HP 20B manual

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  • Brand: HP
  • Product: Calculator
  • Model/name: 20B
  • Filetype: PDF
  • Available languages: English, Dutch

Table of Contents

Page: 0
HP 20b Business Consultant
Financial Calculator Manual
For free training, visit www.hp.com/go/calctraining
HP part number: F2219-90201
First edition: August 2008
Page: 1
Legal Notices
2
Legal Notices
This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard
Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of
merchantability, non-infringement and fitness for a particular purpose.
Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the
furnishing, performance, or use of this manual or the examples contained herein.
Copyright © 2008 Hewlett-Packard Development Company, L.P.
Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard
Company, except as allowed under the copyright laws.
Hewlett-Packard Company
16399 West Bernardo Drive
MS 8-600
San Diego, CA 92127-1899
USA
Revision History
Revision History
Revision Date
Edition 1, v. 12 August 7, 2008
Page: 2
Contents
3
Contents
Legal Notices
Revision History..................................................................................................................2
HP 20b Business Consultant Keyboard
Keyboard Map Legend .......................................................................................................6
1 Basic Features
Welcome to the HP 20b Financial Calculator .....................................................................7
Turning the Calculator On and Off......................................................................................7
Selecting a Language.........................................................................................................7
Adjusting the Display Contrast............................................................................................7
Cursor.................................................................................................................................7
Two Line Display ................................................................................................................8
The Mode Menu: Setting Preferences................................................................................8
Changing the Calculation Mode........................................................................................10
Key Presses and the Secondary Function : Key..........................................................11
Annunciators.....................................................................................................................11
The I Key ..................................................................................................................12
The = Key......................................................................................................................12
Using the I and = Keys..........................................................................................12
Editing and Clearing Entries .............................................................................................13
The On/CE O Key ..........................................................................................................13
The Reset :x Menu ....................................................................................................13
Notes about Special Menus..............................................................................................13
Memory and the Memory Menu........................................................................................13
Accessing Menus and Menu Maps...................................................................................14
2 Mathematical Calculations
Mathematical Functions....................................................................................................16
Number Entry and Display................................................................................................16
Chain Mode ......................................................................................................................17
Algebraic Mode.................................................................................................................17
Reverse Polish Notation (RPN) Mode ..............................................................................18
The RPN Stack.................................................................................................................18
Last Number .....................................................................................................................19
One-Number Functions and the Math Menu ....................................................................22
The Math :s Menu.....................................................................................................23
The Probability Sub-menu ................................................................................................25
Page: 3
Contents
4
Two-Number Functions ....................................................................................................26
Storing and Recalling Numbers........................................................................................27
Recall Arithmetic...............................................................................................................28
Storing and Recalling with Time Value of Money (TVM) Keys .........................................28
Recalling a Menu Item Value in a Menu...........................................................................28
Rounding Numbers...........................................................................................................28
Percentages......................................................................................................................28
3 Time Value of Money
Time Value of Money (TVM) Keys....................................................................................30
Calculating Payments on a Loan ................................................................................32
Amortization......................................................................................................................33
Creating an Amortization Schedule ............................................................................34
Interest Conversion Menu.................................................................................................35
Using the Interest Conversion Menu...........................................................................35
Canadian Mortgages: TVM Canada .................................................................................36
Canadian Mortgage Example .....................................................................................38
4 Cash Flows
Cash Flow Example..........................................................................................................40
Analyzing Cash Flows.................................................................................................42
Editing Cash Flows .....................................................................................................44
Sample Cash Flow Diagrams ...........................................................................................45
5 Bonds
The Bond Menu ................................................................................................................46
Bond Calculation Example..........................................................................................47
6 Date Calculation
The Date Calculation Menu ..............................................................................................49
Date Calculation Example...........................................................................................49
7 Break-even
The Break-even Menu ......................................................................................................51
Break-even Example...................................................................................................51
8 Business Problems
The Percent Calculation Menu .........................................................................................53
Percent Calculation Examples ....................................................................................54
9 Depreciation
The Depreciation Menu ....................................................................................................56
Depreciation Example.................................................................................................58
10 Statistical Operations
The Data and Stats Menus...............................................................................................61
Page: 4
Contents
5
Statistics Example.......................................................................................................63
11 Errors
Error Messages and Calculator Status.............................................................................65
12 Warranty, Regulatory, and Contact Information
Replacing the Batteries.....................................................................................................67
HP Limited Hardware Warranty and Customer Care........................................................67
Customer Care .................................................................................................................68
Product Regulatory & Environment Information ...............................................................71
Index
Page: 5
HP 20b Business Consultant Keyboard
6
HP 20b Business Consultant Keyboard
Keyboard Map Legend
No. Feature Chapter(s) No. Feature Chapter(s)
1 Time Value of Money keys 3 16 Annunciator display area 1
2 Cash Flows, IRR, and NPV
menus
4 15 Amortization and Depreciation
menus
3,8
3 Data and Statistics menus 9 14 % key and Percent
Calculation menu
2,6
4 Input key 1 13 Store and Recall 2
5 Memory menu 1 12 Break-even menu 6
6 Up/Insert and Down/Delete
keys
1 11 Backspace key and Reset
menu
1
7 Secondary function key 1 10 Math Menu 2
8 On/Off and clear entry key 1 9 Mathematical function keys 2
Page: 6
Basic Features
7
1 Basic Features
Welcome to the HP 20b Financial Calculator
This manual is designed to familiarize you with the many features of your new 20b Financial Calculator. It includes menu
maps, example problems and solutions with key presses, screen shots, and examples of cash flow diagrams. There are also
sections which list the error messages and explain how RPN works. Refer to the section titled, Contents for quick access to
various topics. If you need more information about your calculator, or about calculator operation and features, please refer to
the training materials available at: www.hp.com/go/calctraining.
Turning the Calculator On and Off
To turn on your calculator, press O. To turn it off, press :a.
Turning the calculator off does not erase any data. The calculator automatically turns itself off after approximately five minutes
to conserve energy. If you see the low battery symbol () in the display, replace the batteries. See Chapter 12, Warranty,
Regulatory, and Contact Information for instructions on replacing the batteries.
Selecting a Language
English is the default language for messages displayed on the screen. To select a language other than English:
1. Press :u to access the Mode menu. FIX displays on the top line of the screen.
2. Press < repeatedly until English displays on the screen.
3. Press Iuntil the desired language is displayed. The displayed language is the active setting.
4. Press O to return to the default calculator screen.
For more information on accessing menus and changing calculator settings, refer to the sections below titled, The Mode
Menu: Setting Preferences, and Accessing Menus and Menu Maps.
Adjusting the Display Contrast
To adjust the contrast of the display, press and hold O while pressing the + or - keys. Each press of the + or
- keys slightly increases or decreases the contrast of the display.
Cursor
When you enter a number, the cursor (_) blinks in the display and indicates you are in number entry mode.
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Basic Features
8
Two Line Display
There are two lines in the display screen as shown in Figure 1.
Figure 1 Display Screen
The top line of the screen displays operation status, operator symbols, annunciators, and abbreviations of the registers,
variables, and menu names. Throughout this manual, this line is referred to as the top line. In Figure 1, SIN is on the top line.
