Sharp EL-738FB Installation Manual

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Page 1

MODEL

EL-738F

FINANCIAL CALCULATOR

OPERATION MANUAL

Contents

Introduction ..................... 3

Getting Started ................ 5

General Information ........ 11

Financial Functions ......... 17

Scientific Functions ........ 60

Statistical Functions ....... 64

Appendix .......................... 72

Index ................................. 83

Page

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Page 3

NOTICE

• SHARP makes no guarantee that this product or this

manual is suitable or accurate for any purpose, commercial or otherwise.

• Rules and practices in ﬁ nancial calculation vary ac-

cording to country, locality, or ﬁ nancial institution. It is the consumer’s responsibility to determine whether or not the results produced by this product conform to applicable rules and regulations.

• SHARP will not be liable nor responsible for any incidental or consequential economic or property damage caused by misuse and/or malfunctions of this product and its peripherals, unless such liability is acknowledged by law.

• The material in this manual is supplied without representation or warranty of any kind. SHARP assumes no responsibility and shall have no liability of any kind, consequential or otherwise, from the use of this material.

• SHARP assumes no responsibility, directly or indirectly, for ﬁ nancial losses or claims from third persons resulting from the use of this product and any of its functions, the loss of or alteration of stored data, etc.

• SHARP strongly recommends that separate permanent written records be kept of all important data. Data may be lost or altered in virtually any electronic memory product under certain circumstances. Therefore, SHARP assumes no responsibility for data lost or otherwise rendered unusable whether as a result of improper use, repairs, defects, battery replacement, use after the speciﬁ ed battery life has expired, or any other cause.

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Contents

Introduction .................................................................. 3

Operational Notes ...............................................................3

Key Notations in This Manual ..............................................4

Chapter 1: Getting Started ..........................................5

Preparing to Use the Calculator ..........................................5

Resetting the Calculator In Case of Difﬁ culty ......................5

Calculator and Display Layout .............................................6

The SET UP Menu ..............................................................8

Operating Modes...............................................................10

Chapter 2: General Information ................................ 11

Basic Calculations .............................................................11

Clearing the Entry and Memories .....................................11

Editing and Correcting an Entry ........................................13

Memory Calculations ........................................................14

Chapter 3: Financial Functions ................................ 17

General Information ..........................................................17

TVM (Time Value of Money) Solver ..................................22

Amortization Calculations .................................................33

Discounted Cash Flow Analysis ........................................37

Bond Calculations .............................................................44

Depreciation Calculations .................................................48

Conversion between APR and EFF ..................................51

Day and Date Calculations ................................................52

Percent Change/Compound Interest Calculations ............54

Cost/Sell/Margin/Markup Calculations ..............................56

Breakeven Calculations .....................................................58

Chapter 4: Scientiﬁ c Functions ................................ 60

Constant Calculations .......................................................60

Chain Calculations ............................................................60

Scientiﬁ c Calculations .......................................................61

Random Functions ............................................................62

Modify Function .................................................................63

Chapter 5: Statistical Functions ............................... 64

Statistical Calculations and Variables ................................67

Appendix .................................................................... 72

Financial Calculation Formulas .........................................72

Statistical Calculation Formulas ........................................75

Errors and Calculation Ranges .........................................76

Battery Replacement ........................................................80

Priority Levels in Calculations ...........................................81

Speciﬁ cations ....................................................................82

Index ...........................................................................83

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Introduction

Thank you for purchasing a SHARP Financial Calculator. After reading this manual, store it in a convenient location for future reference.

• Display of examples shown in this manual may not look exactly the same as what is seen on the product. For instance, screen examples will show only the symbols necessary for explanation of each particular calculation.

• All company and/or product names are trademarks and/or registered trademarks of their respective holders.

• Some of the models described in this manual may not be available in some countries.

Operational Notes

• Do not carry the calculator around in your back pocket, as it may break when you sit down. The display is made of glass and is particularly fragile.

• Keep the calculator away from extreme heat such as on a car dashboard or near a heater, and avoid exposing it to excessively humid or dusty environments. Since this product is not waterproof, do not use it or store it where

• ﬂ uids, for example water, can splash onto it. Raindrops, water spray, juice, coffee, steam, perspiration, etc. will also cause malfunction.

•

Clean with a soft, dry cloth. Do not use solvents or a wet cloth. Avoid using a rough cloth or anything else that may cause scratches.

• Do not drop the calculator or apply excessive force.

• Never dispose of batteries in a ﬁ re.

• Keep batteries out of the reach of children.

• This product, including accessories, may change due to upgrading without prior notice.

Hard Case

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Key Notations in This Manual

Key operations are described in this manual as follows:

To specify log : . h .....................

To specify 1 : 1 or 1 .......................

To specify Σxy : i V .....................

1 2 3

To specify CLR-D : . ? .....................

To specify ENT :

To specify Z : i Z .....................

To specify DATA : J ..............................

Functions that are printed in orange above the key require

to be pressed ﬁ rst before the key.

Number entry examples are shown with ordinary numbers

(i.e., “100” will be indicated instead of “1 0 0”).

To specify a memory function (printed in green), press

ﬁ rst.

Functions that are printed in black adjacent to the keys are

effective in speciﬁ c modes.

Using the . and i keys

Press s .

A x ,

• . mean you have to press . followed by ) key and i followed by * key.

Notes:

• The multiplication instruction “×” and alphabetic letter “X” are

distinguished as follows:

Key Display Multiplication instruction → x

Alphabetic letter → X X

• Examples in this manual are performed using default settings (e.g., SET UP menu items) unless values are otherwise assigned.

and i A

10.

πA˚_

3 4

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Chapter 1

Getting Started

Preparing to Use the Calculator

Before using your calculator for the ﬁ rst time, you must reset (initialize) it.

Resetting the calculator

Press the RESET switch located on the back of the calculator with the tip of a ball-point pen or similar object. Do not use an object with a breakable or sharp tip.

• After resetting the calculator, the initial display of the NORMAL mode appears.

Resetting the Calculator In Case of Difﬁ culty

Caution:

The RESET operation will erase all data stored in memory and restore the calculator’s default setting.

In rare cases, all the keys may cease to function if the calculator is subjected to strong electrical noise or heavy shock during use. If pressing any of the keys (including s) has no effect, reset the calculator.

Resetting the calculator

See the above procedure.

Note: Pressing . k and 1 = will also erase all

data stored in memory and restore the calculator’s default setting.

000

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Calculator and Display Layout

Calculator layout

Display

screen

Power

3 Key

operation keys

SET UP

key

Display screen: The calculator display consists of a 12-char-

acter dot matrix character line and a 12-digit 7-segment character line (10-digit mantissa and 2-digit exponent).

Power ON/OFF and Clear key: Turns the calculator ON.

This key also clears the display. To turn off the calculator, press ., then c.

Key operation keys:

: Activates the second function (printed in orange) as-

signed to the following key.

: Activates the memory (printed in green) assigned to

the following key.

SET UP key: Displays the SET UP menu to select the

display notation, angular unit, depreciation method and date format.

Cursor keys: Move the cursor.

MODE key: Switches between NORMAL and STAT modes.

ON/OFF and Clear key

Cursor keys

MODE key

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Display layout

Equation/ variable name display

Symbol

Mantissa

Exponent

• During actual use, not all symbols are displayed at the same time.

• Only the symbols required for the operation being explained are shown in the screen examples of this manual.

Appears when the entire equation cannot be displayed.

Press g / y to see the remaining (hidden) part.

Indicates that variables or data are present above/be-

c /d

low the screen. Press z / i to scroll up/down.

2ndF : Appears when . is pressed, indicating that the

functions shown in orange are enabled.

HYP : Indicates that . ] has been pressed and the

hyperbolic functions are enabled.

ALPHA : Indicates that i, g or f has been pressed,

and storing or recalling memory values or TVM solvers/statistics variables can be performed.

BGN : Indicates that calculations are annuity due (payment

at the beginning of each interval) calculations. When

BGN is not displayed, calculations are ordinary annu-

ity (payment at the end of each interval) calculations.

360

Indicates that date calculations are based on a

360-day year (12 months with 30 days). When 360 is not displayed, date calculations use the actual calendar.

ENT

Indicates that a value can be assigned to the displayed

variable using Q.

COMP : Indicates that the displayed variable can be solved for

by using @.

FLOAT A / FLOAT B / TAB / SCI: Indicates the notation used to

display values. It can be changed in the SET UP menu.

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DEG / RAD / GRAD : Indicates which angular units are in use.

It can be changed in the SET UP menu.

: Appears when statistics mode is selected.

M : Indicates that a numerical value is stored in the inde-

pendent memory (M).

: Indicates that the value of the displayed variable has

not been calculated yet (for variables that can be calculated).

The SET UP Menu

Press ~ to display the SET UP menu.

DSP DRG DEPR

• A menu item can be selected by:

• Using g / y to select a number (the selected number will blink), then pressing =, or

• pressing the number key corresponding to the menu item number.

• If c or d is displayed on the screen, press z or i to view the previous/next part of the menu.

• Press s to exit the SET UP menu.

Selecting the display notation and number of decimal places

The calculator has three display notation systems (ﬁ xed decimal point, scientiﬁ c notation and ﬂ oating point) for displaying calculation results.

• If ~ 0 0 (TAB) is pressed, “DIG(0-9)?” will be displayed and the number of decimal places can be set to any value between 0 and 9.

• If ~ 0 1 (SCI) is pressed, “SIG(0-9)?” will be displayed and the number of signiﬁ cant digit can be set to any value between 0 and 9. Entering 0 will set a 10-digit display.

• If a ﬂ oating point number does not ﬁ t in the speciﬁ ed range, the calculator will display the result in scientiﬁ c notation (exponential notation). See the next section for details.

• The default setting is a ﬁ xed decimal point with two decimal places.

→

DAtE

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Selecting the ﬂ oating point number system in scientiﬁ c notation

The calculator has two settings for displaying a ﬂ oating point number:

FLO_A (FLOAT A) and FLO_B (FLOAT B). In each display setting, a number is automatically displayed in scientiﬁ c notation outside the following preset ranges:

• FLO_A ~ 0 2: 0.000000001

• FLO_B ~ 0 3: 0.01

| X | ≤ 9,999,999,999

≤

| X | ≤ 9,999,999,999

≤

Switching the notation setting

Procedure Key operation Display

100000

3 8

(see page 61)

1 2

8 3

1000

—————©3=

3333333

—————©3=

3333333333

3©1

———=

0003

3©1

———=

3©1

———=

000

(see page 48)

-03

100000 ÷ 3 =

Fixed decimal point with two decimal places

Scientiﬁ c notation

→

(SCI) with two signiﬁ cant digits

Floating point

→

(FLO_A)

3 ÷ 1000 = Floating point (FLO_A)

Floating point

→

(FLO_B)

Fixed decimal point

→

with two decimal places

s =

~ 0 1

~ 0 2

s =

~ 0 3

~ 0 0

Selecting the angular unit

• DEG (°) : ~ 1 0 (default setting)

• RAD (rad) : ~ 1

• GRAD (g) : ~ 1

Selecting the depreciation method

• SL (Straight-line method): ~ 2 0 (default setting)

• SYD (Sum-of-the-years’ digits method): ~ 2

• DB (Declining balance method): ~ 2

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Selecting the date format

• US (Month-Day-Year): ~ 3 0 (default setting)

• EU (Day-Month-Year): ~ 3

(see page 44)

Operating Modes

This calculator has two operating modes, which can be selected using the MODE key.

