HP 20B User Manual

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

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.

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 Date

Edition 1, v. 12 August 7, 2008

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

Contents

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

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

Contents

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

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

Contents

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

3 Data and Statistics menus 9 14 % key and Percent

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

7 Secondary function key 1 10 Math Menu 2

8 On/Off and clear entry key 1 9 Mathematical function keys 2

4 15 Amortization and Depreciation

menus

Calculation menu

1 11 Backspace key and Reset

3,8

2,6

Basic Features

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, 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.

Contents

for quick access to

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

Regulatory, and Contact Information

for instructions on replacing the batteries.

, Warranty,

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.

2. Press < repeatedly until

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,

Menu: Setting Preferences

, and

English

Accessing Menus and Menu Maps

displays on the screen.

FIX

displays on the top line of the screen.

The Mode

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.

Basic Features

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

The bottom line displays numbers you have entered, or results. Throughout this manual, this line is referred to as the

line

When no operations have been entered and no operations are pending, the bottom line of the screen displays of the calculator is referred to as the

default calculator screen

top line

. In Figure 1,

SIN

is on the top line.

0.00

bottom

. This state

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

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

FIX=2

(the number of digits displayed to the right of the decimal point).

Basic Features

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 is2. 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

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

press . instead of a numbered key, FIX=-1 is selected.

Degree or Radian Angular mode in degrees or radians for trigonometric functions.

Date: mm.ddyyyy or dd.mmyyyy

Default is Pressing I toggles between these options.

Format for dates. December 3, 2010 is entered as

dd.mmyyyy

Default is Pressing I toggles between these options.

Note that when a date is displayed, a number between1and7also displays at the right of the screen. This number indicates the day of the week corresponding to that date. Monday is1, and Sunday is7.

Note: in 360-day calendar mode (Cal.360), days of the week are displayed only if the date is valid.

Degree

mm.ddyyyy

FIX

setting. FIX settings for 10 and 11 are not available using this shortcut. If you

format. Note the (.) in both formats separating the first and second groups.

format.

FIX

setting often, use the following shortcut:

12.032010inmm.ddyyyy

format, or

3.122010

1.23 or 1,23 Selects point or comma as decimal separator.

1000.00, 1,000.00, 1000,00 or 1.000,00

Default is decimal point, Pressing I toggles between these options.

Selects thousands separator. Default is none,

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

1.23

(.); 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, Pressing I cycles through these options.

Mathematical Calculations

Table 1-1 Mode Menu Settings

Setting (top line) Description

Basic Features

English, Français, Deutch, or Español

Actual or Cal.360

Annual or Semiannual Bond type.

TVM Standard or TVM Canada

Language setting for the messages displayed on the screen. Default is

Pressing I cycles through these options.

Calendar options for bonds and date calculations. Default is

Pressing I toggles between these options.

Default is Pressing I toggles between these options.

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,

Pressing I toggles between these options.

English

Actual

Annual

Changing the Calculation Mode

Canadian Mortgages: TVM Canada

in Chapter 3.

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

<<<<

Opens the Mode menu, starting with first setting option,

FIX

, the number of digits displayed to the right

of the decimal point.

Scrolls to the current setting for the calculation mode,

Chain

(Press five times)

(Press two times)

Selects

RPN

Exits the Mode menu and returns you to the default calculator screen.

RPN

as the active setting. Note the small

annunciator to the right.

Basic Features

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.

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 the key is highlighted, while the7is 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.

SIN

portion of

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.

Figure 3 Annunciator Symbols in the Screen Display

Basic Features

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 of3.

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 :&.

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.

Nom %=

displays on the top line, and the

Figure 4

Basic Features

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.

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 (

choice. At the 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.

Del. All?,Del. Data?

Cash Flow

, and

TVM

), statistics (

Del. CF?

displays on the top line. Press < or > repeatedly to scroll to a

Stats

), or all values (

prompts, press I again to confirm the reset, or O to cancel.

Bond

All

) items, you will be prompted to confirm your

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 Oto 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 (

Memory

memory 1 ( When a memory item is displayed, you can enter a new number and modify the value of the memory by pressing I.

. To enter the menu, press :t. Press < or > repeatedly to scroll through the items starting with

Mem 1

Mem 1-9

) and 0 (

Mem 0),Cash Flow

, Statistics (

Stats

), and

Basic Features

For more information about storing and recalling numbers, refer to the section titled, 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 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?orDel.CF?

Memory

refers to the number of remaining memory slots. When the cash flow or statistics items are

prompts, press I to confirm, or O to cancel.

Storing and Recalling Numbers

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-keycombination, 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 (Figure 7) displays as shown in Figure 5.

Figure 5

The large (=) annunciator shows that the value assigned to displayed by pressing 1+2= for example,

annunciator is now turned off, indicating the3is not the value assigned to

At this point, to return to the display of the

Fixed

menu item shown in Figure 5, press O.

Fixedis120,000

Fixed

is still selected as the current item, but the large (=)

Figure 6

. If you perform a calculation with this item

Fixed

(see Figure 6).

Fixed

item in the Break-even menu

Some menus have sub-menus. If an item represents a sub-menu, pressing I with that menu item displayed opens the sub-menu.

Basic Features

In this manual, diagrams called through the menus used for that section. For an example of a menu map, see Figure 7.

There are four types of menu items:

1. Read/write. Read/write menu items, such as because when they are selected, both the

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 (

Menu Maps

Figure 7 The Menu Map for the Break-even Menu

are included at the beginning of each section to assist you with navigating

Fixed

in the Break-even menu shown above, are easily recognizable,

INPUT

and small (=) annunciators are lit. When lit, these annunciators

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 ( similar to read/write items in that the

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 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).

INPUT

annunciator is lit when these items are selected, indicating that entering a

Degree/Radian

Inv. I%

option in the Mode menu, the items of the Reset menu, and

) in the Net Present Value (NPV) menu, are

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

Mathematical Calculations

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

notation, first enter the mantissa ( The exponent must have a value between -499 and +499.

1.23 )

and then press :w and enter the number (

127 )

representing the exponent.

127

1023.1 

in scientific

Figure 1 Scientific Notation in FIX=2 Mode

Mathematical Calculations





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= returns9. 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

multiplication operation. See Table 2-1 below.

Table 2-1 Simple Arithmetic Calculations in Chain Mode

Keys Display Description

321  , you may enter the problem as written from left to right, with parentheses to prioritize the

Sets operational priority, inputs numbers, and multiplies 2 and 3.

(2*3) =

Adds 1 to 6 and returns the final result.