The bottom line displays numbers you have entered, or results. Throughout this manual, this line is referred to as the bottom
line.
When no operations have been entered and no operations are pending, the bottom line of the screen displays 0.00. This state
of the calculator is referred to as the default calculator screen.
The Mode Menu: Setting Preferences
The Mode menu allows you to customize the calculator. To access the Mode menu, press :u. Press < or >
repeatedly to scroll through the menu starting with FIX=2 (the number of digits displayed to the right of the decimal point).
Once an item is displayed, press I to cycle through the other options for that setting. To exit the Mode menu, press
O. Table 1-1 lists the items in the Mode menu.
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Basic Features
9
Table 1-1 Mode Menu Settings
Setting (top line) Description
FIX= 2 Display precision (number of digits displayed to the right of the decimal point).
Default is 2.
Key in the number of digits you want and press I, or press = until the number of digits
you want is displayed.
The display precision can be any number from 0-11. If you specify -1, the calculator displays
numbers with the most appropriate number of digits after the decimal point.
If you find you need to change the FIX setting often, use the following shortcut:
1 Press : and release it. Check that the secondary function indicator is displayed.
2 Press : again, and, without releasing it, press a key, 0through 9 that corresponds
to the desired FIX setting. FIX settings for 10 and 11 are not available using this shortcut. If you
press . instead of a numbered key, FIX=-1 is selected.
Degree or Radian Angular mode in degrees or radians for trigonometric functions.
Default is Degree.
Pressing I toggles between these options.
Date:
mm.ddyyyy or
dd.mmyyyy
Format for dates. December 3, 2010 is entered as 12.032010 in mm.ddyyyy format, or 3.122010 in
dd.mmyyyy format. Note the (.) in both formats separating the first and second groups.
Default is mm.ddyyyy format.
Pressing I toggles between these options.
Note that when a date is displayed, a number between 1 and 7 also displays at the right of the
screen. This number indicates the day of the week corresponding to that date. Monday is 1, and
Sunday is 7.
Note: in 360-day calendar mode (Cal.360), days of the week are displayed only if the date is valid.
1.23 or 1,23 Selects point or comma as decimal separator.
Default is decimal point, 1.23
Pressing I toggles between these options.
1000.00, 1,000.00,
1000,00 or 1.000,00
Selects thousands separator.
Default is none, 1000.00
Pressing I toggles between these options.
Note: the 1000.00 and 1,000.00 options are only available if the decimal separator is set for point
(.); 1000,00 and 1.000,00 are available only if the decimal separator is set for comma (,).
Chain, Algebraic, or
RPN
Calculation mode. For more information, refer to Chapter 2, Mathematical Calculations.
Pressing I cycles through these options.
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Basic Features
10
Table 1-1 Mode Menu Settings
Setting (top line) Description
English, Français,
Deutch, or Español
Language setting for the messages displayed on the screen.
Default is English.
Pressing I cycles through these options.
Actual or
Cal.360
Calendar options for bonds and date calculations.
Default is Actual.
Pressing I toggles between these options.
Annual or Semiannual Bond type.
Default is Annual.
Pressing I toggles between these options.
TVM Standard or TVM
Canada
Activate or deactivate the compounding per year (C/YR) option in time value of money (TVM)
calculations. This option is primarily used for Canadian mortgage calculations. For more
information, refer to the section titled, Canadian Mortgages: TVM Canada in Chapter 3.
Pressing I toggles between these options.
Changing the Calculation Mode
After viewing the default settings, suppose you want to change the calculation mode from Chain to RPN. See Table 1-2.
Table 1-2 Changing the Calculation Mode
Keys Display Description
:u Opens the Mode menu, starting with first setting
option, FIX, the number of digits displayed to the right
of the decimal point.
<<<<
<
(Press five times)
Scrolls to the current setting for the calculation mode,
Chain.
II
(Press two times)
Selects RPN as the active setting. Note the small
RPN annunciator to the right.
O Exits the Mode menu and returns you to the default
calculator screen.
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Basic Features
11
Key Presses and the Secondary Function : Key
To execute the function associated with a key, press and release the desired key. Most of the 20b's keys have two functions:
the primary function and the secondary function. The primary function is printed on the top of the key. The secondary function
is printed on the bevel of the key. See Figure 2.
R
Primary
Function
Secondary
(shifted) Function
Figure 2 Primary and Secondary Key Functions
To activate the secondary function of a key, press and release : followed by the key with the desired secondary function
printed on the bevel. Unlike the shift key on a typewriter or computer keyboard, it is not necessary to press and hold :
while pressing another key.
When : is active, the down arrow annunciator appears on screen, indicating that the next key pressed will execute the
secondary function of the key. To cancel an accidental press of :, simply press : a second time.
In this manual, commands using the secondary key functions are represented by the secondary function key symbol, :,
followed by the key with the secondary function. For example, to execute sine, press :p. Note how the SIN portion of
the key is highlighted, while the 7 is grayed out. This highlighting focuses on the function of the key that will be activated in a
given command, and it is used throughout the manual to make the examples easier to follow. Key commands for example
problems are provided throughout the text and in tables. Key symbols are placed in the order they are to be pressed, from left
to right.
Annunciators
Annunciators are symbols that appear in the display as messages, or after certain keys or key combinations have been
pressed. Annunciators are special symbols indicating a specific status in the calculator. Figure 3 illustrates the annunciator
symbols in the display.
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Basic Features
12
Figure 3 Annunciator Symbols in the Screen Display
The I Key
The I key is used to input values for variables and execute menu items.
The I key is also used in Reverse Polish Notation (RPN) mode to enter a number on the stack or duplicate it.
The = Key
The = key is used at the end of a mathematical operation to calculate the final result. For example, 1+2=
returns a final result of 3.
The = key, when pressed outside of a mathematical operation, also allows you to request a calculation for the value of an
item. This request only applies to items that can be calculated.
Using the I and = Keys
Suppose you wanted to calculate the effective interest rate for a 12% nominal interest rate with 12 payments per year in the
Interest Conversion (IConv) menu. To open the IConv menu, press :&. Nom %= displays on the top line, and the
current value assigned to the nominal interest rate is displayed on the bottom line. With this screen displayed, press
12I to input a new value for the nominal rate. Press < followed by = to calculate the value for the
effective rate. See Figure 4.
Figure 4
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Basic Features
13
When an item for which the = key is valid displays, the small annunciator (=) is displayed on the top line at the right of the
screen. Do not confuse this small annunciator (=) with the larger annunciator (=) found to the right of a variable.
When an item for which the I key is valid displays, the INPUT annunciator is displayed on the top line at the right of
the screen.
Editing and Clearing Entries
The On/CE O Key
Pressing O one time cancels current number entries, mathematical operations, or a menu selection, in that order.
Pressing O repeatedly when performing multiple operations cancels one operation at a time, from the latest to the earliest.
The Reset :x Menu
The Reset menu allows you to reset some, or all, of the menu items, variables, and registers to their default values.