Selecting a mode

1. Press m.

The menu display appears.

NORMAL StAt

2. Press 0 or = to se-

lect NORMAL mode.

000

• Press 1 or y = to select STAT mode.

Operations available in each mode

NORMAL mode:

Allows you to perform ﬁ nancial, arithmetic, or scientiﬁ c calculations.

STAT (statistics) mode:

Allows you to perform statistical, arithmetic, or scientiﬁ c calculations. The

symbol appears in the display.

SD LINE QUAD

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Chapter 2

General Information

Basic Calculations

Entering numbers and arithmetic operations

• Use the number keys 0 to 9, decimal point key ., and sign change key , to enter numbers into the calculator. To clear the display or entry, press s.

• Use the S key to enter a value in scientiﬁ c notation.

• Use the arithmetic keys + - x 8 to perform the standard arithmetic calculations of addition, subtraction, multiplication, and division. Press = to perform each calculation.

• Use the ( and ) keys to place parentheses around inner parts of expressions. The closing parenthesis ) just before = or h may be omitted.

• When you enter a series of operations in one sequence, the calculator performs the calculation according to the priority levels in calculation on page 81.

Example Key operation Result

45 + 285 ÷ 3 =

18 + 6

15 – 8

42 × (–5) + 120 =

(5 × 103) ÷ (4 × 10–3) =

( (

(5 ,)

S 3 8 4 S

Clearing the Entry and Memories

The following methods of clearing the calculator (restoring default settings) are available:

285

45 +

18 + 6 ) 15 - 8

x , 5 +

8 3

120

125000000

14000

343

-9000

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Listed

Cash

A-H,

(MEM)

(RESET)

Entry

(display)

M, X-Z

× × ×

Operation

s . b

(Mode selection)

m . k 0

. k 1

RESET switch

: Cleared or restored to the default setting : Retained

N, I/Y, PV, PMT, and FV (P/Y and C/Y are not included.)

Note that listed ﬁ nancial variables sharing common memory

with TVM variables, such as “COUPON (PMT)” used in bond calculations, are also cleared or restored to default settings.

Listed variables used in ﬁ nancial calculations (such as “RATE

(I/Y),” etc.) including P/Y and C/Y

When you press * to enter a ﬁ nancial calculation, AMRT

P1 and AMRT P2 both revert to their default values. The same holds true for YEAR when you press O.

With one of the variables of a listed group (such as those

used in bond calculations) displayed, when . b is pressed, all the variables in the listed group are cleared or restored to their default settings. Note that TVM variables sharing common memory with listed ﬁ nancial variables are also cleared or restored to default settings.

Press . b when a cash ﬂ ow value is displayed.

Statistical data (entered data) and variables (n, x, etc.)

Are cleared when changing between sub-modes in STAT mode.

Notes:

• To clear any of the “A-H, M, X-Z” or “ANS” memories, press

g and then specify the memory.

• To clear or restore to the default setting one variable or value of TVM variables, listed ﬁ nancial variables, cash ﬂ ow data, or STAT, refer t o the relevant section.

• If you turn off the calculator (by pressing . c or by letting it turn itself off automatically), it will resume wherever you left off when you turn it on again.

TVM

variables

ANS

× ×××

*2*

financial

variables

flow

data

STAT

Delete key

To delete a number/function, move the cursor to the number/ function you wish to delete, then press L. If the cursor is located at the right end of an equation or if you are entering a value, the L key will function as a back space key.

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Memory clear key

Press . k to display the menu.

• To clear all (A-H, M, X-Z, ANS, TVM variables, listed ﬁ nancial variables, cash ﬂ ow data, and STAT), press 0 0 or

0 =

• To RESET the calculator, press 1 0 or 1 =. The RESET operation erases all data stored in memory, and restore the calculator’s default settings.

MEM RESEt

Editing and Correcting an Entry

Cursor keys

• In a menu, such as the SET UP menu, use g or y to select a number (the selected number will blink), then press =. If you need to scroll up or down the screen, use z or i.

• In ﬁ nancial calculations, such as bond calculations, press

or z to move through the variables (items).

Playback function

After obtaining an answer, pressing g brings you to the end of the equation and pressing y brings you to the beginning. Press g or y to move the cursor. Press . g or

. y

equation.

Insert and overwrite modes in the equation display

• This calculator has two editing modes: insert mode (default),

• To insert a number in the insert mode, move the cursor to the

• This mode setting will be retained until you press . d

to jump the cursor to the beginning or end of the

and overwrite mode. Pressing . d switches between the two modes. A triangular cursor indicates an entry will be inserted at the cursor, while the rectangular cursor indicates existing data will be overwritten as you make entries.

place immediately after where you wish to insert, then make the desired entry. In the overwrite mode, data under the cursor will be overwritten by the number you enter.

or RESET the calculator.

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Changing “15 ÷ 3 =” into “25 ÷ 13 =”

Procedure Key operation Display

15 ÷ 3 =

15 8 3

15©3=

500

Enter the playback function.

Switch to overwrite mode.

Change “15” to “25” and move the cursor to “3”.

Change to insert mode.

Change “3” to “13” and calculate.

Errors

An error will occur if an operation exceeds the calculation ranges, or if a mathematically illegal operation is attempted. When an error occurs, pressing g or y automatically moves the cursor to the place in the equation/number where the error occurred. Edit the equation/number or press s to clear the equation. For details, see page 76.

15©3

25©3

25©13=

192

Memory Calculations

This calculator has 11 temporary memories (A-H and X-Z), one independent memory (M) and one last answer memory (ANS). It also has various variables for use in ﬁ nancial calculations and statistical calculations.

Memory use in each mode for memory calculations

TVM

Mode

NORMAL STAT

A-H,

X-Z

: Available : Unavailable

ANS

variables

Listed financial

variables

Statistical

× ×

variables

Page 17

N, I/Y, PV, PMT, FV

All ﬁ nancial variables, except for TVM variables

x, sx,

Temporary memories (A-H, X-Z)

Press g and the variable key to store a value in memory. Press f and the variable key to recall a value from the

memory.

x, n

, y, sy,

xy, r, a, b, c

To place a variable in an equation, press i and the variable key.

Independent memory (M)

In addition to all the other features of temporary memories, a value can be added to or subtracted from an existing memory value.

Press s g M to clear the independent memory (M).

Last answer memory (ANS)

• The calculation result obtained by pressing = or any other calculation ending instruction (including storing and recalling operations) is automatically stored in the last answer memory.

• Listed ﬁ nancial variables are automatically stored in the last answer memory by displaying the variable and the value.

TVM variables

TVM variables can be recalled using f in the same way as temporary memories. It is not necessary to press g to store a value.

Listed ﬁ nancial variables

Financial variables are speciﬁ c to the type of calculation they are used in. For example, the variable N is available to the TVM solver but not to discounted cash ﬂ ow analysis calculations. If you want to carry a value from a variable over into a different type of calculation, use one of the following methods:

Last answer memory (ANS): Within the original calculation, dis-

• play the variable and value that you wish to carry over. The value is automatically entered into last answer memory. Press s to exit the calculation (the listed ﬁ nancial variables will disappear from the screen), and press i / to bring up the value from the previous calculation. M-D-Y (D-M-Y) 1 and M-D-Y (DM-Y) 2 are not stored in last answer memory.

•

Variables common to both calculations: If the value that you wish to carry over is held in a variable that exists in both types

Page 18

of calculation (for example, both bond calculations and the TVM solver use the variable I/Y), you can retrieve the value simply by switching calculation types and bringing up the variable.

Statistical variables

Statistical data is not entered into variables. Statistical variables are the results of the calculation of statistical data. Therefore, you cannot enter values directly into statistical variables. After calculation, however, you can use the values held in statistical variables in subsequent calculations.

Note: Use of f or i will recall the value stored in

memory using up to 14 digits.

Memory calculations

Example Key operation Result

8 x 2 g

24 ÷ (8 × 2) = (8 × 2) × 5 =

$150×3:M

+)$250:M2=M1+250

–)M

$1 = ¥110 ¥26,510 = $? $2,750 = ¥?

r = 3 cm (r→Y)

= ?

= 2.4...(A)

4 + 6 3 × (A) + 60 ÷ (A) =

8 i M

M x 5

150

x 3

250

M x 5 .

. j

110

26510

8 f Y

2750

x f Y

;

8 ( 4 + 6 ) =

x i / + 60 8

i Y*

1600

150

8000

000 45000 25000

3500

66500

11000 24100

30250000

300

2827

240

3220

* Entry of the multiplication procedure is omitted between “π”

and a variable.

Page 19

Chapter 3

Financial Functions

General Information

Financial calculations

The following ﬁ nancial functions are available. Use NORMAL mode to perform ﬁ nancial calculations.

TVM (Time Value of Money) solver: Analyze equal and regular cash ﬂ ows. These include calculations for mortgages, loans, leases, savings, annuities and contracts or investments with regular payments.

Amortization calculations: Calculate and create amortization schedules using values stored in the TVM solver.

Discounted cash ﬂ ow analysis: Analyze unequal cash ﬂ ows and calculate NPV (net present value) and IRR (internal rate of return).

Bond calculations: Solve bond prices or yields to maturity with accrued interest.

Depreciation calculations: Obtain depreciation base values using three types of calculation methods.

Conversion between APR and EFF: Interest rates can be converted between APR (annual, or nominal percentage rate) and EFF (effective interest rate).

Day and date calculations: Calculate dates and the number of days between dates.

Percent change/Compound interest calculations: Calculate percent change (increase or decrease) and compound interest rates.

Cost/Sell/Margin/Markup calculations: Calculate cost, selling price and margin/markup.

Breakeven calculations: Calculate breakeven points (quantity) using ﬁ xed costs, variable costs per unit, unit prices, and proﬁ t.

Page 20

Variables used in ﬁ nancial calculations

Financial calculations use multiple variables. By entering known values into variables, you can obtain unknown values. Variables used in ﬁ nancial calculations are categorized into the following two types, depending on the entry method.

TVM variables:

Variables that are used in the TVM solver. These include N, I/Y, PV, PMT and FV. You can store, recall or calculate values directly using the corresponding keys.

Listed ﬁ nancial variables:

Variables that are organized into lists in different categories. These variables can be accessed using the z/i cursor keys in each calculation. P/Y and C/Y in the TVM solver are of this type of variable.

Variables shared among calculations

Financial variables are speciﬁ c to the type of calculation they are used in. Values are stored in these variables and recalled as required. Some variables are shared (in the memory area) among calculations. If you change the value of a variable in one calculation, the value will change in all the other calculations as well. The following list shows the variables shared between calculations. While calculating, be aware of the values stored in these variables.