7.00

on the bottom line as

Algebraic Mode

To set the calculator in Algebraic mode, refer to the section titled, 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 of

9.00.

The Mode Menu: Setting Preferences

7.00

. In Chain mode, the same key presses return a result

in Chapter 1

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

For example, key in 1+ 2 x 5 nPr22in Algebraic mode by pressing:

1+2*5:b2:m=. The result is 241.

Mathematical Calculations

Note: the calculator is limited to 12 pending operations. An operation is the result of an operation of higher priority.

pending

when it is waiting for the input of a number or

Reverse Polish Notation (RPN) Mode

To set the calculator in RPN mode, refer to the section titled, 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, 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 Mode Menu: Setting Preferences

in Chapter 1.In RPN

3.00

, is calculated

The RPN Stack

RPN works by placing numbers in storage registers called the are stacked on top of one another. See Figure 3.

Stack Level 4

Stack Level 3

Stack Level 2 41

Stack Level 1

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,

stack

. The RPN stack has four levels numbered 1-4. The levels

-15

, is pushed out and is lost.

Mathematical Calculations







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

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:

123.5623.1

 

123.56

See Table 2-2 for an example using the

Table 2-2 Last Number

Keys Display Description

:u3I

<<<<<

last number

function.

Sets

FIX=

Selects

to 3.000

RPN

as the operating mode.

II O1c23

Inputs 1.23 and 56.123

I56c1 23

Table 2-2 Last Number





Keys Display Description

Mathematical Calculations

+:d/

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:

Adds 1.23 and 56.123, then divides the sum by the last number, 56.123. Returns results in the selected display format.

6543 

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

5I6+

Inputs the numbers and the operation in the second set of parentheses. Intermediate results are displayed. Note the (+) annunciator.

Mathematical Calculations

Table 2-3 Simple Arithmetic Calculations in RPN Mode

Keys Display Description RPN Stack

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

on the stack, making Levels 1 and 2 equal. See Figure 5.

Previous Value

Finishes the operation and displays the results.

Figure 5 Duplicating a Number on the Stack

In RPN, the parentheses keys () manipulate the stack. Pressing ( performs a causes the stack to 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.

roll

towards the bottom of the stack, during which the number in Level 2 moves down to Level 1, the

roll down

of the stack. A roll down

Mathematical Calculations

Figure 6 The RPN Stack and the Roll Down Operation

Pressing ) performs a 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.

Note: when no menu is selected, the < key performs the same function as the ( key. The > key performs the inverse operation called,

swap

. A swap operation exchanges the numbers on Levels 1 and 2 of the stack. The ) key has

Figure 7 The RPN Stack and the Swap Operation

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.

Mathematical Calculations

For example, to calculate6, press 6:n. The result of 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

more information on the Mode menu and calculator settings, refer to the section titled, in Chapter 1

Table 2-4 lists one-number functions along with their corresponding keys.

) or radians (

Table 2-4 Shifted Function Mathematical Operations

Keys Description

:p :q :r :k

Radians

). You will need to change the setting if the active mode is not what your problem requires. For

Calculates sine.

Calculates cosine.

Calculates tangent.

Calculates natural log.

2.45

is calculated immediately and displayed on the

The Mode Menu: Setting Preferences

:l :m :n :f :g

:h :i :d

Calculates natural exponent to the power ofx.

Calculates square ofx.

Calculates square root.

Executes the

Calculates factorial ofx(where -253 <x≤ 253). The Gamma function is used to calculate x! for non-integers or negative numbers.

Calculatesyto thexpower.

Calculates the reciprocal.

In Chain or Algebraic mode, recalls the result of the last operation. In RPN mode, returns the content of the

Roundsxinternally to the number specified by the display format.

The Math :s Menu

Random

Last Number

function. Returns a random number in the range 0 < x <1.

variable.

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.

Mathematical Calculations

Figure 8 The Menu Map for the Math Menu

Press < to scroll through the menu items, starting with

Trigonometry.

The

Trigonometry, Hyperbolic,

and

Probability

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.

items

Table 2-5 Math Menu Example

Keys Display Description

Mathematical Calculations

.5I

Enters 0.5 and opens the Math menu starting with

Trigonometry

I or =

In the Math menu,PIdoes not menu to execute a function, and continue calculating with your original operation without losing your work.

perform

calculations; it enters

Selects the Note the value for Sin-1is calculated immediately and

displayed.

Validates the result.

PI for

calculations. You may start an operation, use the Math

Trigonometry

sub-menu and scrolls to Sin-1.

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 Chi2require (N), the number of degrees of freedom, and F-Distribution requires (N1) and (N2), two degrees of freedom.

To perform Student and Chi2operations 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 =.

Mathematical Calculations

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

Enters 10 degrees of freedom and the number for which probability is to be calculated. Opens theMath menu.

8I :s

<<I

Selects the

<<<< I or =

Table 2-7 Inverse Probability Example

Keys Display Description

10I

Validates the result.

Enters 10 degrees of freedom and the probability. Opens the Math menu.

0.37

Probability

menu item and scrolls to Chi2.

12I :s

<<I

Selects the

Probability

menu item. Scrolls to Chi

<<<< <

I or =

Validates the result.

Two-Number Functions

Apart from +-*/, the three additional two-number functions accessible on the keyboard are:

 Y

2-1

 nCr  nPr

is the power function,

number of permutations ofnitems takenrat a time.

Combination=

 

nCr

stands for the number of combinations ofnitems takenrat a time, and

rnr



Mathematical Calculations

nPr

stands for the

Permutation=

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.

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.

 



!!rn

Figure 9

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 store15in 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:$2 to store5in memory 2. To add12to the value of memory 2, press 12:$+2. Later on, during a calculation, you can

Mathematical Calculations

press L2 to recall memory 2. Note how the new current value stored in memory 2 is17, (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 (

memory by selecting the memory and typing a number followed by the t key.

Mem 1

). Note that in the Memory menu, you can change the value of any

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

when you need to insert the contents of a menu item into an algebraic operation.

Nom.%

displayed, pressing 2*L= recalls the nominal rate. This feature is useful

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

menu. The default setting is two digits to the right of the decimal point. For more information, refer to the section titled,

Mode Menu: Setting Preferences

Note: the

FIX

setting only affects the display; it does not affect the actual numbers.

in Chapter 1

FIX

item in the Mode

The

Percentages

In Algebraic or Chain modes, pressing % divides a number by 100. For example, pressing 25% returns

0.25.

Mathematical Calculations

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 of50.

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 of55. In RPN mode, the % key calculatesx% of the number on Level 2 of the stack, whenxis 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 subtractx% from the number.

