance payments, 63
ALL CLr, 24, 133
[AMORT], 52
Amortization, 66
equations, 130
interest, 66
loan balance, 66
principal, 66
range of payments, 67
schedule, 68
single payment, 69
Amortization at a glance, 15
Amortize, single payment, 67
Annual percentage rate, 48, 101
Annualized yield, 84
Annuity account, 61
Annunciators, 24
Answers to questions, 116
Application registers, 29
APR, 48, 101
Arithmetic in registers, 39
Arithmetic operators, 21
Aulo increment, 67
Automatic constant, 35
Automobile loan, 104
Average, 88
Backspace, 22
DAL, 67
Balance, 43, 67
Balloon payment, 43, 56
Basics at a glance, 10
Batteries, 118
changing, 118
(BEG/END), 52
Begin, 13
Begin mode, 53
Borrowing equity , 112
Brightness of display, 21
Buy out value, 62
(C), 21
Canadian mortgage, 105
Capitalized value, 62
Car loan, 53, 104
Cash flow
calculations, 75
clearing, 75
diagrams, 43
discount, 77
cntering, 78
cquations, 131
group, 77
mistakes, 79
problems, 47
replacing, 79
viewing, 79
Cash paid out, 44
Cash received, 44
(CF), 78
Chain calculations, 22
Changing batteries, 118
[CHG], 26
Clear display, 10
Clear statistics, 20
Clearing, 23
Clearing messages, 23
(CL 2), 85
Colon, 24
Comma, 28
Comparing investments, 71
Compound interest, 45, 46
annual, 60
daily, 72
monthly, 72
periods, 71
quarterly, 72
Constant, 12, 35
Continuous compounding, 98
Continuous memory, 21
Correcting statistics, 87
Correlation coefficient, 88
Cost, 11
Cost of no discount, 96
Cost per unit, 95
(CST), 33
Cursor, 23
Daily compounding, 72
Decimal point, 26, 28
Digit separator, 28
Digits, 26
Dim display, 21
Discounted contract, 80
Discounted mortgage, 99
(DISP), 27, 58
C), 28
Index 137
Display all digits, 28
Display format, 21
Dot, 28
Down payment, 53, 55
(e“], 40
E, 27
(E), 27
[EEF%), 51, 71
annual rate, 47
rate, 71
Effective rate, 16
End, 13
End mode, 53
Entering a Guess, 127
Equations, 129
amortization, 130
cash Flow, 131
interest rate conversion, 131
margin and markup, 129
statistics, 132
TVM, 130
Equity, borrow against, 112
Erase, 22, 23
Erase memory, 120
Error messages, 133
Estimate for JRR%, 127
Estimate of x, 88
Estimate of y, 88
Exponents, 27
Factorial, 40
Fees up front, 101
FLA, 20
Forccasting based on history, 95
Format the display, 26
138 Index
Future value, 43, 48
[FV], 43, 48, 52
Grouping cash flows, 77
Guess for IRR/YR, 127
Hclp for questions, 116
History based forecasting, 95
Home mortgage, 55
Individual retirement account, 60
Initial cash flow, 77
(INPUT), 25
Input annunciator, 24
Installing batteries, 118
Int, 67
compound, 45, 52
simple, 45
Interest conversion at a glance, 16
Interest rate conversion, 71
equations, 131
Interest wath fees, 101
Interest-only loan, 102
Intermediate result, 41
Internal precision, 28
Internal rate of relurn,
17, 49, 75, 83
Investment comparisons, 71
IRA, 60
IRR, 49
IRR/YR, 77
[IRR/YR], 49, 75
IRR /YR al a glance, 18
IRR /YR Calculations, 127
(/YR], 48, 52
K, L
K], 35
Lease, 62
advance payments, 03
Lincar regression, 85, 91
[LN], 40
Loan, with fees, 101
Loans, 53
interest only, 102
number of payments, 52
odd first payment, 102
[M+], 35, 37
M register, 29, 37, 35
Malfunction, 116
(MAR), 33
Margin, 11, 33
Markup, 11, 33
Maturity value, 43
Mean, 88
weighted, 94
Memory, 29
clearing, 23
Mcmory keys at a glance, 12
Messages, 29, 133
Canadian, 105
discounted, 99
premium, 99
wrap-around, 112
[MU], 33
Mutual fund, 48, 49
[ni], 40
[N], 48, 52
n, 85
Natural logarithm, 40
cash flows, 44
numbers, 22
sign, 13
Net future value, 114
Net present value, 17, 49, 80
Netted value, 82
(NJ), 78
[NOM%], 51, 71
annual rate, 47
rate, 71
Nominal rate, 16
[NPV], 49, 75
NPV at a glance, 18
Odd first payment, 102
[OFF], 21
[ON], 21
One payment per year, 58
One-number functions, 25
One-variable statistics, 86
Option to buy, 62
Parentheses, 41
Partial first payment, 102
Payments, 48, 52
PEND, 24
Percent, 11, 31
change, 32
Percent at a glance, 11
Period, 26, 28
Periodic rate, 47
Periods, 48
[PMT], 48, 52
Population standard deviation, 88
Positive cash flows, 44
[PRC], 33
Premium mortgage, 99
index 139
Present value, 48
Price, 11
Prin, 67
Principal, 45, 67
Principal reduction, 66
[PV], 48, 52
(PZYR), 51, 52, 71
Questions, 116
Quick reference, 10
Range of numbers, 129
[RCL], 33, 35, 38
Recall, 38
Recall memory, 52
Reciprocal, 40
Register, 12
Register labels, 85
Registers, 29
Remaining amount, 43
Reset, 24, 120
Residual, 43
value, 62
Retirement account, 111
(ВМ), 35, 37
(RND), 28
Rounding, 28
errors, 58
Sample standard deviation, 89
Saving for college, 107
Savings account, 58
Scientific notation, 27
Self-test, 121
Selling price, 33
Service, 124
140 Index
Setting a sales price, 95
Shift key, 10, 24
Short term investment, 75
change, 51
convention, 45
Simple interest, 45, 97
Slope, 88
Square root, 26, 40
[Sx,Sy), 88
Statistics, 85
clearing, 85
corrections, 129
equations, 132
forecasting, 91
limit of values, 86
lincar estimation, 85, 91
lincar forecasting, 85
lincar regression, 85, 91
mean, 85, 89
memory, 85
mistakes, 87
one-variable, 85
population standard
deviation, 89
.. 00
sample standard deviation, 89
standard deviation, 85
summation , 89
[SWAP], 88
two-variable, 85
weighted mean, 85
Statistics at a glance, 19
Statistics, weighted mean, 94
Status, 24
[STO], 35, 38
Stock investment, 75
Store, 38
Subtract percent, 31
Summation statistics, 85
Summed value, 82
[SWAP], 25
Taxable retirement account, 111
Tax-deferred account, 110
Tax-free account, 110
3 Key Memory, 35
Time out, 21
Trailing zeros, 28
Turn off, 21
Turn on, 21
TVM, 14
cquations, 130
problems, 47
TVM at a glance, 13
Two-number functions, 26
Two-variable statistics, 86
Uneven cash flows, 80
Value of a fund, 114
Viewing cash Mows, 79
Warranty, 123
Weighted mcan, 94
What if ..., 14, 106
What if ... al a glance, 14
Won't turn on, 120
Wrap-around mortgage, 112
Yellow shift key, 21
Yield, 83
y-intercept, 88
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