To open the Reset menu, press :x. TVM displays on the top line. Press < or > repeatedly to scroll to a
specific item. To validate a choice and reset the selected items, press I. Press O to cancel. If you select the
command to reset the cash flow (Cash Flow ), statistics (Stats ), or all values (All ) items, you will be prompted to confirm your
choice. At the Del. All?, Del. Data?, and Del. CF? prompts, press I again to confirm the reset, or O to cancel.
While working within a specific menu, pressing :x takes you directly to the item of the Reset menu that allows you to
reset that specific menu. For example, if you are working in the Bond menu and you wish to reset all your entries in the Bond
menu, with any item of the Bond menu displayed, press :x. Bond displays on screen. At this prompt, pressing
I resets the Bond menu and returns you to the last item you were working with in the Bond menu.
Notes about Special Menus
The Mode, Memory, Math and Reset menus are special menus; if you were working in a menu prior to entering one of these
special menus, pressing O to exit them returns you to your previous menu,. This feature allows you to work in two or more
menus simultaneously without having to exit a menu.
Memory and the Memory Menu
The Memory menu contains the following items: memories 1-9 (Mem 1-9 ) and 0 (Mem 0 ), Cash Flow, Statistics (Stats), and
Memory. To enter the menu, press :t. Press < or > repeatedly to scroll through the items starting with
memory 1 (Mem 1 ).
When a memory item is displayed, you can enter a new number and modify the value of the memory by pressing I.
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Basic Features
14
For more information about storing and recalling numbers, refer to the section titled, Storing and Recalling Numbers in
Chapter 2.
The Cash Flow and Statistics menus share the same memory and are limited to a combined total of 50 memory slots. The
number displayed with Memory refers to the number of remaining memory slots. When the cash flow or statistics items are
displayed, a number also appears on the bottom line. This number indicates the number of memory slots used by the menu.
Pressing I with this number displayed resets the memory of the displayed menu item and erases all entered data.
Since entering data in these menus can represent a significant amount of work, you will be asked to confirm your choice. At
the Del.Data? or Del.CF? prompts, press I to confirm, or O to cancel.
Accessing Menus and Menu Maps
Many of the calculator's functions are located within menus. To access a menu, press the key, or secondary-function-key-
combination, for the menu in which you wish to work. To exit a menu, press O.
For example, to access the Break-even menu, press :!. Once opened, you can scroll through the items in the menu
by pressing <or> repeatedly. When you arrive at the last item in a menu, pressing < returns you to the first item.
Similarly, pressing > one time on the first menu item scrolls to the last item in the menu.
Most items consist of two parts: a name and an associated number. For example, the Fixed item in the Break-even menu
(Figure 7) displays as shown in Figure 5.
Figure 5
The large (=) annunciator shows that the value assigned to Fixed is 120,000. If you perform a calculation with this item
displayed by pressing 1+2= for example, Fixed is still selected as the current item, but the large (=)
annunciator is now turned off, indicating the 3 is not the value assigned to Fixed (see Figure 6).
Figure 6
At this point, to return to the display of the Fixed menu item shown in Figure 5, press O.
Some menus have sub-menus. If an item represents a sub-menu, pressing I with that menu item displayed opens the
sub-menu.
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Basic Features
15
In this manual, diagrams called Menu Maps are included at the beginning of each section to assist you with navigating
through the menus used for that section. For an example of a menu map, see Figure 7.
Figure 7 The Menu Map for the Break-even Menu
There are four types of menu items:
1. Read/write. Read/write menu items, such as Fixed in the Break-even menu shown above, are easily recognizable,
because when they are selected, both the INPUT and small (=) annunciators are lit. When lit, these annunciators
indicate that entering a number and pressing I will store the entered number in the displayed menu item.
Pressing = (outside of a mathematical operation) calculates the value for that item based on available data.
2. Read-only. Read-only items such as Internal Rate of Return (IRR% ) in the IRR menu are display-only; they are
calculated values computed internally by the calculator.
3. Write-only. Write-only items, such as investment interest rate (Inv. I% ) in the Net Present Value (NPV) menu, are
similar to read/write items in that the INPUT annunciator is lit when these items are selected, indicating that entering a
number and pressing I stores that number in that menu item. However, the = key does not calculate a
value for that item.
4. Special items. Special items, such as the Degree/Radian option in the Mode menu, the items of the Reset menu, and
the items of the Percent Calculation (%calc ) menu perform an action when I is pressed. Depending on the
menu, this action can be the selection of a sub-menu (%calc menu), changing a mode or setting (Mode menu), or
erasing data (Reset menu).
Page: 15
Mathematical Calculations
16
2 Mathematical Calculations
Mathematical Functions
Mathematical functions are located:
 On keys, such as, +-*/, etc.
 On shifted, or secondary functions, such as, :p
 In the Math menu, :s
Number Entry and Display
Numbers are entered by pressing:
 Numbered keys, 0-9
 The decimal point .
 The } key
 The :w keys
To correct a number entry, press the backspace key, {. Each press of { erases the last digit or symbol you entered.
To enter a number in the display, press the number digits successively. A number can have up to 12 digits.
To change the sign of a number from positive to negative, press }.
Use scientific notation to enter very large and very small numbers. For example, to enter the number
127
10
23
.
1  in scientific
notation, first enter the mantissa (1.23 ) and then press :w and enter the number (127 ) representing the exponent.
The exponent must have a value between -499 and +499.
Figure 1 Scientific Notation in FIX=2 Mode
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Mathematical Calculations
17
Chain Mode
Calculations in Chain mode are interpreted in the order in which they are entered. For example, entering the following
numbers and operations as written from left to right 1+2*3= returns 9. See Figure 2.
Figure 2 Calculation in Chain Mode
Note: if you press an operator key, +-*/, after =, the calculation is continued using the currently
displayed value.
In Chain mode, if you wish to override the left to right order of entry, use parentheses () to prioritize operations.
For example, to calculate  
3
2
1 
 , you may enter the problem as written from left to right, with parentheses to prioritize the
multiplication operation. See Table 2-1 below.
Table 2-1 Simple Arithmetic Calculations in Chain Mode
Keys Display Description
1+
(2*3)
Sets operational priority, inputs numbers, and
multiplies 2 and 3.
= Adds 1 to 6 and returns 7.00 on the bottom line as
the final result.
Algebraic Mode
To set the calculator in Algebraic mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1.
In Algebraic mode, multiplication and division have a higher priority than addition and subtraction. For example, in Algebraic
mode, pressing 1+2*3= returns a result of 7.00. In Chain mode, the same key presses return a result
of 9.00.
In Algebraic mode, operations between two numbers have the following priority:
 Highest priority: the power function (yx)
 Second priority: combinations and permutations
 Third priority: multiplication and division
 Lowest priority: addition and subtraction
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Mathematical Calculations
18
For example, key in 1+ 2 x 5 nPr22 in Algebraic mode by pressing:
1+2*5:b2:m=. The result is 241.
Note: the calculator is limited to 12 pending operations. An operation is pending when it is waiting for the input of a number or
the result of an operation of higher priority.