For example, 200I25% returns50, but returns

150

, or 200-25%.

200

is still on Level 2 of the stack, and pressing -

Time Value of Money

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.

Time Value of Money

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,

Mortgages: TVM Canada

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.

, or Chapter 4,

Cash Flows

Canadian

Time Value of Money

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 ^ Y V

M [ F

? ]

Stores or calculates the number of payments or compounding periods.

Multiplies a value by the number of payments per year and stores as N

Stores or calculates the nominal, annual interest rate.

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.

Stores or calculates the amount of each periodic payment.

Stores the number of payments or compounding periods per year.

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:[

360

Inputs12as the number of payments per year, or compounding periods per year.

Inputs

360

Inputs

6.5

6.5%

Y 1400

Inputs the present value of the loan at the time of the first payment. This value is positive (+); it is money you receive.

00V 0F

Inputs0as the future value of the loan (the remaining balance).

as the number of payments over 30 years.

as the nominal interest rate percentage per year.

Table 3-2 TVM Example

Keys Display Description

Time Value of Money

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 pressO tocancel.

Returns the monthly payment. This result is negative (-); it is money you pay out.

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

Nb Period Number of periods to group together in the amortization calculation. The default value is

Start Period on which to start amortization. Default is1. If you want to amortize for the second

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.

Opens the Amortization menu

the number of payments per year defined by the [ key.

year with 12 payments per year, enter13(the second year starts at the 13thpayment with 12 payments per year).

Time Value of Money

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

Inputs

12 as

12:

the number of payments per year.

[

Inputs

360

30:

payments for the 30-year loan.

(30 times 12 payments per year) as the number of

^ 10Y

1400 00V

Inputs10as the interest rate percentage per year.

Inputs the value of the loan at the time of the first payment.

Inputs0as the future value of the loan (zero balance).

Calculates the monthly payment.

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.

Time Value of Money

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 compounded monthly (

Eff.% Effective annual interest rate taking compounding into

account.

C/YR Compounding periods per year. Default is12.

P/YR=12

P/YR

, such as 18%

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, is12.

C/YR

. Default value

Table 3-6 Interest Rate Conversion Example

Keys Display Description

Time Value of Money

365 I

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,

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 to0, the resulting interest conversions are calculated assuming a continuous compounding. As stated above,

performing TVM calculations.

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

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%.

Canadian Mortgages: TVM

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 number of compounding periods per year. For more information, refer to Chapter 1,

TVM Canada

option in the Mode menu, which enables you to select the

Basic Features

With

TVM Canada

Time Value of Money

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.

Time Value of Money

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

:[12 I<2 I

O300N 6Y350 00V

To reset the menu, press :x. With

Opens the Mode menu, starting with the current (number of digits to the right of the decimal point).

Scrolls to TVM mode and sets mode to

Returns to default calculator screen.

Opens P/YR menu. Inputs 12 for P/YR and 2 for C/YR.

Exits menu and inputs values for N, I/YR, and PV.

Calculates the monthly payment as required by the example.

TVM

displayed, press I. At the

TVM Reset

FIX

value

TVM Canada

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.

4 Cash Flows

Cash Flows

Figure 1 Cash Flow Diagram

In the calculator, a cash flow list is a set of numbered pairs, 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; flow. By default, multiple times, using 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 < as1is the default.

#CF(n)

is equal to1, as most cash flows occur only once. However, in cases where a cash flow is repeated

instead of entering the cash flow value multiple times saves calculation time and memory space

#CF(n)

CF(n)

and

#CF(n)

, wherenis the index of the cash flow list. Each

represents the number of consecutive occurrences of that cash

Cash Flows

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 I

>< o j RP

Opens the cash flow list.

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.

Inserts cash flows into a cash flow list.

Removes cash flows from a cash flow list.

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

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.

Cash Flow Amount Occurrences

Table 4-2 Cash Flow Example

Keys Display Description

Cash Flows

8000 0}I

5000I

4500I

Opens the cash flow list.

Inputs

-80000

as the monetary value of the initial cash flow. Note: the sign of the cash outflow is negative.

Accepts1as the number of occurrences for CF(0). Displays the current monetary value of CF(1).

Inputs

5000

as the monetary value of CF(1). Displays the current value,1, for the number of times CF(1) occurs.

Accepts1as the number of occurrences for CF(1). Displays the current monetary value of CF(2).

Inputs

4500

as the monetary value of CF(2). Displays the current value,1, for the number of times CF(2) occurs.

Accepts1as the number of occurrences for CF(2). Displays the current monetary value of CF(3).

4000I

5000I

Accepts0as the monetary value of CF(3). Displays the current value,1, for the number of times CF(3) occurs.

Accepts1as the number of occurrences for CF(3). Displays the current monetary value of CF(4).

Inputs

4000

as the monetary value of CF(4). Displays the current value,1, for the number of times CF(4) occurs.

Accepts1as the number of occurrences for CF(4). Displays the current monetary value of CF(5).

Inputs

5000

as the monetary value of CF(5). Displays the current value,1, for the number of times CF(5) occurs.

Inputs5for the number of occurrences for CF(5). Displays the current monetary value of CF(6).

Table 4-2 Cash Flow Example

Keys Display Description

Inputs

115000 I

115000

Displays the current value,1, for the number of times CF(6) occurs.

Cash Flows

as the monetary value of CF(6).

Accepts1as 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 orP 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

Cash Flows

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

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

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% is0.

#CF/Yr The number of cash flows per year. The default is1.

IRR% Internal rate of return. This is the discount rate for the cash flow that returns a Net

Present Value of0.

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

10.

Opens the NPV menu.

Inputs

10.5

for investment rate.

5I <

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.

Table 4-4 NPV and IRR Example

Keys Display Description

Cash Flows

Displays the number of periods required for the cash flow to repay the investment.

Scrolls to the totalvalue of the cash flow.

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)=

You can also modify the number of occurrences of a cash flow in the same manner with

displayed, press 200 followed by I.

CF(3)

, in the example in Table 4-2 from0to

#CF(n)

displayed. Pressing

200

, with

: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.

Sample Cash Flow Diagrams

Cash Flows

Figure 3 Sample Cash Flow Diagrams

5 Bonds

Bonds

DWN

Set.Date Mat.Date CPN% Call

Yield%

DWN DWN DWN

DWN

Price

Figure 1 The Menu Map for the Bond Menu

DWN

Accrued

DWN

Actual/

Cal.360

DWN

Annual/

Semi-

annual

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

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,

To open the Bond menu, press B.