Discounted

TVM

cash ﬂ ow

solver

analysis

N — CPN/Y (N) LIFE (N) PERIODS (N) —

I/Y RATE (I/Y) YIELD (I/Y) DB (I/Y) % (I/Y) —

PV — PRICE (PV) COST (PV) OLD PRC (PV) —

PMT —

FV —

——

*The variable names vary according to the data format settings.

Bond

calculations

COUPON

(PMT)

REDEMPT

(FV)

M-D-Y 1 D-M-Y 1

M-D-Y 2 D-M-Y 2

Depreciation calculations

SALVAGE (FV) NEW PRC (FV) —

Percent change/

Compound inter-

est calculations

———

——

Day and date

calculations

M-D-Y 1 D-M-Y 1

M-D-Y 2 D-M-Y 2

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Basic variable operations

TVM variables (N, I/Y, PV, PMT, FV)

A. Entering a value

Enter a value and then press the corresponding TVM vari-

able key.

Note: You can also enter values into variables using arithmetic

operations. Ex. 100 x 12

B. Displaying a value

Press f and the corresponding TVM variable key.

C. Executing calculation

Press @ and the corresponding TVM variable key.

Listed ﬁ nancial variables

A. Entering a value

1. Select the desired ﬁ nancial calculation method by pressing the corresponding ﬁ nancial calculation key.

2. Use z/i to select the variable you wish to enter.

3. Enter the value and press Q when the “ENT” symbol appears.

Note: In step 3, you can also enter values into variables using

arithmetic operations. Ex. 100 x 12

B. Displaying a value

Use z/i to show the variable and value.

C. Executing calculation

1. Use z/i to select the variable you wish to calculate.

2. Press @ when the “COMP” symbol appears.

Note: Pressing . b resets all the variables in the dis-

played listed ﬁ nancial group to the default values. For details, see the relevant sections for each ﬁ nancial calculation.

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The ENT and COMP symbols

Listed ﬁ nancial variables are categorized by whether they are known or unknown. When the variable is selected (displayed), the “ENT” and/or “COMP” symbols will appear to indicate that the current variable may be entered (known variable) and/or calculated (unknown variable), respectively. For details, refer to the explanations or examples for each ﬁ nancial function.

Note: TVM variables (N, I/Y, PV, PMT and FV) can be entered

(known variables) and calculated (unknown variables), however, neither “ENT” nor “COMP” will appear on the display.

Category Display symbols Descriptions

For entry only ENT

For calculation only COMP

For entry or calculation

Calculated automatically

ENT COMP

—

Notes:

• During ﬁ nancial calculation, the word “calculating!” will be displayed on the screen. You can press s at this time to cancel the calculation.

• Calculation-only and automatically calculated variables have no default values.

• The

symbol will be displayed if the value of the displayed variable has not been calculated yet (for variables that can be calculated).

Variable can be used as a known, but not as an unknown.

Variable can be used as an unknown, but not as a known.

Variable can be used as either a known or an unknown.

Unknown variable, but the calculator calculates the value automatically.

Page 23

Compound interest

This calculator assumes interest is compounded periodically in ﬁ nancial calculations (compound interest). Compound interest accumulates at a predeﬁ ned rate on a periodic basis. For example, money deposited in a passbook saving account at a bank accumulates a certain amount of interest each month, increasing the account balance. The amount of interest received each month depends on the balance of the account during that month, including interest added in previous months. Interest earns interest, which is why it is called compound interest.

It is important to know the compounding period of a loan or investment before starting, because the whole calculation is based on it. The compounding period is speciﬁ ed or assumed (usually monthly).

Cash ﬂ ow diagrams

The direction of arrows indicates the direction of cash movement (inﬂ ow and outﬂ ow) with time. This manual uses the following cash ﬂ ow diagrams to describe cash inﬂ ows and outﬂ ows.

Present

Inflow (+)

Cash flow

Outflow (–)

value (PV)

Payment (PMT)

Time

......

Future value (FV)

Page 24

TVM (Time Value of Money) Solver

Analyze equal and regular cash ﬂ ows. These include calculations for mortgages, loans, leases, savings, annuities, and contracts or investments with regular payments.

Note: Discounted cash ﬂ ow analysis can be done using un-

equal cash ﬂ ows (see page 37). An amortization schedule can be calculated using the information stored in the TVM solver (see page 33).

Variables used in the TVM solver

Corresponding

Variable

N I/Y PV PMT FV P/Y C/Y

variable key

. w

. w i

Description

Total number of payments 1 Interest rate per year 0 Present value 0 Payment 0 Future value 0 Number of payments per year 1 Number of compounding

periods per year

Setting the payment period (payment due)

You can toggle between ordinary annuity (payment at the end of the period) and annuity due (payment at the beginning of the period) using . ". The default setting is ordinary annuity (BGN is not displayed).

Refer to page 28 for details.

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

• All the TVM solver variables retain their previously entered values. If you wish to clear all the data, press . b.

2. Select ordinary annuity or annuity due using . ".

Default

value

Page 25

3. Enter values into TVM solver variables.

• Enter a value and press the appropriate TVM variable key (N, f,

, u, t).

• Press . w and then enter a value for P/Y. The same value is automatically assigned to C/Y as well. Values entered into P/Y or C/Y must be positive. After entering values, press s to quit the P/Y and C/Y settings.

• After setting P/Y (number of payments per year), you can use . < to enter N (total number of payments). Enter the number of years and press . <. The calculator automatically calculates the total number of payments.

• By pressing

you can use the result of the pre-

vious normal calculation stored in ANS memory as a TVM variable.

• Note that some variables are shared by other calculations and may have values assigned by those calculations.

4. Press @ and the TVM variable key that you wish to solve.

• The calculation is performed and the obtained values are displayed.

Basic examples for the TVM solver

Calculating basic loan interest

A $56,000 mortgage loan (compounded monthly) requires monthly payments of $440 during its 20-year amortization period. Calculate the annual interest rate on the mortgage.

PV = $56,000

FV = 0

......

PMT = –$440

N = 12 × 20 years = 240

Default values for the number of payments per year (P/Y) and the number of compounding periods per year (C/Y) are both set to 1. Set these values before entering TVM variable values.

I/Y = ?%

Page 26

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set the number of payments per year to 12.

The number of compounding periods per year is automatically set to the same value as P/Y.

Conﬁ rm the number of compounding periods per year.

Quit the P/Y and C/Y settings.

Calculate the total number of payments and store in N.

Enter the present value.

. w

. <

56000

000

P/Y=

1200

C/Y=

1200

000

ANS~N

24000

56———~PV

5600000

Enter payment.

440

(-44—)~PMT

-44000

Enter the future value.

—~FV

000

Calculate the annual interest rate.

Answer: The annual interest rate is 7.17%.

Note: If you make a mistake, press L to erase the number

and enter the correct number to continue. After pressing the TVM variable key, you must re-enter values from the beginning.

@ f

I/Y=

717

Page 27

Calculating basic loan payments

Calculate the quarterly payment for a $56,000 mortgage loan at 6.5% compounded quarterly during its 20-year amortization period.

PV = $56,000

I/Y = 6.5%

PMT = ?

N = 4 × 20 years = 80

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set the number of payments per year to 4.

Conﬁ rm the number of compounding periods per year.

Quit the P/Y and C/Y settings.

Calculate the total number of payments and store in N.

Enter the present value.

. w

. <

56000

FV = 0

......

000

P/Y=

400

C/Y=

400

000

ANS~N

8000

56———~PV

5600000

Enter the future value.

—~FV

000

Enter the annual interest rate.

Calculate the quarterly payment.

Answer: The quarterly payments are $1,255.86.

6.5

@ u

6.5~I/Y

650

PMT=

-125586

Page 28

Calculating future value

You will pay $200 at the end of each month for the next three years into a savings plan that earns 6.5% compounded quarterly. What amount will you have at the end of period if you continue with the plan?

FV = ?

I/Y = 6.5% (quarterly)

PV = 0

......

PMT = –$200

N = 12 × 3 years = 36

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set the number of payments per year to 12.

Set the number of compounding periods per year to 4.

Quit the P/Y and C/Y settings.

Calculate the total number of payments and store in N.

Enter the present value.

. w

. <

000

P/Y=

1200

C/Y=

400

000

ANS~N

3600

—~PV

000

Enter payment.

200

(-2——)~PMT

-20000

Enter the annual interest rate.

Calculate the future value.

Answer: You will have $7,922.19 at the end of the three-year

period.

6.5

@ t

6.5~I/Y

650

FV=

792219

Page 29

Calculating present value

You open an account that earns 5% compounded annually. If you wish to have $10,000 twenty years from now, what amount of money should you deposit now?

FV = $10,000

N = 20 years

PV = ? I/Y = 5%

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set the number of payments per year to 1.

The number of compounding periods per year is automatically set to 1. Press s to exit the P/Y and C/Y settings.

Enter the total number of payments.

Enter the future value.

. w

10000

000

P/Y=

100

2—~N

2000

1————~FV

1000000

Set payment to zero.

—~PMT

000

Enter the annual interest rate.

Calculate the present value.

Answer: You should deposit $3,768.89 now.

5~I/Y

500

PV=

-376889

Page 30

Specifying payments due (

This calculator can select ordinary annuity or annuity due depending on the regular cash ﬂ ow (payment) conditions.

. "

)

Ordinary annuity (END):

This is the default setting for ﬁ nancial calculations. BGN is not displayed. A regular cash ﬂ ow (payment) is received at end of each payment period. Often applied to loan calculations, etc.

Annuity due (BGN): BGN appears on the display. A regular cash ﬂ ow (payment) is

received at the beginning of each payment period. Often applied to the ﬁ nance lease of an asset.

To toggle between ordinary annuity and annuity due, press

Note: The above selection only affects the TVM solver.

Ordinary annuity

Your company wishes to accumulate a fund of $300,000 over the next 18 months in order to open a second location. At the end of each month, a ﬁ xed amount will be invested in a money market savings account with an investment dealer. What should the monthly investment be in order to reach the savings objective, assuming the account will earn 3.6% interest compounded monthly?

FV = $300,000

PV = 0

I/Y = 3.6%

......

PMT = ?

N = 18

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set the number of payments per year to 12.

The number of compounding periods per year is automatically set to

12. Press s to exit the P/Y and C/Y settings.

. w

000

P/Y=

1200

Page 31

Procedure Key operation Display

Enter the total number of payments.

Enter the future value.

300000

18~N

1800

3—————~FV

30000000

Set the present value to zero.

Enter the annual interest rate.

Calculate payment.

3.6

@ u

—~PV

000

3.6~I/Y

360

PMT=

-1624570

Answer: The monthly investment should be $16,245.70.

Calculating lease payments (Annuity due)

You plan to purchase a new car with a value of $87,918 on a 60-month lease. If the annual interest rate is 6.75%, the contractual purchase option price at lease end is $17,500, and payment is due at the beginning of each month, how much should you pay each month?

PV = $87,918

I/Y = 6.75%

....................

PMT = ?