Reverse Polish Notation (RPN) Mode
To set the calculator in RPN mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. In RPN
mode, numbers are entered first, separated by pressing I or =, followed by an operation key.
Note: pressing I or = is optional after entering a number, if the next key pressed is an operation.
Each time you press an operation or function key in RPN, the answer is calculated immediately and displayed. For example,
suppose you wanted to add two numbers in RPN, 1 and 2. Press 1I2+. The result, 3.00, is calculated
and displayed immediately on the bottom line along with the (+) symbol on the top line.
Note: in RPN mode, when you are in a menu for which I or = are valid, pressing these keys enters the number,
but it also performs the action associated with the key for the menu item, which is generally saving the number in the variable
or calculating the item's value.
The RPN Stack
RPN works by placing numbers in storage registers called the stack. The RPN stack has four levels numbered 1-4. The levels
are stacked on top of one another. See Figure 3.
Stack Level 4
Stack Level 1
Stack Level 3
-15
12
Stack Level 2 41
23
Figure 3 The RPN Stack
In Figure 3, the stack contains four numbers, 23, 41, 12, and -15. Each level (1-4) contains one number. When a number is
typed and entered into the stack by pressing I, this new number is "pushed" into level one of the stack, and each
number already in the stack moves up one level. The number in Level 4, -15, is pushed out and is lost.
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Mathematical Calculations
19
When an operation is performed on the stack, addition (+) for instance, the calculator "pops" or moves the two numbers
from the bottom levels (Levels 1 and 2) out of the stack, performs the operation, and "pushes" the results back into the stack.
With the numbers entered into the stack as shown in Figure 3, pressing + changes the stack as shown in Figure 4. Note
that when the numbers are "popped" out to add 23 and 41, Level 4 of the stack remains unchanged.
-15
-15
12
64
Figure 4 The RPN Stack of Figure 3 after the Addition Operation
Last Number
Each time you perform a mathematical operation, the content of Level 1 of the stack is saved. Pressing :d recalls that
number. This functionality can be used to undo an erroneous key press, or if you want to reuse a number, such as 56.123 in
the expression:
 
 
123
.
56
123
.
56
23
.
1 
See Table 2-2 for an example using the last number function.
Table 2-2 Last Number
Keys Display Description
:u3I Sets FIX= to 3.000
<<<<<
II
Selects RPN as the operating mode.
O1c23
I56c1
23
Inputs 1.23 and 56.123
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Mathematical Calculations
20
Table 2-2 Last Number
Keys Display Description
+:d/ Adds 1.23 and 56.123, then divides the sum by the
last number, 56.123. Returns results in the selected
display format.
For more complex problems requiring two or more operations, you do not need to enter parentheses to set operational priority.
Key in numbers and operations inside the parentheses first, followed by those outside of the parentheses. If a problem has
more than one set of parentheses, start by working with the operations and numbers in the innermost parentheses and work
out. For example, calculate:
   
6
5
4
3 


One way to calculate this problem is to key in the numbers and operations within the parentheses first, followed by the
operation outside of the parentheses. See Table 2-3.
Table 2-3 Simple Arithmetic Calculations in RPN Mode
Keys Display Description RPN Stack
3I4+ Inputs the numbers and the
operation in the first set of
parentheses. Intermediate
results are displayed. Note
the (+) and (RPN)
annunciators.
Previous Value
Previous Value
Previous Value
7
5I6+ Inputs the numbers and the
operation in the second set of
parentheses. Intermediate
results are displayed. Note
the (+) annunciator.
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Mathematical Calculations
21
Table 2-3 Simple Arithmetic Calculations in RPN Mode
Keys Display Description RPN Stack
* Finishes the operation and
displays the results.
Pressing I or = when you are not entering a number duplicates the number on Level 1. That is, the number on
Level 1 is pushed on the stack, making Levels 1 and 2 equal. In the example above, pressing I after * duplicates
77 on the stack, making Levels 1 and 2 equal. See Figure 5.
Previous Value
Previous Value
77
77
Figure 5 Duplicating a Number on the Stack
In RPN, the parentheses keys () manipulate the stack. Pressing ( performs a roll down of the stack. A roll down
causes the stack to roll towards the bottom of the stack, during which the number in Level 2 moves down to Level 1, the
number in Level 3 moves down to Level 2, the number in Level 4 moves down to Level 3, and the number in Level 1 moves
up to Level 4. The ( key has a small down arrow on it as a reminder of the roll down feature. With the numbers entered
into the stack shown in the left column in Figure 6, pressing ( performs the roll down of the stack shown in the right
column.
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Mathematical Calculations
22
Figure 6 The RPN Stack and the Roll Down Operation
Pressing ) performs a swap. A swap operation exchanges the numbers on Levels 1 and 2 of the stack. The ) key has
a small symbol on it as a reminder of the swap feature. With the numbers entered into the stack shown in the left column in
Figure 7, pressing ) performs a swap to the stack as shown in the right column.
Figure 7 The RPN Stack and the Swap Operation
Note: when no menu is selected, the < key performs the same function as the ( key. The > key performs the
inverse operation called, roll up.
One-Number Functions and the Math Menu
The key presses for the one-number mathematical functions listed in Table 2-4 below apply to all modes, Chain, Algebraic,
and RPN. To execute one-number functions, with a number displayed, press the key or key combination corresponding to the
operation you wish to execute. The result is displayed on the bottom line.
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23
For example, to calculate 6 , press 6:n. The result of 2.45 is calculated immediately and displayed on the
bottom line. The square root symbol ( ) appears on the top line.
Note: before doing any trigonometric calculations in the Math menu, check whether the angle mode is set for degrees
(Degrees) or radians (Radians). You will need to change the setting if the active mode is not what your problem requires. For
more information on the Mode menu and calculator settings, refer to the section titled, The Mode Menu: Setting Preferences
in Chapter 1.
Table 2-4 lists one-number functions along with their corresponding keys.
Table 2-4 Shifted Function Mathematical Operations
Keys Description
:p Calculates sine.
:q Calculates cosine.
:r Calculates tangent.
:k Calculates natural log.
:l Calculates natural exponent to the power of x.
:m Calculates square of x.
:n Calculates square root.
:f Executes the Random function. Returns a random number in the range 0 < x <1.
:g Calculates factorial of x (where -253 < x ≤ 253). The Gamma function is used to calculate x! for
non-integers or negative numbers.
:h Calculates y to the x power.
:i Calculates the reciprocal.
:d In Chain or Algebraic mode, recalls the result of the last operation. In RPN mode, returns the
content of the Last Number variable.
:e Rounds x internally to the number specified by the display format.
The Math :s Menu
There are additional functions available in the Math menu. To open the Math menu, press :s. See Figure 8 for the
menu map of the Math menu.
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Mathematical Calculations
24
Figure 8 The Menu Map for the Math Menu
Press < to scroll through the menu items, starting with Trigonometry. The Trigonometry, Hyperbolic, and Probability items
have sub-menus. Press I with these items displayed to access the functions within the sub menus.
Press O to cancel the Math menu and return to current work. Press :s to return to the top of the Math menu.