, but it can be set for

dd.mmyyyy

The Mode Menu: Setting Preferences

. Bond day counts (360/365) and annual or semiannual coupon payment

in Chapter 1

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.

Bonds

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

<4.28

Opens the Bond menu.

Scrolls to bond coupon (payment) frequency.

Selects semiannual coupon payment, as required by the example.

Inputs April 28, 2010 for the settlement date ( format).

mm.ddyyyy

2010 I

<6.04 2020 I

<6.75 I

Inputs June 4, 2020 for the maturity date.

Inputs

6.75%

for the value for

CPN%

Table 5-2 Bond Calculation Example

Key Display Description

Bonds

Displays current call value. Default is requires another value, key in the number followed by

100

. Note: if

Inputs

4.75%

for

Yield%

<4.75

I <=

:$1

+L1=

To reset the menu items to their default values, with any item of the Bond menu displayed press :x. With

Calculates the current value for

Stores

115.89

in memory 1.

Displays the current value for accrued interest.

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.

Price

Call

Bond

displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu.

Date Calculation

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,

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.

The Mode Menu: Setting Preferences

in Chapter 1

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

6.04

Opens the Date Calculation menu. Note:2in the right of the display represents the day of the week.2represents Tuesday.

Inputs the starting date in the selected format.

2010 I

Table 6-1 Date Calculation Example

Key Display Description

Date Calculation

<10.3

Inputs the ending date in the selected format.

12010 I

To reset the menu items to their default values, with any item of the Date menu displayed press :x. With displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu.

Calculates the number of actual days between the starting and ending dates.

Date

Break-even

7 Break-even

Figure 1 The Menu Map for the Break-even Menu

The Break-even Menu

To open the Break-even menu, press :!. To change the value of the displayed item, key in a number and press

I. Once you have entered all known data, press < or > repeatedly to scroll to the unknown item and press = to calculate it.

The break-even function allows you to study problems involving a profit, when a quantity of items, with a cost to manufacture and a fixed price to develop and market, is sold at a given price. See Figure 1.

Break-even Example

The sale price of an item is 300.00, the cost is 250.00, and the fixed cost is 150,000.00. How many units would have to be sold to make a profit of 10,000.00?

Table 7-1 Break-even Example

Keys Display Description

1500

Opens the Break-even menu starting with the current value for fixed costs.

Inputs

150,000.00

for fixed cost

00I <250

for variable cost per unit

Inputs

250.00

I <300

for price

Inputs

300.00

I <1000

00I

Inputs

10,000.00

for profit.

Table 7-1 Break-even Example

Keys Display Description

Break-even

To reset the menu items to their default values, with any item of the Break-even menu displayed press :x. With

BrkEven

displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu.

Calculates the current value for the unknown item. 3200 units would have to be sold to return a profit of 10,000.00.

8 Business Problems

Business Problems

Figure 1 The Menu Map for the Percent Calculation (%calc) Menu

The Percent Calculation Menu

Press :# to open the menu. There are four items in this menu: markup as a percentage of cost ( as a percentage of price (

items allow you to access sub-menus. Press < or > repeatedly to scroll to the desired sub-menu, then press I to open it. See Figure 1.

To change the value of a displayed item, key in a number and press I. Once you have entered all known data, press

Mkup. %P),

part as a percentage of total (

Part%Tot.

), and percent change (

< or > repeatedly to scroll to the unknown item and press = to calculate it.

To return to the percent calculation menu, from anywhere within the menu or sub-menus, press :#. To exit the menu, press O

Mkup. %C

%Change

), markup

). These

Business Problems

Note: for business problems, margin is based on price; markup is based on cost. The examples below are shown with RPN as the active operating mode.

Percent Calculation Examples

See Tables 8-1 through 8-4 for examples of calculations in the %calc menu.

1. Find the markup on an item if the cost price is $15.00 and the selling price is $22.00. See Table 8-1.

Table 8-1 Markup Example

Keys Display Description

15I

<22I

2. Find the percent change between 20 and 35 with no compounding.

Table 8-2 Percent Change Example

Keys Display Description

Opens the %calc menu

Opens the

Inputs15for

Inputs22for

Calculates the value of

Opens the %calc menu

Mkup.%C

Cost

Price

sub-menu.

Mkup.%C

for the given data.

<<<

20I

<35I

Scrolls to

Opens the

Inputs20for

Inputs35for

Calculates the current value of data.

%Change

Old

New

sub-menu.

%Change

for the given

Business Problems

Note: although the example in Table 8-2 calls for no compounding, you may specify the number of compounding periods used in calculations with the

Nb Period

item in the

%Change

sub-menu.

Nb Period

is the number of compounding periods used in

calculations between the old value and new value. The default is1, but to change the setting, key in a number with displayed, followed by I.

After calculating the example above with no compounding, say, for example, you wish to calculate the percent change over six compounding periods:

Table 8-3 Percent Change Example with Compounding

Keys Display Description

<6I

3. What is 30% of 80?

Table 8-4 Part % of Total Example

The current value of

Inputs 6 for the number of compounding periods.

Calculates the percent change between the old value and the new value over six compounding periods.

%Change

for the given data.

Nb Period

Keys Display Description

80I

<30I

To reset the menu items to their default values, with any item of the %calc menu displayed press :x. Press > or

< to scroll until

%Calc

displays and press Ito reset the menu, or O to cancel. Press O to exit the menu.

Opens the %calc menu

Scrolls to the

Opens the

Inputs80for

Inputs30for

Calculates the value of

Part %Total

Part as %Total

Total

Part.

menu item.

sub-menu.

Part%Total

for the given data.

9 Depreciation

Depreciation

Figure 1 The Menu Map for the Depreciation Menu

The Depreciation Menu

Press :\ to open the Depreciation menu. To select a depreciation method, press I repeatedly. See Figure 1. Input the values required for the calculation:

 Asset life  Starting date or month of the deprecation  Cost and salvage values  Declining balance factor (DecBal and DBXover only)  The first year for which you want to view the depreciation schedule

Scroll through the items of the sub-menu for the selected depreciation method by pressing < or > repeatedly. To change the value of the displayed item, key in a number and press I. For the actual date, depending on the type of depreciation selected. Press < repeatedly to view the depreciation schedule.

Start

item, enter either a number or an

Depreciation

Note: pressing < on the last item of a sub-menu returns you to the Year item, not to the top of the sub-menu (see Figure

1). By scrolling through all the items of a sub-menu, you incrementally advance the Year item. This allows you to see the

depreciation schedule for the next year without additional entries.