N = 60

Procedure Key operation Display

Set all the variables to default values.

Set to annuity due (BGN is displayed).

Set the number of payments per year to 12.

. "

. w

FV = –$17,500

P/Y=

1200

000

Page 32

Procedure Key operation Display

The number of compounding periods per year is automatically set to

12. Press s to exit the P/Y and C/Y settings. Enter the total number

of payments.

Enter the future value.

Enter the present value.

Enter the annual interest rate.

Calculate payment.

Answer: You should pay $1,476.20 each month.

Calculating the present value of a lease with

Your client wishes to buy a machine currently leased from your company. On a ﬁ ve-year lease with payments of $200 at the beginning of each month, the machine has a trade-in value of $1,500 with 34 monthly payments remaining. If your company sells the machine at the present value of the lease, discounted at an annual interest rate of 18%, compounded monthly, how much should your company charge for the machine?

trade-in value

PMT = –$200

87918

6.75

@ u

PV = ?

17500

I/Y = 18%

......

N = 34

—~N

6000

175

——)~FV

-1750000

87918

~PV

8791800

6.75

~I/Y

675

PMt=

-147620

FV = –$1,500

Page 33

Procedure Key operation Display

Set all the variables to default values.

Set to annuity due (BGN is displayed).

Set the number of payments per year to 12.

The number of compounding periods per year is automatically set to

12. Press s to exit the P/Y and C/Y settings.

Enter the total number of payments.

Enter payment.

Enter the annual interest rate.

Enter the future value. ,

Calculate the present value.

. "

. w

200

1500

000

P/Y=

1200

3400

(-2——)~PMt

20000

~I/Y

1800

(-15——)~FV

-150000

PV=

627995

Answer: $6,279.95 should be charged for the machine.

Calculating down payment and amount to

borrow

You wish to buy a house for $180,000. The ﬁ nance company charges a 5.5% APR, compounded monthly, on a 25-year loan. If you can afford a monthly payment of $900, how much can you borrow? How much do you need for a down payment?

PV = ?

PMT = –$900

N = 12 × 25 years = 300

I/Y = 5.5%

......

FV = 0

Page 34

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set the number of payments per year to 12.

The number of compounding periods per year is automatically set to 12. Press s to exit the P/Y and C/Y settings.

Enter the total number of payments.

Enter payment.

. w

25 . <

s N

900

000

P/Y=

1200

ANS~N

30000

(-9——)~PMT

-90000

Enter the annual interest rate.

Set the future value to zero.

Calculate the present value.

Calculate the down payment.

Answer: You can borrow $146,558.92 in total. The price of the

house is $180,000, so: Down payment = $180,000 – present value = $180,000 – $146,558.92 You need $33,441.08 for a down payment.

5.5

180000

5.5~I/Y

550

—~FV

000

PV=

14655892

18————-PV=

3344108

Page 35

Amortization Calculations

Calculate and create amortization schedules using values stored in the TVM solver.

Note: Prior to using amortization, you need to enter values into

TVM variables.

Variables used in amortization

Variable Description Default value

AMRT P1 Start of payment (nth time) 1 AMRT P2 End of payment (nth time) 1 BALANCE Remaining balance after payment —

PRINCIPAL Principal paid —

INTEREST Interest paid over the speciﬁ ed periods —

• BALANCE, ΣPRINCIPAL and ΣINTEREST are calculated automatically, so no default values are set.

• AMRT P1 and AMRT P2 must be between 1 and 9,999.

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

• All the TVM solver variables retain their previously entered values. If you wish to clear all the data, press

2. Select ordinary annuity or annuity due using

3. Enter the appropriate numeric values for the variables used

in the TVM solver.

• Conﬁ rm the values of N, I/Y, PV, PMT, FV, P/Y and C/Y.

4. Press * to use amortiza- tion calculation.

5. Enter a value for “AMRT P1” and press Q.

6. Press i, enter a value for “AMRT P2” and press Q.

7. Display values for BALANCE, ΣPRINCIPAL and ΣINTEREST

by pressing i once for each. Each value is calculated automatically.



AMRt P1=

100

Page 36

8. Press i to calculate the next period of the amortization schedule.

9. Repeat steps 5 to 7 above.

• If you press @ during “AMRT P1” and “AMRT P2” entry,

the values for the next period of payment will be automatically calculated and displayed.

• To end amortization calculations, press s. Pressing s

during entry will clear the value entered.

Calculating mortgage payments and generat-

ing an amortization schedule

1. Calculate the monthly payment of a 20-year loan with a loan

amount of $90,000 and a 5.45% APR.

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set TVM solver variables and calculate payment.

. w

20 . <

90000

5.45

t u

12 Q

f @

000

PMT=

-61656

Answer: The monthly payment is $616.56.

Now generate an amortization schedule for the ﬁ rst 5 years of the loan. If the ﬁ rst payment is in August, the ﬁ rst year has 5 payment periods and the following years have 12 payment periods each.

2. Calculate the amortization schedule for the ﬁ rst year.

Procedure Key operation Display

Change to amortization calculation and enter 1 (August) for the starting payment.

Enter 5 (December) for the ending payment.

Display the remaining balance.

AMRT P1=

100

AMRT P2=

500

BALANCE=

8895148

Page 37

Procedure Key operation Display

Display the principal paid.

Display the interest paid.

3. Calculate the amortization schedule for the second year.

Procedure Key operation Display

Change amortization schedule to the second year and enter 6 (January) for the starting payment.

Enter 17 (December) for the ending payment.

Display the remaining balance.

Display the principal paid.

Display the interest paid.

4. Calculate the amortization schedule for the third year.

Procedure Key operation Display

Change amortization schedule to the third year and enter the next 12 months automatically.

Display the remaining balance.

Display the principal paid.

Display the interest paid.

5. Repeat the above operation for the fourth and ﬁ fth years.

i @ i

ÍPRINCIPAL=

-104852

ÍINTEREST=

-203428

AMRT P1=

600

AMRT P2=

1700

BALANCE=

8633592

ÍPRINCIPAL=

-261556

ÍINTEREST=

-478316

AMRT P2=

2900

BALANCE=

8357421

ÍPRINCIPAL=

-276171

ÍINTEREST=

-463701

Page 38

Calculating payments, interest, and loan bal-

ance after a speciﬁ ed payment

You have taken out a 30-year loan for $500,000, with an annual interest rate of 8.5%. If, after the 48th period, you want a balloon payment due, what amount of monthly payment must you make with monthly compounding and how much will the balloon payment be?

Procedure Key operation Display

Set all the variables to default values.

Make sure ordinary annuity is set (BGN is not displayed).

Set TVM solver variables and calculate payment.

s .

. w

30 . <

500000

8.5

t u

12 Q

f @

PMT=

000

-384457

Answer: The monthly payment is $3,844.57.

Now generate an amortization schedule from the ﬁ rst to the 48th payments.

Procedure Key operation Display

Change to amortization calculation and enter 1 for the starting payment.

Enter 48 (December) for the ending payment.

Display the balance after 48 months. (balloon payment)

Display the principal paid over 48 months.

Display the interest paid over 48 months.

AMRT P1=

100

AMRT P2=

4800

BALANCE=

48275524

ÍPRINCIPAL=

-1724476

ÍINTEREST=

-16729460

Answer: The balloon payment after the 48th period would be

$482,755.24.

Page 39

Discounted Cash Flow Analysis

–

Analyze unequal cash ﬂ ows and calculate the net present value (NPV) and the internal rate of return (IRR).

Note: Use the TVM solver for equal and regular cash ﬂ ow

analysis (see page 22).

Entering cash ﬂ ow data

To ﬁ nd NPV and IRR using discounted cash ﬂ ow analysis, enter cash ﬂ ow data, one data item at a time, in the following format:

Single cash ﬂ ows

Cash ﬂ ow value

Repeated cash ﬂ ows

Cash ﬂ ow value > frequency value

Notes:

• Before entering data, press > . b to clear any

previously entered cash ﬂ ow data.

• Press , to enter a negative cash ﬂ ow (outﬂ ow).

• Make sure the calculator is in NORMAL mode. It is not pos-

sible to enter cash ﬂ ow data when listed ﬁ nancial variables are shown on the display. Press s to exit.

• You can enter a total of up to 100 cash ﬂ ow and/or statistical

data items. A single cash ﬂ ow value is counted as one data item, while a cash ﬂ ow value with an associated frequency value is counted as two.

• Frequency values must be integers between 1 and 999.

• If you wish to correct a value before pressing J, press

Entering cash ﬂ ow data

Enter cash ﬂ ow data according to the following cash ﬂ ow diagram.

to delete the entry and enter the correct value.

$7,000 $9,000 $5,000 $5,000

$8,000

$25,000

Page 40

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Enter cash ﬂ ow data.

7000

25000

000

DATA SET:CF

000

DATA SET:CF

100

9000

DATA SET:CF

200

5000

> 2

DATA SET:CF

300

8000

DATA SET:CF

400

If there is cash ﬂ ow data stored, press > . b to

clear it.

The format of the data set (cash ﬂ ow and frequency values)

number, which is initially set to “0.00,” is dependent on calculator display notation settings.

Conﬁ rming and editing data

Conﬁ rming data

Press > to display any previously entered cash ﬂ ow data. The data is displayed in order by data item (identiﬁ er, number, and value). Use z/i to display a data item from a previously entered data set.

Cash flow

identifier

Frequency

identifier

CF D—=

-2500000

CF N—=

100

Data set number

Cash flow value

Data set number

Frequency value

Page 41

• Press . z or . i to jump to the ﬁ rst or the last

–

data item, respectively.

• Each data item is displayed in the form CF Dn= (cash ﬂ ow

value) or CF Nn= (frequency), where n indicates the data set number.

Editing data

• Display the data item you wish to modify by using z/i,

enter a new value and press J.

• If a frequency value is set to zero, then the associated data

set is deleted.

Deleting data

• Display the data item to be deleted by using z/i, and

press . ?.

• If a cash ﬂ ow value/frequency is deleted, the corresponding

frequency/cash ﬂ ow value is also deleted.

• If you wish to delete all data, press . b.

Inserting data

Using the z and i keys, specify the correct place to insert your new data by displaying the value that is to come directly after, and then press . e. A new data set with a cash ﬂ ow value of zero and a frequency value of one will be inserted. Modify the new data set to include your data.

Correcting cash ﬂ ow data

Currently the cash ﬂ ow data is that shown in chart A. Change it according to chart B.

Chart A

$7,000 $9,000 $5,000 $5,000 $8,000

Chart B

$7,000 $9,000 $6,000 $5,000 $8,000

$25,000

Display previously entered cash ﬂ ow data. (Example on page 37)

–$30,000

Procedure Key operation Display

s >

CF D—=

-2500000

Page 42

Procedure Key operation Display

Change the ﬁ rst cash ﬂ ow value from –25,000 to –30,000.

Change the frequency of 5000 from 2 to 1.

Add a new data set (6000) immediately before 5000.

30000

i i i i i i i

. e

6000

CF D—=

-3000000

CF N3=

CF D3=

600000

100

To conﬁ rm the corrections, press . z to jump to the ﬁ rst data item and press i to browse through each data item.