For an example using the math menu to calculate Sin -1 (0.5), see Table 2-5.
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25
Table 2-5 Math Menu Example
Keys Display Description
.5I
:s
Enters 0.5 and opens the Math menu starting with
Trigonometry.
I< Selects the Trigonometry sub-menu and scrolls to Sin-1.
Note the value for Sin-1 is calculated immediately and
displayed.
I or = Validates the result.
In the Math menu, PI does not perform calculations; it enters PI for calculations. You may start an operation, use the Math
menu to execute a function, and continue calculating with your original operation without losing your work.
The Probability Sub-menu
Lower Tail Normal Distribution (LTND) calculates the probability for a normally distributed, random variable to be less than the
input.
Inverse Lower Tail Normal Distribution (LTND-1) is the inverse function for LTND; it calculates the value (V) for which the
probability of a normally distributed, random variable to be less than V is the given input. Student, Inverse Student, Chi2,
Inverse Chi2, F-Distribution and Inverse F-Distribution perform similar operations for Student, Chi2, and F-Distributions.
Student, Chi2, and F-Distribution and their inverse operations are special cases, as they require more than one number as
input. Student and Chi2 require (N), the number of degrees of freedom, and F-Distribution requires (N1) and (N2), two degrees
of freedom.
To perform Student and Chi2 operations or their inverse:
1. Enter the number of degree(s) of freedom by typing the number and pressing I or =.
2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which
you want the number.
3. Navigate to the appropriate function in the Probability sub-menu of the Math menu.
To perform F-Distribution operations or their inverse:
1. Enter the two degrees of freedom by typing each number followed by I or =.
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Mathematical Calculations
26
2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which
you want the number.
3. Navigate to the appropriate function in the Probability sub-menu of the Math menu.
Table 2-6 Probability Example
Keys Display Description
10I
8I
:s
Enters 10 degrees of freedom and the number for which
probability is to be calculated. Opens the Math menu.
<<I
<<<<
Selects the Probability menu item and scrolls to Chi2.
I or = Validates the result.
Table 2-7 Inverse Probability Example
Keys Display Description
10I
0.37
12I
:s
Enters 10 degrees of freedom and the probability. Opens
the Math menu.
<<I
<<<<
<
Selects the Probability menu item. Scrolls to Chi2-1.
I or = Validates the result.
Two-Number Functions
Apart from +-*/, the three additional two-number functions accessible on the keyboard are:
 Yx
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27
 nCr
 nPr
Yx is the power function, nCr stands for the number of combinations of n items taken r at a time, and nPr stands for the
number of permutations of n items taken r at a time.
Combination=
 !
!
!
r
n
r
n

Permutation=
 !
!
r
n
n

Perform calculations with these functions in the same way you would perform calculations with +-/ and *,
but press : to access the secondary function key. For example, to calculate 153 :
1. Press 15.
2. Press :h.
3. Press 3=. The results are shown Figure 9.
Figure 9
In RPN mode, key in the numbers first, followed by I, then press the function key. For example, for the power function
example above, in RPN press: 15I3:h.
Storing and Recalling Numbers
The calculator has ten memories available for use during calculations. These memories are numbered from 1-9 and 0. To
store a number in a memory, press :$, followed by the key representing the memory number. To recall a number
stored in a memory, press L followed by the key representing the memory number. You can use the store and recall
functions for these memories any time a number is displayed, or when you wish to enter a number.
For example, to store 15 in memory 1, press 15:$1.
To recall the number in memory 1, press L1.
You can also perform operations to numbers stored in memories. For example, press 5:$2 to store 5 in
memory 2. To add 12 to the value of memory 2, press 12:$+2. Later on, during a calculation, you can
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Mathematical Calculations
28
press L2 to recall memory 2. Note how the new current value stored in memory 2 is 17, (5 +12). +-* and
/ are valid mathematical operations for memories.
To view the stored values in memories 1-9 and 0, press :t, followed by < or > repeatedly to scroll
through each memory starting with memory 1 (Mem 1 ). Note that in the Memory menu, you can change the value of any
memory by selecting the memory and typing a number followed by the t key.
Recall Arithmetic
In RPN, typing 12L+2 adds the value of memory 2 to the first level of the stack, but it will not modify the
stored value of memory 2. This is useful, as it "saves" one stack level. You can also use -* and / after L.
To perform the same operation in Algebraic and Chain modes, press 12+L2=.
Storing and Recalling with Time Value of Money (TVM) Keys
To store the current number in the Time Value of Money (TVM) variables, press :$ followed by the desired TVM key.
To recall the stored value of a TVM variable, press L followed by the key of the desired TVM variable. Note: pressing L
does not calculate the variable; it recalls the current value.
Recalling a Menu Item Value in a Menu
In a menu, you can recall the current value of a menu item. For example, open the Interest Conversion menu (IConv) by
pressing :&. With Nom.% displayed, pressing 2*L= recalls the nominal rate. This feature is useful
when you need to insert the contents of a menu item into an algebraic operation.
Rounding Numbers
All calculations are performed internally with 15-digit precision and are rounded to 12 digits when returning the results. In
certain instances, calculations are performed internally with greater than 15-digit precision.
When displayed, a number is further rounded to the number of digits after the decimal point set by the FIX item in the Mode
menu. The default setting is two digits to the right of the decimal point. For more information, refer to the section titled, The
Mode Menu: Setting Preferences in Chapter 1.
Note: the FIX setting only affects the display; it does not affect the actual numbers.
Percentages
In Algebraic or Chain modes, pressing % divides a number by 100. For example, pressing 25% returns 0.25.
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29
To find a percentage of a given number, enter the number and multiply it by the desired percentage, followed by =. For
example, to find 25% of 200, press 200*25%= to return a result of 50.
To add or subtract a percentage of a number, enter the first number, followed by + or - and the percentage followed
by %. Finish your calculation with =. For example, to add 10% to 50, press 50+10%= to
return a result of 55.
In RPN mode, the % key calculates x % of the number on Level 2 of the stack, when x is the number on Level 1 of the
stack. It does not modify the number on Level 2 of the stack, and thus allows you to perform addition or subtraction after
pressing % to add or subtract x % from the number.
For example, 200I25%returns 50, but 200 is still on Level 2 of the stack, and pressing -
returns 150, or 200-25%.
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Time Value of Money
30
3 Time Value of Money
The examples in the following sections are calculated with the Mode menu preferences in their default settings, unless
otherwise noted. For more information about basic features and setting preferences, see Chapter 1, Basic Features.
Time Value of Money (TVM) Keys
Cash flow diagrams are useful tools for analyzing financial situations, as they help you identify the TVM functions needed to
resolve your problem.
A cash flow diagram is a drawing with a set of vertical arrows arranged on a horizontal line. The horizontal line represents the
period of time from the beginning of the financing to the end. The vertical arrows represent the money or cash flows at certain
times throughout the period. The arrows' length is proportional to the cash flow amount each arrow represents; a longer arrow
indicates a larger amount, a shorter arrow, a smaller amount. Each arrow's position on the line represents the time at which
the cash flow occurs. The orientation of the arrow, up or down, represents the "direction" of the cash flow: up for money
received, down for money paid out. See Figure 1.