Brief descriptions of the methods used to calculate depreciation are provided in Table 9-1. Table 9-2 describes the items found in the depreciation sub-menus. For an example calculating depreciation using the straight-line method, see Table 9-3.

Table 9-1 Depreciation Methods

Depreciation Method Description

Sline

SOYD

DecBal

DBXover

French SL

Amort F

Straight line is a method of calculating depreciation presuming an asset loses a certain percentage of its value annually at an amount evenly distributed throughout its useful life.

Sum-of-the-years' digits is an accelerated depreciation method. In SOYD, the depreciation in yearYis (Life-Y+1)/SOY/100% of the asset, where

the sum-of-the-years for the asset, or, for an asset with a 5-year life, 5+4+3+2+1=15.

Declining balance is an accelerated depreciation method that presumes an asset will lose the majority of its value during the first few years of its useful life.

Declining balance crossover is an accelerated depreciation method that presumes an asset will lose the majority of its value in the first few years of its useful life, but that it will revert to a consistent depreciation during the latter part of its life, which is then calculated using the straight line method.

Straight line French. This method of depreciation is similar to the Straight line method, except an actual calendar date in the selected format is entered in for when the asset was first placed into service.

French amortization. This method is an accelerated depreciation method with a crossover to the French Straight Line method.

Start

SOY

to indicate

Table 9-2 Depreciation Menu Items

Item Description

Life The expected useful life of the asset in years.

Start

Cost The depreciable cost of the asset at acquisition.

Start

refers to the date or month in which the asset is first placed into service. Depending on the type of depreciation, this can be the month (1-12), or, in the case of French Straight-line and Amort F, the actual date in the selected format. Note: for non-French depreciations, if the asset were placed into service in the middle of March, for example, you would enter

3.5

for

Start

Depreciation

Table 9-2 Depreciation Menu Items

Item Description

Salvage The salvage value of the asset at the end of its useful life.

Factor The declining balance factor as a percentage. This is used for

declining balance and declining balance crossover methods only.

Year Year for which you want to calculate the depreciation.

Depreciation Depreciation in the given year.

R.Book Value Remaining book value at the end of the given year.

R.Depreciable Value Remaining depreciable value at the end of the given year.

Depreciation Example

A metalworking machine, purchased for 10,000.00, is to be depreciated over five years. Its salvage value is estimated at

500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first two years of the machine's life. See Table 9-3.

Table 9-3 Straight Line Depreciation Example

Key Display Description

<5I

<1000

Opens the Depreciation menu starting with the straight line method.

Inputs5for the useful life.

Displays the current value of default value. For this example, this value remains unchanged, since the depreciation of the machine starts January 1st(

Inputs

10,000.00

Inputs

<500

500.00

I <

Year for which to calculate the depreciation. the default value. To calculate for a year other than1,

Start.1

1.00

for the cost of the item

for the salvage value of the item

(January) is the

Year 1

type a number and press I.

Depreciation of the asset in year one.

Table 9-3 Straight Line Depreciation Example

Key Display Description

Depreciation

To reset the menu items to their default values, with any item of the Depreciation menu displayed press :x. With

Depreciation

displayed, press I to reset the menu, or O to cancel. Press O to exit the menu.

Remaining book value after year one.

Remaining depreciable value after year one.

The next year for which to calculate the depreciation. To calculate for a year other than2, type a number and

press I.

Depreciation of the asset in year two.

Remaining book value after year two.

Remaining depreciable value after year two.

10 Statistical Operations

Statistical Operations

Figure 1 The Menu Maps for the Data and Statistics Menus

Statistical Operations

The Data and Stats Menus

Statistics analysis functions are located in the Data and Statistics menus accessible with the :yand:z keys.

See Figure 1 for assistance with navigating through the menus.

Press :y to open the Data menu. In this menu, enter a list ofxvalues for one-variable statistics, a list of pairs, (x, F) for weighted, one-variable statistics, a list of numbersxfor one-variable statistics, or a list of pairs, (x, y) for two-variable

statistics. To enter data, key in a number and press I. Press :z to analyze the data. If you attempt to open the Statistics (Stats) menu before entering data, you will be

redirected to the Data menu. When opened, the Stats menu displays repeatedly to select the type of statistical operations desired, two-variable, ( weighted (

After selecting the type of statistical operation you want, select a sub-menu by pressing < or >, and press I to open it. Once in a sub-menu, press < or > repeatedly to view the results. To return from the sub-menu to the Statistics menu, press :z.

Note: in one-variable modes, there are no items foryand the Pressing I with the

types of regression lines. See Figure 1. To select a specific type of regression line in the

1 Weight

Predictions

sub-menu displayed opens a sub-menu, in which you can choose among six different

2 Vars

for two-variable statistics. Press I

2 Vars),

sub-menu is not available.

one-variable,

Predictions

(1 Var

), or one-variable

sub-menu, press

I to cycle through the options. Note: if you press =, the calculator automatically selects the curve that is the best

fit for your data. Once you select a regression line, press < to see the regression line parameters and perform predictions.

Table 10-1 The Statistics Menu Items

Menu Item Description

Statistical Operations

Nb Item

Mean

X Std. Dev Standard deviation for X: a measure of how dispersed the x data values are

Y Std. Dev Standard deviation for Y: a measure of how dispersed the y data values are

X Population Dev Population Standard deviation for X: a measure of how dispersed the X data

Y Population Dev Population Standard deviation for Y: a measure of how dispersed the y data

S.E.SamP.X Sample error for X: a measure of how dispersed the X data values are about

Number of items.

Average of X values.

Average of Y values.

about the mean.

values are about the mean, assuming the data constitutes a complete set of data.

the mean sample standard deviation, assuming the data is a sampling of a larger, more complete data set.

S.E.SamP.Y Sample error for Y: a measure of how dispersed the Y data values are about

the mean sample standard deviation, assuming the data is a sampling of a larger, more complete data set.

Pred X Predicts X for a given hypothetical value of Y, based upon the model calculated

to fit the data.

Pred Y Predicts Y for a given hypothetical value of X, based upon the model calculated

to fit the data.

a Theacoefficient for the chosen regression model, which is the slope for a linear

model.

b Thebcoefficient for the chosen regression model, which is the y-intercept for a

linear model.

Correlation The correlation coefficient for the given (x, y) data. The correlation coefficient is

a number in the range -1 through 1 that measures how closely the calculated line fits the data.

Covariance A measure of how much two variables change in relation to one another.

Sigma X The sum of the x values.

Table 10-1 The Statistics Menu Items

Menu Item Description

Sigma Y The sum of the y values.