Variables used in discounted cash ﬂ ow analysis

Variable Description Default value

RATE (I/Y) Internal rate of return (IRR) 0 NET_PV Net present value (NPV) —

• The variable RATE (I/Y) is shared by the variable I/Y. NET_PV

is for calculation only and has no default value.

• The BGN/END setting is not available for discounted cash ﬂ ow

analysis.

NPV and IRR

The calculator solves the following cash ﬂ ow values:

Net present value (NPV):

The total present value of all cash ﬂ ows, including cash paid out (outﬂ ows) and cash received (inﬂ ows). A proﬁ table investment is indicated by a positive NPV value.

Internal rate of return (IRR):

The interest rate that gives a net present value of zero.

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

Page 43

2. Enter cash ﬂ ow data.

–

• Refer to page 37 for instructions on entering cash ﬂ ow data.

3. Press . < to begin discounted cash ﬂ ow analysis.

• If a previously entered cash ﬂ ow value is displayed, press to exit and then press . <.

4. To ﬁ nd NPV or IRR, do the following:

To obtain NPV:

Enter the interest rate (discounted rate) into RATE(I/Y) and press Q. Move to NET_PV and calculate by pressing i and @.

To obtain IRR:

Press @ to calculate IRR (RATE(I/Y)).

Note: If “Error 5” is displayed in step 4, or if you want to ﬁ nd

another IRR, enter an estimated value into RATE(I/Y) and calculate again in step 4.

Solving for unequal cash ﬂ ows

Your company pays $12,000 for a new network system, and expects the following annual cash ﬂ ows: $3,000 for the ﬁ rst year, $5,000 for the second to fourth years, and $4,000 for the ﬁ fth year. At what IRR does the net present value of the cash ﬂ ows equal zero?

$3,000 $5,000 $5,000 $5,000

$4,000

$12,000

1. Enter cash ﬂ ow data.

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

000

Page 44

Procedure Key operation Display

Enter cash ﬂ ow data.

12000

DATA SET:CF

000

3000

DATA SET:CF

100

5000

> 3

DATA SET:CF

200

4000

DATA SET:CF

300

Return to the initial display in NORMAL mode.

If there is cash ﬂ ow data stored, press > . b to

clear it.

2. Calculate IRR.

Procedure Key operation Display

Select discounted cash ﬂ ow analysis, and set all the variables to default values.

Calculate IRR (RATE (I/Y)).

Answer: The net present value of the cash ﬂ ows equals zero at

an IRR of 23.14%.

Calculating the present value of variable cash

Your company has prepared forecasts for the development costs and operating proﬁ ts of the next generation of your product. Development costs for each of the next three years (Years 1 to

3) will be $50,000. Manufacturing equipment costing $100,000 will be purchased at the end of Year 3. Annual proﬁ ts for the ﬁ ve-year product life (from Year 4 to Year 8) are projected to be $80,000. The salvage value of the manufacturing equipment at the end of Year 8 is $20,000. Given a 12% discount rate, should your company proceed with the product development?

ﬂ ows

. < .

000

RATE(I/Y)=

000

RATE(I/Y)=

2314

Page 45

$80,000 $80,000 $80,000 $80,000 $80,000

–

$50,000

–$50,000

–$100,000

1. Enter the cash ﬂ ow data.

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Enter cash ﬂ ow data.

Return to the initial display in NORMAL mode.

If there is cash ﬂ ow data stored, press > . b to

, J

80000

60000

50000

150000

> 4

> 2

DATA SET:CF

clear it.

2. Calculate NPV.

Procedure Key operation Display

Select discounted cash ﬂ ow analysis, and set all the variables to default values.

Enter the discount rate.12

Calculate NPV (NET_PV).

. < .

i @

RATE(I/Y)=

NET_PV=

Answer: As NPV = 6,627.52 > 0, the product can be developed.

–$20,000

000

100

200

300

000

1200

662752

Page 46

Bond Calculations

Using bond calculations, you can obtain bond prices, yields to maturity, and accrued interest.

Variables used in bond calculations

Variable Description Default value

COUPON (PMT) Annual coupon rate (%) 0 REDEMPT (FV) Redemption value 0

M-D-Y 1 Settlement date (date of bond pur-

M-D-Y 2 Redemption date 1-1-2001 CPN/Y (N) Number of coupons per year 1 YIELD (I/Y) Yield to maturity (%) 0 PRICE (PV) Bond price 0 ACCU INT Accrued interest —

Redemption value of the security per $100 par value.

You can change the date format to D-M-Y (see page 10).

You can only enter “1” or “2” — “1” for annual coupons and “2”

for semi-annual coupons.

Per $100 par value.

Note: Bonds are associated with payment methods known as

chase)

coupons. A coupon is like an “interest-only payment,” and it is based on the future value of the bond. COUPON is a percentage of the bond par value, usually annually, by the owner of the bond. For bonds that have annual coupons, the owner receives one payment of the coupon amount each year. Some bonds have semi-annual coupons. For these, each year’s coupon amount is paid in two equal payments six months apart. The date on which a coupon payment is made is called the “coupon date.” The bond maturity date is usually the last coupon date.

Setting the day-count method

You can toggle between the actual calendar (365 days plus leap years) and a 360-day calendar (12 months of 30 days each) using . &. The actual calendar is set by default (360 is not displayed). The calendar range is from January 1, 1901 to December 31, 2099.

1-1-2001

Page 47

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

2. Select bond calculations by pressing #.

• To end bond calculations, press s.

• If you press s during entry, any entered values will be cleared.

3. Change the day-count setting, if necessary, by pressing

. &

4. Enter the coupon rate (%) into COUPON (PMT) by entering the value and pressing Q.

5. Enter the redemption value into REDEMPT (FV) by pressing

6. Enter the date of bond purchase into M-D-Y 1 (or D-M-Y 1) by pressing i, entering the date, and pressing Q.

• For date entry, refer to page 47, ”Entering dates”.

7. Enter the redemption date into M-D-Y 2 (or D-M-Y 2) by pressing i, entering the date, and pressing Q.

• For date entry, refer to page 47, ”Entering dates”.

8. Enter the number of coupon payments per year into CPN/Y (N) by pressing i, entering the value, and pressing Q.

9. To ﬁ nd bond price or yield to maturity, do the following:

To obtain bond price (PRICE (PV)):

Enter annual yield (%) into YIELD(I/Y) by pressing i, entering the value, and pressing Q. Move to PRICE (PV) and calculate by pressing i and @. Display the accrued interest (ACCU INT) by pressing i. The accrued interest is calculated automatically.

To obtain yield to maturity (YIELD (I/Y)):

Move to PRICE (PV) and enter the bond price by pressing i

yield, YIELD (I/Y) and calculate by pressing z @. Display the accrued interest (ACCU INT) by pressing i i. The accrued interest is calculated automatically.

, entering the value, and pressing Q.

, entering the value, and pressing Q. Move to annual

COUPON(PMt)=

000

Page 48

Calculating bond price and accrued interest

A $100, 20-year, 6.5% coupon bond is issued to mature on August 15, 2023. It was sold on November 3, 2006 to yield the purchaser

7.2% compounded semiannually until maturity. At what price did

the bond sell? Also calculate the accrued coupon interest.

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Select bond calculations.

Make sure the actual calendar is set (360 is not displayed). Enter the coupon rate

(%).

Enter the redemption value.

Enter the settlement date.

Enter the redemption date.

Enter the number of coupon payments per year.

Enter the annual yield (%).

Calculate bond price.

6.5

100

11032006

08152023

7.2

i @

COUPON(PMT)=

REDEMPT(FV)=

M-D-Y 1=[FR]

11- 3-2006

M-D-Y 2=[TU]

8-15-2023

CPN/Y(N)=

YIELD(I/Y)=

PRICE(PV)=

000

650

10000

200

720

9323

Calculate the accrued interest.

Calculate bond price including accrued interest.

Answer: The bond sold at $93.23 and the accrued coupon

interest was $1.41 (the bond price including accrued interest would be $94.64).

The asking price on the above bond is $92.50. What will your yield be?

i /

ACCU INT=

141

PV+ANS=

9464

Page 49

Procedure Key operation Display

Change the bond price to $92.50.

Calculate the yield.

# i i i i i i Q

z @

92.5

PRICE(PV)=

9250

YIELD(I/Y)=

728

Answer: The yield will be 7.28%.

Entering dates

Refer to the following notes for date entry.

• Enter using US date format (MM-DD-YYYY) or EU date for-

mat (DD-MM-YYYY). Refer to the previous example and the following explanation.

Month entry

Enter two digits. From 2 to 9, the preceding zero may be omitted.

Day entry

Enter two digits. From 4 to 9, the preceding zero may be omitted.

Year entry

Enter four digits. From 2010 to 2099, the zero following the ﬁ rst “2” may be omitted. From 1901 to 1989, the “9” following the ﬁ rst “1” may be omitted.

• After entry, the date will be stored and the abbreviated day of

the week will be displayed.

• [SU]: Sunday, [MO]: Monday, [TU]: Tuesday, [WE]: Wednesday, [TH]: Thursday, [FR]: Friday, [SA]: Saturday.

• The default value for dates is: January 1, 2001 (1-1-2001).

• The effective range of dates is: January 1, 1901 to December 31, 2099.

• If an inappropriate date is entered (e.g., February 31), an error message (Error 7) will appear immediately after pressing Q. In this case, follow either of the following procedures:

• Press s to return to the display before the entry, enter

the appropriate date, and press Q.

• Press g/y to go back to the display that was shown

before you pressed Q. Press s or L, enter the appropriate date, and press Q again.

• If you wish to correct numbers during entry, use L as a backspace key.

Page 50

Depreciation Calculations

Using depreciation calculations, you can obtain depreciation base values using three types of calculation methods: the straight-line method, the sum-of-the-years’ digits method, and the declining balance method.

Variables used in depreciation calculations

Variable Description Default value

DB (I/Y) Interest per year 0 LIFE (N) Years of depreciation 1 START MONTH Starting month 1 COST (PV) Cost of asset 0 SALVAGE (FV) Salvage value 0 YEAR DEPRECIATE Depreciation value of above year — RBV Remaining book value — RDV Remaining depreciation value —

DB (I/Y) appears only when you select DB (declining balance

Year for calculating depreciation value

method) for the depreciation method.

Setting the depreciation method

• Select the depreciation method in the SET UP menu. It is initially set to SL.

Key operation Description

~ 2 0

~ 2 1

~ 2 2

SL (Straight-line method) SYD (Sum-of-the-years’ digits method) DB (Declining balance method)

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

Page 51

2. Select the depreciation method (see page 48).

3. Select depreciation calculations

by pressing O.

• When using the declining balance method, DB (I/Y) appears. Enter the number and press Q.

• To end depreciation calculations, press s. If you press

during entry, any entered values will be cleared.

4. Enter the number of years of depreciation into LIFE (N) by pressing i, entering the value, and pressing Q.

• When using the straight-line method, the value should be a

positive real number, while for the SYD or DB methods, it should be a positive integer.