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Time Value of Money
31
Figure 1 Cash Flow Diagram Example with Corresponding TVM Keys
The TVM functions of the calculator can solve problems with at least one cash flow, and problems in which all the cash flows,
except the first and last, are of the same value. To solve other types of cash flows, refer to the section below titled, Canadian
Mortgages: TVM Canada, or Chapter 4, Cash Flows.
Figure 1 illustrates a cash flow diagram and how the data in the diagram corresponds to the TVM keys. For a complete list of
keys used for TVM problems, along with their descriptions, see Table 3-1.
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Time Value of Money
32
To save values for the TVM variables, enter the desired number, followed by the corresponding TVM key. To calculate an
unknown value, enter all known values and press the key of the item you want solved.
Table 3-1 TVM Keys
Keys Description
N Stores or calculates the number of payments or compounding periods.
^ Multiplies a value by the number of payments per year and stores as N.
Y Stores or calculates the nominal, annual interest rate.
V Stores or calculates the present value (PV). To a lender or borrower, PV is the amount of a loan;
to an investor, PV is the initial investment. PV always occurs at the beginning of the first period.
M Stores or calculates the amount of each periodic payment.
[ Stores the number of payments or compounding periods per year.
F Stores or calculates the future value (FV), a final cash flow. FV always occurs at the end of the
last compounding period.
? Sets Begin mode (Beg). Payments occur at the beginning of each compounding period.
] Sets End mode (End). Payments occur at the end of each compounding period.
Calculating Payments on a Loan
You borrow 140,000.00 for 30 years (360 months) at 6.5% annual interest, compounded monthly. What is your monthly
payment to the lender? Note: at the end of the 30 years, you expect to have a zero balance (FV=0).
Table 3-2 TVM Example
Keys Display Description
12:[ Inputs 12 as the number of payments per year, or
compounding periods per year.
360
N
Inputs 360 as the number of payments over 30 years.
6.5
Y
Inputs 6.5% as the nominal interest rate percentage per year.
1400
00V
Inputs the present value of the loan at the time of the first
payment. This value is positive (+); it is money you receive.
0F Inputs 0 as the future value of the loan (the remaining
balance).
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Time Value of Money
33
Table 3-2 TVM Example
Keys Display Description
M Returns the monthly payment. This result is negative (-); it is
money you pay out.
To reset the TVM variables to their default values, with any TVM variable displayed press :x. Press < or >
repeatedly until TVM displays. Press I to reset the TVM values, or press O to cancel.
Amortization
Refer to Figure 2 for a menu map of the Amortization menu (Amort). Table 3-3 lists the keys and variables of the Amortization
menu. To open the menu, press A. The Amortization menu calculations are based on values stored in the following TVM
registers: N, Y, V, M and [.
To enter values for the TVM variables, enter a number followed by the corresponding key.
For an amortization example, see Table 3-4.
Figure 2 The Menu Map for the Amortization Menu
Table 3-3 Amortization Menu Items
Menu Item/Key Description
A Opens the Amortization menu.
Nb Period Number of periods to group together in the amortization calculation. The default value is
the number of payments per year defined by the [ key.
Start Period on which to start amortization. Default is 1. If you want to amortize for the second
year with 12 payments per year, enter 13 (the second year starts at the 13th payment
with 12 payments per year).
Balance The loan balance at the end of the assigned amortized period.
Principal Amount of the loan payment applied to the principal at the end of the amortized period.
Interest Amount of the loan payment applied to the interest at the end of the amortized period.
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Time Value of Money
34
Enter the values for the TVM keys for the example below. Press A followed by < or > to view the amortization
schedule.
Creating an Amortization Schedule
You borrow 140,000.00 for 360 months at 10% interest. Create an amortization schedule for the loan. How much interest
did you pay for the first year? What is the balance of your loan after the first year? See Table 3-4. The example below is
shown with RPN as the active operating mode.
Table 3-4 Amortization Example
Keys Display Description
12:
[
Inputs 12 as the number of payments per year.
30:
^
Inputs 360 (30 times 12 payments per year) as the number of
payments for the 30-year loan.
10Y Inputs 10 as the interest rate percentage per year.
1400
00V
Inputs the value of the loan at the time of the first payment.
0F Inputs 0 as the future value of the loan (zero balance).
M Calculates the monthly payment.
A Displays the number of periods to group together in the
amortization schedule. Default is the current value of P/YR.
< Displays the first period of the group of periods to amortize.
< Displays the current balance remaining after the first year.
< Displays the current amount of the principal applied towards
the loan for the first year.
< Displays the amount of interest paid on the loan for the first
year. The amount of your payments applied towards interest
for the first year is about 14,000.00.
< Displays the first payment in the next period to amortize (the
second year). Note that the calculator automatically updates
Start to the next group of periods to amortize.
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Time Value of Money
35
To reset the menu items to their default values, with any item of the Amortization menu displayed press :x. With TVM
displayed, press I. At the TVM Reset prompt, press I to reset, or O to cancel.
Interest Conversion Menu
Figure 3 The Menu Map for the Interest Conversion Menu
To open the Interest Conversion menu (IConv) press :&.
Table 3-5 Interest Conversion Menu Items
Item Description
Nom.% Nominal interest rate: the stated annual interest rate
compounded as represented by P/YR, such as 18%
compounded monthly (P/YR=12 ).
Eff.% Effective annual interest rate taking compounding into
account.
C/YR Compounding periods per year. Default is 12.
Using the Interest Conversion Menu
Find the effective rate of a 36.5% nominal rate compounded daily. See Table 3-6. See Figure 3 for help with navigating
through the menu.
Table 3-6 Interest Rate Conversion Example
Keys Display Description
:& Opens the IConv menu, starting with the current value of the
nominal percentage rate.
36.
5I
Inputs 36.5 as the nominal percentage rate.
> Scrolls to compounding periods per year, C/YR. Default value
is 12.
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Time Value of Money
36
Table 3-6 Interest Rate Conversion Example
Keys Display Description
365
I
Inputs 365 as the value for the number of compounding
periods per year.
>= Scrolls to the variable for the effective rate and calculates it. A
36.5% nominal rate compounded daily equals an effective
rate of 44.03%.
Note: C/YR is the same number as P/YR in TVM calculations, since most interest calculations are based on the same number
of payments and compounding periods per year, and interest rate conversions are commonly linked to a subsequent TVM
calculation. This feature is provided for your convenience, but this means modifying one number also modifies the other. If
your TVM problem requires different values for P/YR and C/YR, refer to the section below titled, Canadian Mortgages: TVM
Canada.
The IConv menu permits you to solve for C/YR, but the result is not always a positive integer. TVM calculations, however,
require C/YR to be an integer larger than zero. If you attempt to perform a TVM calculation without a valid value for C/YR or
P/YR, an invalid P/YR error (ER: Invalid P/YR) will occur.
If you set C/YR to 0, the resulting interest conversions are calculated assuming a continuous compounding. As stated above,
0 is not a valid value for P/YR or C/YR when used in TVM calculations, and you will have to reset it to a valid value before
performing TVM calculations.