Statistical Operations

Sigma X

Sigma Y

Sigma XY The sum of the products of the x and y values.

The sum of the squares of the x values.

The sum of the squares for the y values.

Statistics Example

Sales for the last five months are represented by the pairs of values shown below, with the month number as x, and the sales values as y. Enter these into the Data menu. Using the Statistics menu for Predictions, predict sales for month seven. What is the linear regression line? What is the sum of all the y values? See Tables 10-2 and 10-3.

Table 10-2 Months and Sales

Month Sales Values

1 150

2 165

3 160

4 175

5 170

Table 10-3 Statistics Example

Keys Display Description

1I1

Opens Data menu.

Inputs values for X(1) and Y(1).

50I 2I1

Inputs values for X(2) and Y(2).

65I 3I1

Inputs values for X(3) and Y(3).

60I 4I1

Inputs values for X(4) and Y(4).

75I

Table 10-3 Statistics Example

Keys Display Description

Statistical Operations

5I1 70I

:z<< I

<7I

Inputs values for X(5) and Y(5).

Opens Stats menu.

Opens Descriptive sub-menu.

Displays averagey.

Opens Predictions sub-menu. Note: this example performs calculations based on a linear

(a*X+b)regression line.

Inputs7as the

Calculates

Prediction X

Prediction Y

value (month 7).

value (sales at month 7).

:z<<

Displays value fora: the slope of the regression line.

Displays current value forb: the y-intercept of the regression line.

Displays value for

Opens

Sums

values (Sigma Y).

Correlation

sub-menu. Displays the sum of all y

<I<

To reset the menu items to their default values, with any item of the Data or Statistics menus displayed press :x. At the prompt,

Stats

, press I. Confirm your choice by pressing I.

11 Errors

Error Messages and Calculator Status

Table 11-1 Error Messages

Error Message Status

ER: Underflow The calculation generated an underflow (result of 0). ER: x/0 Division by zero. ER: 0/0 Zero divided by zero.

Errors

ER: ∞*0

ER: ∞/∞

ER: √/ (x<0) ER: LN (0) LN of 0. ER: LN (x<0) LN of a negative number. ER: ATrig(|x|>1) ASIN or ACOS of a number for which the absolute

ER: 1^∞

ER: (x<0)^∞

ER: ∞^0

ER: ∞^(Frac) ER: (x<0)^(Frac) Attempted calculation of (-x) ^ (non-integer y). ER: Out of Bounds Input out of bounds.

Infinite multiplied by zero.

Infinite divided by infinite.

Square root of a negative number.

value is > 1. Attempted calculation of 1^+/-Infinite.

Attempted calculation of the infinite power of a negative number.

Attempted calculation of +/-∞^0.

Attempted calculation of +/-∞^ (non-integer y).

ER: Invalid P/YR Returned by TVM functions if payments per year are

invalid (<0 or non-integer). ER: Invalid Input Returned if arguments are invalid for any reason. ER: Invalid I% Returned by finance functions if I is ≤ 100%. ER: No Solution Returned when there is no solution to the problem. ER: Many or No Solutions Returned if there is no solution, or more than one

solution to the problem.

Errors

Table 11-1 Error Messages Error Message Status

ER: Many Solutions Returned when there are many solutions to the

problem. ER: Invalid N Returned by TVM/Amort if N is invalid. ER: User Abort Returned by long functions if user stops the calculation

prior to completion.

ER: ∞ Result ER: Insufficient Data Returned by statistics functions if there is insufficient

ER: No Payback Returned by payback function if there is no payback on

ER: Unique solution to IRR Not Found Returned if IRR tries to calculate a solution but cannot

ER: Stack Stack overflow when performing calculations with more

ER: Parenthesis: An error linked to use of parentheses: unmatched, too

ER: Insufficient Memory Insufficient memory to complete the operation. ER: No Solution Found No solution found.

Returned if the result is infinite.

data for analysis.

this problem.

find it. User should supply a new guess…

than 12 pending operations.

many, etc.

Warranty, Regulatory, and Contact Information

12 Warranty, Regulatory, and Contact Information

Replacing the Batteries

Use only fresh batteries. Do not use rechargeable batteries. The calculator takes two, 3-volt CR2032 lithium batteries. To install a new battery:

1. With the calculator turned off, slide the back cover off.

2. Remove one of the old batteries and replace it with a new battery with the positive polarity symbol facing outward.

3. Remove the second battery and replace it with a new battery with the positive polarity symbol facing outward.

4. Replace the back cover.

Warning! There is danger of explosion if the battery is incorrectly replaced. Replace only with the same or equivalent type recommended by the manufacturer. Dispose of used batteries according to the manufacturer's instructions. Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals.

HP Limited Hardware Warranty and Customer Care

This HP Limited Warranty gives you, the end-user customer, express limited warranty rights from HP, the manufacturer. Please refer to HP’s Web site for an extensive description of your limited warranty entitlements. In addition, you may also have other legal rights under applicable local law or special written agreement with HP.

Limited Hardware Warranty Period Duration: 12 months total (may vary by region, please visit www.hp.com/support for latest information) General Terms HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and

workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. Replacement products may be either new or like-new.

HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used. If HP receives notice of such defects during the warranty period, HP will replace software media which does not execute its programming instructions due to such defects.

HP does not warrant that the operation of HP products will be uninterrupted or error free. If HP is unable, within a reasonable time, to repair or replace any product to a condition as warranted, you will be entitled to a refund of the purchase price upon prompt return of the product with proof of purchase.

HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use. Warranty does not apply to defects resulting from (a) improper or inadequate maintenance or calibration, (b) software, interfacing, parts or

supplies not supplied byHP, (c) unauthorized modification or misuse, (d) operation outside of the published environmental specifications for the product, or (e) improper site preparation or maintenance.

HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY, SATISFACTORY QUALITY, OR FITNESS FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH ABOVE. Some countries, states or provinces do not allow limitations on the duration of an implied warranty, so the above limitation or exclusion might not apply to you. This warranty gives you specific legal rights and you might also have other rights that varyfrom country to country, state to state, or province to province.

TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR OTHERWISE. Some countries, States or provinces do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you.

The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. HP shall not be liable for technical or editorial errors or omissions contained herein.

FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU.

Warranty, Regulatory, and Contact Information

Customer Care

In addition to the one year hardware warranty your HP calculator also comes with one year of technical support. If you need assistance, HP customer care can be reached by either email or telephone. Before calling please locate the call center nearest you from the list below. Have your proof of purchase and calculator serial number ready when you call.