5. Enter the starting month into START MONTH by pressing

, entering the value, and pressing Q.

• You can enter values between 1 and 13.

• Generally, it is not necessary to enter a decimal value.

However, if you wish to enter, for example, the middle of July, enter 7.5; where the decimal is equal to the number value of the given date divided by the total number of days in the month.

6. Enter the cost of asset into COST (PV) by pressing i, entering the value, and pressing Q.

7. Enter the salvage value into SALVAGE (FV) by pressing i, entering the value, and pressing Q.

8. Enter

the year for calculating depreciation value

pressing i, entering the value, and pressing Q.

•

The year for calculating depreciation value Pressing @ increments this number by 1.

•

This value must be a positive integer

9. Calculate depreciation for the year by pressing i.

10. Calculate the remaining book value by pressing i.

11. Calculate the remaining depreciation by pressing i.

12. To calculate depreciation value for another year, press z

three times to go back to YEAR, enter a value for the new year, and recalculate.

----------

into YEAR by

is initially 1.

Page 52

Calculating straight-line depreciation

In April, your company begins depreciation of a commercial building with a 30-year life and no salvage value. The building costs $1,500,000. Calculate the depreciation amount, remaining book value and remaining depreciable value for the third year using the straight-line depreciation method.

Procedure Key operation Display

Bring up the initial display in NORMAL mode, and select the straight-line depreciation method.

Select depreciation calculations.

Enter the number of years of depreciation.

Enter the starting month.

Enter the cost of asset. i

s ~ 2 0

1500000

000

----------

LIFE(N)=

3000

START MONTH=

400

COST(PV)=

150000000

Enter the salvage value.i 0

SALVAGE(FV)=

000

Enter t

he year for calcu-

lating depreciation value

Calculate depreciation for the year.

Calculate the remaining book value.

Calculate the remaining depreciation value.

Answer: At the third year, the depreciation amount is $50,000,

the remaining book value is $1,362,500, and the remaining depreciable value is $1,362,500.

YEAR=

300

DEPRECIATE=

5000000

RBV=

136250000

RDV=

136250000

Page 53

Conversion between APR and EFF

Interest rates can be converted between APR (annual, or nominal percentage rate) and EFF (effective interest rate).

• The APR is an investment’s annual rate of interest when com-

pounding happens only once a year. The interest rate printed on a bond is an example of an APR.

• The EFF is an investment’s annual rate of interest when com-

pounding happens more often than once a year. It reﬂ ects the actual amount of return for a given nominal rate. For example, if your investment compounds monthly, then the stated nominal percentage rate becomes a monthly rate, and the EFF reﬂ ects your actual annual rate of return.

Basic operations

1. Press s to clear the display. Make sure the calculator is

in NORMAL mode.

2. Enter the calculation data in the following format:

• To change APR to EFF:

Number of compounding periods per year > Nominal

percentage rate .

• To change EFF to APR:

Number of compounding periods per year > Effective

interest rate .

Converting between APR and EFF

Procedure Key operation Display

Calculate the effective interest rate for twelve compounding periods with an 18% APR.

Convert this rate back to the original APR.

12 > 18 .

19.56

12,18¬EFF

12,19.56¬APR

1956

1800

Page 54

Day and Date Calculations

Using day and date calculations, you can ﬁ nd dates and the numbers of days between dates.

Variables used in day and date calculations

Variable Description Default value

M-D-Y 1 The ﬁ rst date 1-1-2001

M-D-Y 2 The last date 1-1-2001 DAYS Number of days 0

You can change the date format to D-M-Y (see page 10).

Setting the day-count method

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

2. Select day and date calculations by pressing K.

• To end day and date calcula-

tions, press s. If you press

during entry, any entered values will be cleared.

3. Change the day-count method, using . &, if neces- sary.

4. Enter the values of any two known variables: the ﬁ rst date, the last date, or the number of days.

• For date entry, refer to page 47, ”Entering dates”.

5. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate.

• If the calculator is set to 360-day calendar mode (360 is

displayed), it is not possible to obtain either the ﬁ rst or last dates, only the number of days.

M-D-Y1=[MO]

1- 1-2001

Page 55

Calculating number of days

Calculate the number of days between December 25, 2008 and August 10, 2009 (using US date format and the actual calendar).

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Select day and date calculations, and set all the variables to default values.

Make sure the actual calendar is set (360 is not displayed).

Enter the ﬁ rst date.

K .

12252008

000

M-D-Y 1=[MO]

1- 1-2001

M-D-Y 1=[TH]

12-25-2008

Enter the last date.

8102009

M-D-Y 2=[MO]

8-10-2009

Move to DAYS and calculate.

Answer: 228 days

• If the 360-day calendar is selected, the answer will be 225 days.

Finding a date

Find the date 100 days after November 13, 2010 (using US date format and the actual calendar).

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Select day and date calculations, and set all the variables to default values.

Make sure the actual calendar is set (360 is not displayed).

Enter the ﬁ rst date.

i @

K .

1113210

DAYS=

22800

000

M-D-Y 1=[MO]

1- 1-2001

M-D-Y 1=[SA]

11-13-2010

Move to DAYS and enter the number of days.

i i

100

DAYS=

10000

Page 56

Procedure Key operation Display

Move to the last date and calculate.

Answer: The last date is February 21, 2011.

z @

M-D-Y 2=[MO]

2-21-2011

Percent Change/Compound Interest Calculations

Using percent change/compound interest calculations, you can determine the values of percentage rates of change (increase or decrease) or interest rates compounding periodically.

Variables used in percent change/compound interest calculations

Variable Description Default value

OLD PRC (PV) Old price (old value) 0 NEW PRC (FV) New price (new value) 0 % (I/Y) Percent change 0 PERIODS (N) Number of compounding periods 1

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

2. Select percent change/ compound interest calculations by pressing . B.

• To end percent change/compound interest calculations, press s.

• If you press s during entry, any entered values will be cleared.

3. Enter the values of any three known variables: old price, new price, percent change, or number of compounding periods.

4. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate.

OLD PRC(PV)=

000

Page 57

Calculating percent change

Sales in a company were $75,000 during the ﬁ rst year of operation. The second year’s sales were $116,000. What percentage greater were the second year’s sales than ﬁ rst year’s sales? In this calculation, the number of compound periods is set to 1 (default).

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Select percent change/ compound interest calculations, and set all the variables to default values.

Enter the old value.

75000

B .

000

OLD PRC(PV)=

000

OLD PRC(PV)=

7500000

Enter the new value.

116000

NEW PRC(FV)=

11600000

Calculate the percent change.

Answer: The second year’s sales increased by 54.67% over

the ﬁ rst year’s sales.

Calculating compound interest rate

You opened an account compounding annually and deposited $8,000 eighteen years ago. You currently have $9,800. What is the compound interest rate?

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

Select percent change/ compound interest calculations, and set all the variables to default values.

Enter the old value.

i @

B .

8000

%(I/Y)=

5467

000

OLD PRC(PV)=

000

OLD PRC(PV)=

800000

Page 58

Procedure Key operation Display

Enter the new value.

9800

NEW PRC(FV)=

980000

Set the number of compound periods to 18.

Calculate the compound interest rate.

Answer: The compound interest rate is 1.13%.

i i

z @

PERIODS(N)=

1800

%(I/Y)=

113

Cost/Sell/Margin/Markup Calculations

Using cost/sell/margin/markup calculations, you can determine costs, selling prices, margins and markup.

Variables used in cost/sell/margin/markup calculations

Variable Description Default value

COST Cost 0 SELL Selling price 0 MARGIN Proﬁ t margin (%) 0 MARK UP Markup (%) —

Proﬁ t margin (%) is calculated based on selling price.

Markup (%) is calculated based on cost.

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

2. Select cost/sell/margin/ markup calculations by pressing I.

• To end cost/sell/margin/markup calculations, press s.

• If you press s during entry, any entered values will be cleared.

COSt=

000

Page 59

3. Enter the values of any two known variables as follows:

Unknown variable Known variables

COST SELL, and MARGIN or MARK UP SELL COST, and MARGIN or MARK UP MARGIN COST and SELL MARK UP COST and SELL

Because only either MARGIN or MARK UP is used in any

cost/sell/margin/markup calculation, the unused variable is given a value of “----------”. Initially, MARK UP is set to “--------

--”. If you enter a value for MARK UP, MARGIN is set to “-----

-----”, and vice versa.

4. Move to the variable you wish to calculate, using the z and i keys, and press @ to calculate.

Determining selling price

In a furniture business, it is desirable to realize a 95% markup from cost to retail price for each item. A certain sofa costs $455.60. What should its selling price be?

Procedure Key operations Display

Bring up the initial display in NORMAL mode.

Select cost/sell/margin markup calculations, and set all the variables to default values.

Enter cost.

I .

455.6

000

COST=

000

COST=

45560

Enter markup rate.

Calculate selling price.z z

i i i Q

MARK UP=

9500

SELL=

88842

Answer: The selling price should be $888.42.

Page 60

Breakeven Calculations

Using breakeven calculations, you can calculate ﬁ xed cost, variable cost per unit, unit price, proﬁ t and quantity.

Variables used in breakeven calculations

Variable Description Default value

FIXED Fixed cost 0 VARIABLE Variable cost per unit 0 PRICE Unit price 0 PROFIT Proﬁ t0 QUANTITY Quantity 0

Basic operations

Refer to page 19 for basic variable operations.

1. Press s to clear the display.

• Make sure the calculator is in NORMAL mode.

2. Select breakeven calculations by pressing $.

• To end breakeven calculations, press s.

• If you press s during entry, any entered values will be cleared.

3. Enter the values of any four known variables.

4. Move to the variable you wish to calculate, using the z

and i keys, and press @ to calculate.

Calculating the breakeven point

Your company has developed a new product and plans to sell it at a price of $120 per unit. The variable cost per unit is $75.80 and the ﬁ xed costs total $15,000. What is the breakeven point for this product?

Procedure Key operation Display

Bring up the initial display in NORMAL mode.

FIXED=

000

Page 61

Procedure Key operation Display

Select breakeven calculations, and set all the variables to default values.

Enter ﬁ xed cost.

$ .

15000

FIXED=

000

FIXED=

1500000

75.80

120

VARIABLE=

7580

PRICE=

Enter variable cost per unit.

Enter unit price.

12000

Leave proﬁ t as is.

PROFIT=

000

Calculate quantity.

i @

QUANTITY=

33937

Answer: The breakeven point of this product is 339.37 units.

Page 62

Chapter 4

Scientiﬁ c Functions

This calculator has a variety of functions. Press m 0 to select NORMAL mode and perform scientiﬁ c calculations.

• For basic calculations, see page 11.

• When a listed ﬁ nancial variable is displayed, you can enter the result of a scientiﬁ c calculation into it by pressing Q immediately after completing the calculation.

• Scientiﬁ c calculations can also be performed in STAT mode.

• The examples in this chapter are all performed under the SET UP menu’s default settings. Before starting calculation, press

to clear the display.