To reset the menu items to their default values, with any item of the Interest Conversion menu displayed press :x.
With IConv displayed, press I to reset, or O to cancel. To exit the menu, press O once again.
Canadian Mortgages: TVM Canada
Figure 4 The Menu Map for the P/YR Menu
In Canada, interest rates for mortgages are, by law, given as a nominal interest rate, compounded twice yearly. This means
that the compounding period for the per-period interest rate calculation differs from the compounding period used to calculate
the nominal rate.
By default, the HP 20b performs calculations assuming that the number of compounding periods always equals the number of
payments per year. You can, however, enable the TVM Canada option in the Mode menu, which enables you to select the
number of compounding periods per year. For more information, refer to Chapter 1, Basic Features.
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Time Value of Money
37
With TVM Canada enabled in the Mode menu, the following TVM features change:
1. The P/YR key,:[, now opens a menu with two items, P/YR and C/YR, in which you can specify the
number of payments and compounding periods per year. Press < or > to scroll through the menu. See
Figure 4.
2. To change the value of an item, with the item displayed, enter the number desired followed by I.
3. In the Interest Conversion menu, the C/YR item has the same value as the C/YR item in the P/YR menu, and
C/YR and no longer affects P/YR.
4. Note, however, if you now change the value of P/YR, the calculator automatically sets C/YR so it equals your
new value assigned to P/YR. This means that if you modify P/YR, you also need to modify C/YR, if P/YR and
C/YR are different values in your TVM problem.
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Time Value of Money
38
Canadian Mortgage Example
Calculate the monthly payment for a 25-year (N=300) Canadian mortgage valued at 350,000.00, if the nominal interest rate is
6.0%, compounded twice yearly (C/YR=2) with 12 payments per year (P/YR).
Table 3-7 Canadian Mortgage Example
Keys Display Description
:u Opens the Mode menu, starting with the current FIX value
(number of digits to the right of the decimal point).
>I Scrolls to TVM mode and sets mode to TVM Canada.
O Returns to default calculator screen.
:[12
I<2
I
Opens P/YR menu. Inputs 12 for P/YR and 2 for C/YR.
O300N
6Y350
00V
Exits menu and inputs values for N, I/YR, and PV.
M Calculates the monthly payment as required by the example.
To reset the menu, press :x. With TVM displayed, press I. At the TVM Reset prompt, press I to
reset, or O to cancel. To exit the menu, press O once again. With the menu set to its default settings, P/YR and C/YR
are both set to 12 payments/compounding periods per year.
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Cash Flows
39
4 Cash Flows
Figure 1 Cash Flow Diagram
In the calculator, a cash flow list is a set of numbered pairs, CF(n) and #CF(n), where n is the index of the cash flow list. Each
pair represents one or more cash flows in a cash flow diagram. As with TVM problems, it helps to sketch a cash flow diagram
as a first step in solving cash flow problems. For some examples of cash flow diagrams, see Figure 3 at the end of this
chapter.
CF(n) represents the monetary value of the cash flow; #CF(n) represents the number of consecutive occurrences of that cash
flow. By default, #CF(n) is equal to 1, as most cash flows occur only once. However, in cases where a cash flow is repeated
multiple times, using #CF(n) instead of entering the cash flow value multiple times saves calculation time and memory space
in the calculator.
To enter a cash flow list, press C to open the cash flow menu.
For each cash flow item, first enter the monetary value followed by I, then enter the number of occurrences followed
by I.
If a cash flow occurs once, you do not need to type 1I. Simply press I or < as 1 is the default.
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Cash Flows
40
To erase a cash flow list, with any cash flow displayed press :x. The number of cash flows in the list is displayed on
the bottom line, along with Cash Flow=. At this prompt, press I. You will be asked to confirm your choice. Either press
I to confirm the reset, or O to cancel.
Table 4-1 lists the keys used for cash flow problems. For a cash flow example, see Table 4-2.
Table 4-1 Cash Flow Keys
Key Description
C Opens the cash flow list.
I Inputs new values for variables in the cash flow list, the Net
Present Value (NPV) menu, and the Internal Rate of Return (IRR)
menu.
>< Scrolls up and down.
o Inserts cash flows into a cash flow list.
j Removes cash flows from a cash flow list.
RP Opens the Internal Rate of Return (IRR) and Net Present Value
(NPV) menus.
Cash Flow Example
After an initial investment of 80,000.00, cash flow (0), you expect returns over the next five years as follows:
Cash Flow
Number
Cash Flow Amount Occurrences
1 5,000.00 1
2 4,500.00 1
3 0.00 1
4 4,000.00 1
5 5,000.00 5
6 115,000.00 1
Given this information, calculate the total of the cash flows and the internal rate of return (IRR) of the investment.
Calculate net present value (NPV) and net future value (NFV), assuming an annual investment interest rate of 10.5%. See
Figure 1 for the cash flow diagram and Table 4-2 for how to enter the cash flows. The example is shown with RPN as the
active operating mode.
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Cash Flows
41
Table 4-2 Cash Flow Example
Keys Display Description
C Opens the cash flow list.
8000
0}I
Inputs -80000 as the monetary value of the initial
cash flow. Note: the sign of the cash outflow is
negative.
I Accepts 1 as the number of occurrences for CF(0).
Displays the current monetary value of CF(1).
5000I Inputs 5000 as the monetary value of CF(1).
Displays the current value,1, for the number of times
CF(1) occurs.
I Accepts 1 as the number of occurrences for CF(1).
Displays the current monetary value of CF(2).
4500I Inputs 4500 as the monetary value of CF(2).
Displays the current value, 1, for the number of times
CF(2) occurs.
I Accepts 1 as the number of occurrences for CF(2).
Displays the current monetary value of CF(3).
I Accepts 0 as the monetary value of CF(3). Displays
the current value, 1, for the number of times CF(3)
occurs.
I Accepts 1 as the number of occurrences for CF(3).
Displays the current monetary value of CF(4).
4000I Inputs 4000 as the monetary value of CF(4).
Displays the current value, 1, for the number of times
CF(4) occurs.
I Accepts 1 as the number of occurrences for CF(4).
Displays the current monetary value of CF(5).
5000I Inputs 5000 as the monetary value of CF(5).
Displays the current value, 1, for the number of times
CF(5) occurs.
5I Inputs 5 for the number of occurrences for CF(5).
Displays the current monetary value of CF(6).
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Cash Flows
42
Table 4-2 Cash Flow Example
Keys Display Description
115000
I
Inputs 115000 as the monetary value of CF(6).
Displays the current value, 1, for the number of times
CF(6) occurs.
I Accepts 1 as the number of occurrences for CF(6).
Analyzing Cash Flows
The various functions used to analyze cash flows are located in the NPV P and IRR R menus. If you press R or P
before entering cash flows, you will be redirected to the cash flow menu to enter values into the cash flow list. The menu maps
for the IRR and NPV menus are shown in Figure 2. Table 4-3 describes the items within these menus.