Telephone numbers are subject to change, and local and national telephone rates may apply. For more support information, please visit the web at: www.hp.com/support.

Contact Information

Table 12-1 Contact Information

Country/Region Contact

Africa (English) www.hp.com/support

Afrique (français) www.hp.com/support

Argentina 0-800-555-5000

Australia 1300-551-664

Belgique (français) 02 620 00 85

Belgium (English) 02 620 00 86

Bolivia 800-100-193

Brasil 0-800-709-7751

Canada 800-HP-INVENT

Caribbean 1-800-711-2884

Česká republikaik 296 335 612

Chile 800-360-999

China 中国

Colombia 01-8000-51-4746-8368

Costa Rica 0-800-011-0524

Denmark 82 33 28 44

010-68002397

Deutschland 069 9530 7103

Ecuador 800-711-2884

El Salvador 800-6160

España 913753382

France 01 4993 9006

Table 12-1 Contact Information

Country/Region Contact

Greece Ελλάδα 210 969 6421

Guatemala 1-800-999-5105

Honduras 800-711-2884

Warranty, Regulatory, and Contact Information

Hong Kong 香港特別行政區

India www.hp.com/support/india

Indonesia +65 6100 6682

Ireland 01 605 0356

Italia 02 754 19 782

Japan 日本

Korea 한국

Magyarország www.hp.com/support

Malaysia +65 6100 6682

México 01-800-474-68368

Middle East International www.hp.com/support

Netherland 020 654 5301

852 2833-1111

81-3-6666-9925

www.hp.com/support/korea

New Zealand 0800-551-664

Nicaragua 1-800-711-2884

Norwegen 23500027

Österreich 01 360 277 1203

Panamá 001-800-711-2884

Paraguay (009) 800-541-0006

Perú 0-800-10111

Philippines +65 6100 6682

Polska www.hp.com/support

Portugal 021 318 0093

Table 12-1 Contact Information

Country/Region Contact

Puerto Rico 1-877 232 0589

Russia Россия 495 228 3050

Schweiz (Deutsch) 01 439 5358

Singapore 6100 6682

South Africa 0800980410

Warranty, Regulatory, and Contact Information

South Korea 한국

Suisse (français) 022 827 8780

Suomi 09 8171 0281

Sverige 08 5199 2065

Svizzera (italiano) 022 567 5308

Türkiye www.hp.com/support

Taiwan 臺灣

Thailand ไทย

United Kingdom 0207 458 0161

United States 800-HP INVENT

Uruguay 0004-054-177

Venezuela 0-800-474-68368

2-561-2700

+852 28052563

+65 6100 6682

Viêt Nam +65 6100 6682

Warranty, Regulatory, and Contact Information

Product Regulatory & Environment Information

Federal Communications Commission Notice

This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures:



Reorient or relocate the receiving antenna.



Increase the separation between the equipment and the receiver.



Connect the equipment into an outlet on a circuit different from that to which the receiver is connected.



Consult the dealer or an experienced radio or television technician for help.

Modifications

The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by HewlettPackard Company may void the user’s authority to operate the equipment.

Declaration of Conformity for products Marked with FCC Logo, United States Only

This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation.

If you have questions about the product that are not related to this declaration, write to

Hewlett-Packard Company P.O. Box 692000, Mail Stop 530113

Houston, TX 77269-2000

For questions regarding this FCC declaration, write to

Hewlett-Packard Company P.O. Box 692000, Mail Stop 510101 Houston, TX 77269-2000

or call HP at 281-514-3333

To identify your product, refer to the part, series, or model number located on the product.

Canadian Notice

This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment Regulations.

Avis Canadien

Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du Canada.

European Union Regulatory Notice

This product complies with the following EU Directives:



Low Voltage Directive 2006/95/EC



EMC Directive 2004/108/EC

Compliance with these directives implies conformity to applicable harmonized European standards (European Norms) which are listed on the EU Declaration of Conformity issued by Hewlett-Packard for this product or product family.

Warranty, Regulatory, and Contact Information

This symbol on the product or on its packaging indicates that this product just not

be disposed

of with your other

This compliance is indicated by the following conformity marking placed on the product:

xxxx*

This marking is valid for non-Telecom products and EU harmonized Telecom products (e.g. Bluetooth).

Hewlett-Packard GmbH, HQ-TRE, Herrenberger Srasse 140, 71034 Boeblingen, Germany

Japanese Notice

Perchlorate Material - special handling may apply

This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California.

Disposal of Waste Equipment by Users in Private Household in the European Union

household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equipment for recycling, please contact your local city office, your household waste disposal service or the shop where you purchased the product.

This marking is valid for EU non-harmonized Telecom products . *Notified body number (used only if applicable refer to the product label)

Chemical Substances

HP is committed to providing our customers with information about the chemical substances in our products as needed to comply with legal requirements such as REACH (Regulation EC No 1907/2006 of the European Parliament and the Council). A chemical information report for this product can be found at: http://www.hp.com/go/reach

Warranty, Regulatory, and Contact Information

产品中有毒有害物质或元素的名称及含量

根据中国《电子信息产品污染控制管理办法》

有毒有害物质或元素

部件名称

铅 (Pb) 汞 (Hg) 镉 (Cd) 六价铬 (Cr(VI))

PCA X O O O O O

多溴联苯 (PBB)

多溴二苯醚

(PBDE)

外觀殼子/字鍵

O：表示该有毒有害物质在该部件所有均质材料中的含量均在SJ/T11363-2006 标准规定的限量要求以下。 X：表示该有毒有害物质至少在该部件的某一均质材料中的含量超出SJ/T11363-2006 标准规定的限量要求。表中标有“X” 的所有部件都符合欧盟RoHS法规 “欧洲议会和欧盟理事会2003年1月27日关于电子电器设备中限制使用某些有害物质的2002/95/EC号指令”

注：环保使用期限的参考标识取决于产品正常工作的温度和湿度等条件

O O O O O O

Index

!: key, 23

% change, 53 % yield, 47

=: key, 12

a: slope, 62 absolute value. See Math menu Algebraic mode, 17 amortization: Amort key, 33; example,

34; menu items, 33 annual: bond, 47 annunciators, 11 ANS. See last number

b: y-intercept, 62 backspace key, 16 balance: amortization, 33 begin mode: Beg key, 32 bond: annual, semiannual, 10; example,