Constant Calculations

Example Key operation Result

34 + 57

57 =

45 + 57 =

68 × 25 =

68 × 40 =

• In constant calculations, the addend becomes a constant. Subtraction and division behave the same way. For multiplication, the multiplicand becomes a constant.

• In constant calculations, constants will be displayed as .

x 25

Chain Calculations

A calculation result (ANS memory) can be used in a subsequent calculation. However, it cannot be recalled after entering multiple instructions.

Example Key operation Result

4 = ANS

ANS

5 =

8 × 2 = ANS

ANS

44 + 37 = ANS ANS =

x 2

;

+ 37

. } =

+ =

9100

10200 170000

272000

1000 1500

1600

25600

8100

900

Page 63

Scientiﬁ c Calculations

Example Key operation Display

sin 60 [°] =

cos — [rad] =

tan–1 1 [g] =

tan–1 1 [°] =

• The range of the results of inverse trigonometric functions

DEG –90 ≤ θ ≤ 90 0 ≤ θ ≤ 180

RAD

GRAD –100 ≤ θ ≤ 100 0 ≤ θ ≤ 200

Example Key operation Result

(cosh 1.5

sinh 1.5)

tanh–1 — =

log 50 =

In 20 =

1.7

e3 =

161

— + — =

8–2 – 34 × 52 =8 . @ , 2 - 3

1 4

(123)– =

49 –

81 =. } 49 - 4 . :

s . { =

~ 1 1 . c ( .

~ 1 2 .

~ 1 0 .

–1

= sin

, θ = tan

π2π

– — ≤ θ ≤ —

s ( . ] c + . ] {

;

. ] ) =

. h

. d

1.7

. :

. R

. ; + 7 . ;

. =

. ; =

@ 4 x 5 . ;

. @ 3 . @ 4

)

(

–1

1.5

)

8 7

sin60=

cos(π©4)=

tan

-|1

= cos

0 ≤ θ ≤

087

071

5000

4500

–1

-202498

2009

090 170

300 5012 2009

031

645

400

Page 64

Example Key operation Result

4! =

10P3

5C2

What is 25% of 500?

What percentage of 400 is 120?

500 + (500 × 25%) =

400 – (400 × 30%) =

. o

. p 2

500

120

500

400

. q 3

x 25 .

400

+ 25 .

- 30 .

2400

72000

1000

12500

3000

62500

28000

Random Functions

This calculator has four kinds of random functions (the 2nd function of the - key).

Random numbers

A pseudo-random number, consisting of three signiﬁ cant digits from zero up to 0.999, can be generated by pressing . |

0 =

press = for each number. Press s to exit.

• To display numbers with three signiﬁ cant digits, set the display

Random dice

To simulate a die roll, a random integer between 1 and 6 can be generated by pressing . | 1 =. To generate further random numbers in succession, press = for each number. Press s to exit.

Random coin

To simulate a coin ﬂ ip, 0 (heads) or 1 (tails) can be randomly generated by pressing . | 2 =. To generate further random numbers in succession, press = for each number. Press s to exit.

. To generate further random numbers in succession,

notation settings to “ﬂ oating point”.

Page 65

Random integer

An integer between 0 and 99 can be generated randomly by pressing . | 3 =. To generate further random numbers in succession, press = for each number. Press

to exit.

Example Key operation Display

Pick a random number between zero and 9.99.

s . | 0

RANDOMx1—=

532

• The result will not be the same each time this operation is performed.

Modify Function

Calculation results are internally obtained in scientiﬁ c notation with a mantissa of up to 14 digits. However, because calculation results are displayed in the form designated by the display notation and the number of decimal places indicated, a displayed calculation result may differ from that held internally. By using the modify function (the 2nd function of the + key), the internal value is converted to match that of the display, so that the displayed value can be used without change in subsequent operations.

Example Key operation Result

5 8 9 =

8 9 =

. l x

056 500

056 504

9 = ANS

ANS

9 =

[FIX, TAB = 2]

5.5555555555555 × 10–1 × 9

0.56

Page 66

Chapter 5

Statistical Functions

Statistical calculations can be performed in STAT mode. The symbol will be visible if you are in STAT mode. There are seven sub-modes within STAT mode, corresponding to each of the functions below:

Key operation Sub-mode Display

m 1 0 m 1 1 m 1 2 m 1 3 m 1 4 m 1 5 m 1 6

SD: Single-variable statistics LINE: Linear regression QUAD: Quadratic regression EXP: Exponential regression LOG: Logarithmic regression PWR: Power regression INV: Inverse regression

Entering statistical data

Before you can perform statistical calculations, you will need to enter your data. In STAT mode, use > and J (the Q key) to enter the following:

For a single-variable data set:

Value

Value > frequency J (To enter multiples of the same value)

For a two-variable data set:

value > y value

value > y value > frequency J (To enter multiples

of the same x and y values)

Note: Before entering data, clear any previously entered data

from memory by doing either of the following:

• Press . b in STAT mode.

• Switch sub-modes within STAT mode.

Stat —

Stat 1

Stat 2

Stat 3

Stat 4

Stat 5

Stat 6

Page 67

• You can enter a total of up to 100 statistical and/or cash ﬂ ow data items. For single-variable data, a data set without a frequency is counted as one data item, and a data set with an assigned frequency is counted as two data items. For twovariable data, a data set without a frequency is counted as two data items, while a data set with an assigned frequency is counted as three data items.

• If you wish to correct a value before pressing J, press

or s to delete the entry, then enter the correct value.

Entering statistical data

Enter the data in the table to the right using the “Stat 0” sub-mode.

Procedure Key operation Display

Enter the “Stat 0” submode.

Enter statistical data.30

s m 1 0

DATA

30 40 40 50

Stat —

000

DATA SET=

100

> 2

DATA SET=

200

DATA SET=

300

Return to the “Stat 0” display.

If there is data stored in memory, press . b (within

STAT mode) to clear it.

The format of the data set (the sample and frequency values)

number, which is initially set to “1.00”, is dependent on calculator notation settings.

Stat —

000

Page 68

Conﬁ rming and editing data

• Use z / i to display a data item from a previously entered data set.

X1=

1000

Y1=

2000

FRQ1=

1100

• Press . z or . i to jump to the ﬁ rst or last data item, respectively.

• Each data item is displayed in the form: “Xn = (x value)”, “Yn = (y value)”, or “FRQn = (frequency)”, where “n” is the data set number.

Editing data

• Display the data item you wish to modify by using z / i, enter a new value and press J.

Deleting data

• Display the data item to be deleted by using z/i, and press . ?.

• If a value/frequency is deleted, the corresponding frequency/ value is also deleted.

• If you wish to delete all data, press . b.

Inserting data

Using the z and i keys, specify the correct place to insert your new data by displaying the value that is to come directly after, and then press . e. A new data set with a value of zero and a frequency of one will be inserted. Modify the new data set to include your data.

Data set number

x value

Data set number

y value

Data set number

Frequency

Page 69

Editing statistical data

Change the previously entered data from page 65 as follows:

DATA

30 40 40 50

Procedure Key operation Display

Display the statistical data.

Change the “40, 2” data set to “45, 3”.

Delete “50”.

i i i

i . ?

45 J

DATA

45 45 45 60

X1=

3000

FRQ2=

300

Stat —

000

Add “60”.

DATA SET=

300

Statistical Calculations and Variables

The following results can be obtained for each statistical calculation (refer to the table below):

Single-variable statistical calculations

Section 1 results only.

Linear regression calculations

Section 1 and 2 results, except for coefﬁ cients c. The estimate of y for a given x (estimate y´) and the estimate of

for a given y (estimate x´) can also be found.

Quadratic regression calculation

Section 1 and 2 results, and coefﬁ cients a, b, and c in the quadratic regression formula (y = a + bx + sion calculations, no correlation coefﬁ cient r can be obtained.

). In quadratic regres-

Page 70

The estimate of y for a given x (estimate y´) and the estimate of x for a given y (estimate x´) can also be found. When there are two x values, the COMP symbol will appear. Press @ to switch between x values.

Exponential regression, logarithmic regression, power regression, and inverse regression calculations

Section 1 and 2 results, except for coefﬁ cients c. The estimate of y for a given x (estimate y´) and the estimate

of x for a given y (estimate x´) can also be found. Because the calculator converts each formula into a linear regression before actual calculation takes place, it obtains all statistics — except coefﬁ cients a and b — from converted data rather than from entered data.

Variables Content

Number of samples

Mean of samples (x values)

Sample standard deviation (x values)

Population standard deviation (x values)

Sum of samples (x values)

Sum of squares of samples (x values)

Mean of samples (y values)

Sample standard deviation (y values)

Population standard deviation (y values)

Sum of samples (y values)

Sum of squares of samples (y values)

Sum of products of samples (x, y)

Coefﬁ cient of regression equation

Coefﬁ cient of quadratic regression equation

Correlation coefﬁ cient

• Use i or f to perform a variable calculation in STAT mode.

Page 71

Single-variable statistical calculation

Example Key operation Result

S a —

DATA SET=

(95 – x)

—

DATA

75 75 75

× 10 + 50 =

m 1 0 .

> 3

f =

f 2

[

f 4

;

95 - i

(

) 8 i

x 10 + 50

000

100

200

300

400

500

– x

7571

≈

1237

Í≈=

Í≈Œ=

700

53000

4120000

1336

Œ=

17857

6443

Page 72

Linear regression calculation

Example Key operation Result

S a

DATA SET=

3y´

46x´

m 1 1

DATA

252 > 5

12 2412 > 24

21 21 21

15 2515 > 25

= 3 y´ = ?

= 46 x´ = ?

40 40

f 4

f 5

> 40 > 3

000

100 200 300

400

500 105 183 100 854

1567

653

2462

Page 73

Quadratic regression calculation

Example Key operation Result

200

S a

DATA SET=

10y´

≈¡=

≈™=

≈¡=

m 1 2

DATA

12 4112 > 41

8138 > 13

525 > 2

23 20023 >

15 7115 > 71

f a

= 10 y´ = ?

= 22 x´ = ?

000

100 200 300 400 500 536

-312 050

2449

963

-343

963

Page 74

Appendix

Financial Calculation Formulas

TVM solver

PMT, PV, FV, N

If PMT ≠ 0 or N ≠ 1 then ﬁ nd i using the fol-

Error

lowing equations:

Error

i≤ –1

Amortization calculations

Calculations (for PV, PMT, and i, see the TVM solver)

END INT(1) = ROUND(–PV × i)

BGN INT(1) = 0

PRN(1) = –INT(1) + ROUND(PMT)

BAL(1) = PRN(1) + PV

INT(m) = ROUND(–BAL(m – 1) × i)

PRN(m) = –INT(m) + ROUND(PMT)

BAL(m) = PRN(m) + BAL(m – 1)

ROUND(NUM): If a display notation tab setting has been chosen, NUM is rounded and truncated to the speciﬁ ed number of places after the decimal point.

Results

I/Y

If PMT = 0 then

If N = 1 then

Error

AMRT P1 > AMRT P2

Discounted cash ﬂ ow analysis

RATE(I/Y)

100

, CFimax = the maxi-

where i =

mum data set number

IRR is obtained as i, which satisﬁ es NPV = 0 in the above equations.