Figure 2 The Menu Map for the NPV and IRR Menus
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Cash Flows
43
Table 4-3 NPV and IRR Menu Items
Item Description
Inv. I% Investment or discount rate. Enter the investment rate or discount rate for the cash
flow followed by I.
Net PV Net present value. Shows the value of the cash flows at the time of the initial cash
flow, discounting the future cash flows by the value set for Inv. I%.
Net FV Net future value. Shows the value of the cash flows at the time of the last cash flow,
discounting the earlier cash flows by the value set for Inv. I%.
Net US Net uniform series. Shows the per-period payment of a regular, periodic cash flow of
equivalent present value to the cash flow list.
Payback Payback. Shows the number of periods for the investment to return value.
Discounted Payback Discounted Payback. Shows the number of periods required for the investment to
return value if the cash flows are discounted using the value set in Inv. I%.
Total The sum of all the cash flows, equivalent to NPV if Inv. I% is 0.
#CF/Yr The number of cash flows per year. The default is 1.
IRR% Internal rate of return. This is the discount rate for the cash flow that returns a Net
Present Value of 0.
See Table 4-4 for an example of the NPV and IRR functions using the cash flow example in Table 4-2.
Table 4-4 NPV and IRR Example
Keys Display Description
P Opens the NPV menu.
10.
5I
Inputs 10.5 for investment rate.
< Displays the NPV of the cash flow with the given Inv. I%.
< Displays the NFV of the cash flow with the given Inv. I%.
< Displays the Net US of the cash flow with the given interest
rate.
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Cash Flows
44
Table 4-4 NPV and IRR Example
Keys Display Description
< Displays the number of periods required for the cash flow to
repay the investment.
<< Scrolls to the total value of the cash flow.
R Displays the IRR for the cash flow.
Editing Cash Flows
In the cash flow list, you can view and modify the current monetary value of a specific cash flow, or cash flows. Press < or
> repeatedly to scroll through the list. To modify the displayed entry, type a new number and press I. For
example, to change the current monetary value of the cash flow three, CF(3), in the example in Table 4-2 from 0 to 200, with
CF(3)= displayed, press 200 followed by I.
You can also modify the number of occurrences of a cash flow in the same manner with #CF(n) displayed. Pressing
:j with a cash flow displayed erases the displayed cash flow. Pressing :o inserts a cash flow into the list
before the displayed cash flow.
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Cash Flows
45
Sample Cash Flow Diagrams
Figure 3 Sample Cash Flow Diagrams
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Bonds
46
5 Bonds
B Set.Date Mat.Date CPN% Call
Yield% Price Accrued
Actual/
Cal.360
Annual/
Semi-
annual
DWN DWN DWN
DWN
DWN DWN DWN DWN
DWN
Figure 1 The Menu Map for the Bond Menu
The Bond Menu
Before you enter the Bond menu, be sure to verify the date format is set appropriately for your problem. The default setting is
mm.ddyyyy, but it can be set for dd.mmyyyy. Bond day counts (360/365) and annual or semiannual coupon payment
schedules may be set from either the Mode menu or the Bond menu. For more information on setting the preferences in the
Mode menu, see the section titled, The Mode Menu: Setting Preferences in Chapter 1.
To open the Bond menu, press B.
Press < or > repeatedly to scroll through the items shown in Figure 1.
To change the value of the displayed item, key in a number or a date and press I. Once you have entered all known
data, press < or > repeatedly to scroll to an unknown item, and press = to calculate it.
Table 5-1 lists the items in the Bond menu.
Table 5-1 Bond Menu Items
Variable Description
Settlement Date Settlement date. Displays the current settlement date. Note: input only.
Maturity Date Maturity date or call date. The call date must coincide with a coupon date.
Displays the current maturity. Note: input only.
CPN% Coupon rate stored as an annual %. Note: input only.
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47
Table 5-1 Bond Menu Items
Variable Description
Call Call value. Default is set for a call price per 100.00 face value. A bond at maturity
has a call value of 100% of its face value. Note: input only.
Yield% Yield% to maturity or yield% to call date for given price. Note: input/output.
Price Price per 100.00 face value for a given yield. Note: input/output.
Accrued Interest accrued from the last coupon or payment date until the settlement date for
a given yield. Note: this item is Read-only.
Actual/Cal.360 Actual (365-day calendar) or Cal.360 (30-day month/360-day year calendar).
Press I to toggle between these options.
Annual/Semiannual Bond coupon (payment) frequency. Press I to toggle between these
options.
Bond Calculation Example
What price should you pay on April 28, 2010 for a 6.75% U.S. Treasury bond maturing on June 4, 2020, if you want a
yield of 4.75%? Assume the bond is calculated on a semiannual coupon payment on an actual/actual basis. See Table 5-
2. The example below is shown with RPN as the active operating mode.
Table 5-2 Bond Calculation Example
Key Display Description
B Opens the Bond menu.
> Scrolls to bond coupon (payment) frequency.
I Selects semiannual coupon payment, as required by the
example.
<4.28
2010
I
Inputs April 28, 2010 for the settlement date (mm.ddyyyy
format).
<6.04
2020
I
Inputs June 4, 2020 for the maturity date.
<6.75
I
Inputs 6.75% for the value for CPN%.
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Table 5-2 Bond Calculation Example
Key Display Description
< Displays current call value. Default is 100. Note: if Call
requires another value, key in the number followed by
I.
<4.75
I
Inputs 4.75% for Yield%.
<= Calculates the current value for Price.
:$1 Stores 115.89 in memory 1.
< Displays the current value for accrued interest.
+L1= Returns the result for total price (value of price + value
of accrued interest). The net price you should pay for the
bond is 118.58.
To reset the menu items to their default values, with any item of the Bond menu displayed press :x. With Bond
displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu.
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49
6 Date Calculation
Figure 1 The Menu Map for the Date Calculation Menu
The Date Calculation Menu
The Date Calculation menu is used to calculate the number of days between two dates, or a second date given a number of
days from an initial, or final date. To open the Date Calculation menu, press :@. Press < or > repeatedly to
scroll through the items shown in Figure 1. Before you enter dates, verify the date is set in the format required for your
problem. Date and calendar formats may be set in the Mode menu. For more information on setting the preferences in the
Mode Menu, see the section titled, The Mode Menu: Setting Preferences in Chapter 1.
To change the value of a displayed item, key in a number or a date and press I. Once you have entered all known
data, press < or > repeatedly to scroll to the unknown item and press = to calculate it.
Date Calculation Example
How many days remain in the 2010 fiscal year if today's date is June 4, 2010? Assume the fiscal year ends on October
31st, and you wish to calculate the actual number of days (Actual).
Table 6-1 Date Calculation Example
Key Display Description
:@ Opens the Date Calculation menu. Note: 2 in the right of
the display represents the day of the week. 2 represents
Tuesday.
6.04
2010
I
Inputs the starting date in the selected format.
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Table 6-1 Date Calculation Example
Key Display Description
<10.3
12010
I
Inputs the ending date in the selected format.
<= Calculates the number of actual days between the
starting and ending dates.
To reset the menu items to their default values, with any item of the Date menu displayed press :x. With Date
displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu.

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