47; key, 46; menu items, 46 bonds, 46 bottom line: display, 8 break-even: BrkEv key, 51; example, 51 business problems, 53; percent

calculation examples, 54

calculation mode: Chain, Algebraic, and

RPN, 10

calendar: Actual, Cal.360, 10 call value, 47 Canada TVM example, 38 Canadian TVM, 36 cash flow: example, 40; keys, 40;

sample diagrams, 45 cash flows, 39; analyzing, 42; editing,

44; number per year, 43 Chain mode, 17 Chi, 25 clearing. See: Reset menu compounding periods: N key, 32 compounding periods per year: P/YR

key, 32 Compounding, per year, 35

contents, 3 contrast, 7 correlation, 61, 62 cosine: COS key, 23 cost: depreciation, 58; fixed. See break-

even; variable per unit. See break-

even coupon rate, 46 covariance, 61, 62 CshFl key. See cash flow cursor, 7

Data key. See Statistics data menu, 61 date: actual, 47; maturity, 46;

settlement, 46 Date 1. See Date calculation Date 2. See Date calculation date calculation: Date key, 49; example,

49 date format, 9 days between. See Date calculation decimal point, 9 decimal separator: point or comma, 9 default calculator screen, 8 degrees, 9 delete: DEL key, 44 delete key, 44 deleting. See Reset menu depreciation, 56; Depr key, 56; example,

58; methods, 56 descriptive: sub menu. See Statistics

menu discounted payback, 43 display, 7; two lines, 8 down arrow key. See scroll

EEX key. See scientific notation end mode: End key, 32 error messages, 65

factor: declining balance. See

depreciation factorial: ! key, 23 F-distribution, 25 Fix: display precision. See Mode menu function: one-number, 22

functions: two-number, 26 future value: FV key, 32

IConv key. See interest conversion INPUT: key, 12 insert: INS key, 44 interest: accrued. See bonds; towards

loan payment. See amortization interest conversion: example, 35 interest rate: effective, 35; nominal, 35;

nominal, I/YR key, 32 inverse tail normal distribution, 25 IRR: key, 42

key: highlighting, 11; presses, 11;

primary function, 11; secondary

function, 11 keyboard map, 6

language: selection, 7 last number, 19; ANS key, 19 life. See depreciation line: regression, 61 log: LN key. See Math menu logarithmic functions, 23 lower tail normal distribution, 25

markup: as cost, 53; as price, 53 math: Math key, 23 math functions, 16 Math menu: Absolute value, 24;

Hyperbolic, 24; Log, 24; Probability,

24; Trigonometry, 24 mean, 61 memory, 13; key, 13 menu: Amortization, 33; Bond, 46;

Break-even, 51; Cash Flow, 39; Date

Calculation, 49; Depreciation, 56;

Interest Conversion, 35; IRR, 42;

Math, 22; Memory, 13; Mode, 8; NPV,

42; Payment per year, 36; Percent

Calculation, 53; Reset, 13; Statistics,

60; TVM, 30; TVM Canada, 36 menu item value: recalling, 28

menus: items, types of, 15; maps, 14;

special, 13; sub-menus, opening, 14 mode menu: key, 7

Index

N key, 32 natural exponent: e to the power of x

key, 23 nCr, 27 negative numbers, 16 net future value, 43 net present value, 43 net uniform series, 43 nPr, 27 NPV: key, 42 NPV, IRR: menu items, 43 number entry, 16 number period: compounding, 55 number periods: amortization, 33 numbers: rounding, 28; storingand

recalling, 27

off: calculator off, 7 Off: key, 7 on: calculator on, 7 On: key, 7

P/YR: key, 32 parentheses: use in Chain mode, 17 parentheses (swap and rolldown): keys

in RPN, 21 payback, 43 percent calculation: % calc key, 53 percentage: % key, 28 percentage of total, 53 percentages: simple, 28 periodic payment: PMT key, 32 PI. See Math Menu population, 61 power functions, 23 Predictions: sub-menu. See Statistics present value: PV key, 32

price: break-even, 51; face value. See

bonds; percent calculation, 54 principal, 33 probability, 25 product: x and yvalues, 63 profit, 51

quantity: break-even, 52

radians, 9 random function: RAND key, 23 recall arithmetic, 28 recalling numbers: RCL key, 27 reciprocal: 1/x key, 23 regression line, 61 remaining book value, 58 remaining depreciable value, 58 Reset: key, 13 roll down. See RPN rounding numbers: RND key, 23 RPN: Reverse Polish Notation, 18 RPN stack, 18

S.E. SamP.X and Y,61 salvage: depreciation, 58 scientific notation: EEX key, 16 scroll: up and down arrow keys, 8 semiannual: bond, 47 Sigma X,Y, 61 sign: positive, negative key, 16 sine: SIN key, 23 slope, 61 square of x: key, 23 square root key, 23 standard deviation, 61 start: amortization period, 33 start date: depreciation, 58

statistics: menu items, 62; one-variable,

61; one-variable weighted, 61; Stats

key, 61; two-variable, 61 statistics example, 63 stats menu, 61 storing numbers: STO key, 27 student, 25 sums: sub-menu. See Statistics swap. See RPN symbol: battery, 7

tangent: TAN key, 23 thousands separator, 9 time value of money: keys, 32 top line: display, 8 total: cash flows, 43 TVM: example, 32; storing and recalling

numbers, 28

up arrow key. See scroll

x: Sigma, 62; square of Sigma x, 63;

times payment per year, xP/YR key,

32 x mean, 62 x mean sample, 62 x population Std. Dev., 62 x prediction, 62 x standard deviation, 62

y: Sigma, 63; square of Sigma y, 63 y mean, 62 y mean sample, 62 y population Std. Dev., 62 y prediction, 62 y standard deviation, 62 y to the x power, 23 y-intercept, 61

HP 20B User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Contents

HP 20b Business Consultant Keyboard

1 Basic Features

Selecting a Language

The Mode Menu: Setting Preferences

Changing the Calculation Mode

Memory and the Memory Menu

Accessing Menus and Menu Maps

2 Mathematical Calculations

Number Entry and Display

Chain Mode

Algebraic Mode

Reverse Polish Notation (RPN) Mode

One-Number Functions and the Math Menu

The Probability Sub-menu

Two-Number Functions

Storing and Recalling Numbers

Recall Arithmetic

Rounding Numbers

Percentages

3 Time Value of Money

Amortization

Interest Conversion Menu

Canadian Mortgages: TVM Canada

4 Cash Flows

Analyzing Cash Flows

Editing Cash Flows

Sample Cash Flow Diagrams

5 Bonds

6 Date Calculation

7 Break-even

8 Business Problems

The Percent Calculation Menu

9 Depreciation

10 Statistical Operations

The Data and Stats Menus

11 Errors

12 Warranty, Regulatory, and Contact Information