Page 75

Bond calculations

In its bond calculations, this calculator conforms to rules set up by the book titled Standard Securities Calculation Methods, by Jan Mayle, Securities Industry Association, 1993. Bond calculation is based on the following rules:

1. Whenever the redemption date happens to be the last day of a month, coupons are also paid on the last days of months. For example, if coupon payments are semi-annual and the redemption date is September 30, coupon payments occur on March 31 and September 30.

2. If coupons are to be paid twice a year and the redemption date is set to August 29, 30, or 31, coupon payments for February occur on the 28th (29th for leap years).

3. The “Odd Coupon” is not supported.

4. All data stored or calculated for bonds are assumed to be posi-

tive values. Negative values in any of the variables used by bond calculations will cause errors.

The formulas used for bond calculations are shown using the following variable deﬁ nitions: TD: Total number of days in the coupon period that begins with the

coupon date previous to the settlement date and ends with the ﬁ rst coupon date after the settlement date. (On the 360-day calendar, TD is 180 for semi-annual coupon and 360 for annual coupon.)

PD: The number of days preceding the settlement date in the cou-

pon period described above. (see “Day and date calculations”)

FD: The number of days following the settlement date in the coupon

period described above (in TD). FD = TD – PD NP: The number of whole coupon periods between the settlement

date and the redemption date (rounded up to the next highest

whole number, if necessary).

For one coupon period or less until redemption of bond: For more than one coupon period until redemption:

where CPN = COUPON(PMT), RDV = REDEMPT(FV), N = CPN/Y(N), YIELD = YIELD(I/Y), PRICE = PRICE(PV). Yield is obtained as YIELD, which satisﬁ es the above equations.

Error

CPN < 0 or RDV < 0 or PRICE < 0 or M-D-Y 1 ≥ M-D-Y 2 or YIELD ≤ –100

Page 76

Depreciation calculations

ROUND(NUM): If a display notation tab setting has been chosen, NUM is rounded and truncated to the speciﬁ ed number of places after the decimal point.

In the following equations, M01 = START MONTH, LIF = LIFE(N), CST = COST(PV), SAL = SALVAGE(FV), and DB = DB(I/Y).

Straight-line method (SL)

Calculations

If 1 < n < end_year then

Results

Sum-of-the-years’ digits method (SYD)

Calculations

Results

Declining balance method (DB)

Calculations

Results

Error

CST < 0

SAL < 0

CST < SAL

LIF: when SL, LIF ≤ 0

when SYD or DB, LIF is not a positive integer

I/Y < 0 (DB only)

Conversion between APR and EFF

EFF

APR

EFF

(( + 1) –1) N 100

100

Error

EFF ≤ –100

APR

EFF

APR

(( + 1) –1) 100

100

Error

APR

≤ –100

Day and date calculations

In day and date calculations, this calculator conforms to rules set up in the book titled Standard Securities Calculation Methods, by Jan Mayle, Securities Industry Association, 1993.

Page 77

30/360

1. Adjust D1 and D2 according to the following rules:

(1) If D2 and D1 are both the last day of

February, change D2 to 30.

(2) If D1 is the last day of February,

change D1 to 30.

(3) If D2 is 31 and D1 is 30 or 31, change

D2 to 30.

(4) If D1 is 31, change D1 to 30.

2. Calculate using the following formula:

DAYS = (Y2 – Y1) × 360 + (M2 – M1) ×

30 + (D2 – D1)

Actual

Percent change/Compound interest calculations

where NEW = NEW PRC(FV), OLD = OLD PRC(PV), %CH = %(I/Y), PD = PERIODS(N)

Error

%CH ≤ –100

NEW × OLD ≤ 0

Cost/Sell/Margin/Markup calculations

where MAR = MARGIN, MU = MARK UP

Breakeven calculations

Statistical Calculation Formulas

Type Regression formula

Linear

Quadratic

Exponential

Logarithmic

Power

Inverse

x =

x = x1 + x2 +

x2 = x

y =

sy =

y =

y = y1 + y2 +

y2 = y

xy = x1y1 + x2y2 +

An error will occur in a statistical calculation if:

• The absolute value of an

• The denominator is zero.

• An attempt is made to ﬁ nd

• No solution exists for a qua-

y = a + bx

y = a + bx + cx

y = a • e

y = a + b • Inx

y = a • x

y = a + b

– nx

n – 1

– nx

+ x

···

– ny

+ x

···

+ x

n – 1

– ny

+ y

···

+ y

intermediate or calculation result is equal to or greater than 1 × 10

the square root of a negative number.

+ y

···

+ xny

···

100

dratic regression calculation.

Page 78

Errors and Calculation Ranges

Errors

An error will occur if an operation exceeds the calculation ranges, or if a mathematically illegal operation is attempted. When an error occurs, pressing g or y automatically moves the cursor back to the place in the equation where the error occurred. Edit the equation or press s to clear the equation.

Note: If an error occurs during the automatic calculation of a

listed ﬁ nancial variable, pressing s, g, or y displays the ﬁ rst variable in the function.

Error codes and error types

Syntax error (Error 1):

• An attempt was made to perform an invalid operation. Ex. 2 + - 5

• During the editing or insertion of cash ﬂ ow or statistical data,

a value was entered but . ? was pressed before J.

Calculation error (Error 2):

• The absolute value of an intermediate or ﬁ nal calculation

result equals or exceeds 10

• An attempt was made to divide by zero.

• The calculation ranges were exceeded while performing cal-

culations.

• There was a ﬁ nancial calculation error, such as:

• an error listed in “Financial Calculation Formulas” (see pages 72 – 75) occurred

• an attempt was made to ﬁ nd I/Y when PV, PMT × N, and FV contain all negative or all positive values

• an attempt was made to ﬁ nd IRR when the cash ﬂ ow data contains all negative or all positive values

• an attempt was made to ﬁ nd YIELD in a bond calculation when any of COUPON, REDEMPT, or PRICE contain negative values

Depth error (Error 3):

• The available number of buffers was exceeded. (There are 10 buffers for numeric values and 24 buffers for calculation instructions).

• The number of entered cash ﬂ ow and statistics data items combined exceeded 100.

100

Page 79

Equation too long (Error 4):

• The equation exceeded its maximum input buffer (160 characters). An equation must be shorter than 160 characters.

No solution (Error 5):

• The iteration limit was exceeded while calculating one of the following values in an overly complex problem:

• I/Y (TVM solver)

• IRR (Discounted cash ﬂ ow analysis)

• YIELD (Bond calculations)

If you get an error while calculating IRR, enter an estimated

value into RATE(I/Y) and calculate again.

Display error (Error 6):

• An attempt was made to display “9.999 × 10

” when the dis-

play notation tab number was set to “2”.

If this happens, press s and ~ 0 2 to set the

display notation settings to “ﬂ oating point”. Then try again.

Input value error (Error 7):

• An attempt was made to enter a nonexistent date.

Ex. February 30th

• An attempt was made to enter an invalid numeric value into a ﬁ nancial calculation.

• a negative value or 0 into P/Y or C/Y

• anything except an integer between 1 and 9,999 into AMRT P1 or AMRT P2

• a non-integer into DAYS

• anything except 1 or 2 into CPN/Y

• anything except an integer between 1 and 999 as a cash ﬂ ow frequency

• anything except a positive integer into YEAR

• anything except a value between 1 and 13 into START MONTH

Page 80

Calculation ranges of functions

• Within the ranges speciﬁ ed, this calculator is accurate to within ±1 of the least signiﬁ cant digit of the mantissa. However, a calculation error increases in continuous calculations due to accumulation of each calculation error. (This is the same for ﬁ nancial calculations, scientiﬁ c calculations [ calculations are performed internally.) Additionally, a calculation error will accumulate and become larger in the vicinity of inﬂ ection points and singular points of functions.

In ﬁ nancial calculations, a calculation error increases if the

interest is low or the number of payments is high. Press s if you’d like to cancel the calculation while the “calculating!” screen is displayed.

• Calculation ranges

–99

±10

to ±9.999999999 × 1099 and 0.

If the absolute value of an entry or a ﬁ nal or intermediate result of a calculation is less than 10 0 in calculations and in the display.

Function Calculation range

sin x, cos x,

tan

–1

x, cos–1 x|

sin

–1

tan

In x, log

x, x

DEG: |

| < 10

RAD: |

| <

GRAD: |

| ≤ 1

100

| < 10

–99

< 10

≤

• y > 0: –10

• y = 0: 0 <

• y < 0: x = n (0 < |

–10

, ln, n!, etc.], where continuous

–99

, the value is considered to be

(tan x : |

| ≠ 90 (2n – 1))*

—

× 10

180

(tan x : |

| ≠

—

(2n – 1))*

| <

—

(tan x : |

| ≠ 100 (2n – 1))*

100

log y < 100

100

< 10

| < 1: 1—x = 2n – 1, x ≠ 0),*

100

log |

| < 100

Page 81

Function Calculation range

100

—x log y < 100 (x ≠ 0)

• y > 0: –10

• y = 0: 0 <

• y < 0: x = 2n – 1

ex –10

10 sinh x, cosh x,

tanh

–1

sinh

cosh–1

tanh–1

–10

< 10

(0 < |

| < 1: 1—x = n, x ≠ 0),*

100

—x log |

–10

100

≤ 230.2585092

100

< 100

| ≤ 230.2585092

| < 10

< 10

≤

| < 1

| < 10

100

< 10

≤

100

| < 10

(x ≠ 0)

100

n! 0 ≤ n ≤ 69*

0 ≤ r ≤ n ≤ 9,999,999,999*

nPr

nCr

n! — (n – r)!

0 ≤ r ≤ n ≤ 9,999,999,999* 0 ≤ r ≤ 69

— (n – r)!

100

< 10

100

< 10

* n, r: integer

| < 100

Page 82

Battery Replacement

Notes on battery replacement

Improper handling of battery can cause electrolyte leakage or explosion. Be sure to observe the following handling rules:

• Make sure the new battery is the correct type.

• When installing, orient the battery correctly, as indicated in the calculator.

• The factory-installed battery may be exhausted before it reaches the service life stated in the speciﬁ cations.

Note on the erasure of memory contents

When the battery is replaced, the memory contents are erased. Erasure can also occur if the calculator is defective or when it is repaired. Make a note of all important memory contents in case accidental erasure occurs.

When to replace the battery

If the display has poor contrast, or if nothing appears on the screen, even when s is pressed, it is time to replace the battery.

Caution

• Fluid from a leaking battery accidentally entering an eye could result in serious injury. Should this occur, wash with clean water and immediately consult a doctor.

• Should ﬂ uid from a leaking battery come into contact with your skin or clothes, wash them immediately with clean water.

• If the product is not to be used for some time, to avoid damage to the unit from leaking battery, remove it and store in a safe place.

• Keep battery out of the reach of children.

• Exhausted battery that is left in the calculator may leak and damage the unit.

• Explosion risk may be caused by incorrect handling.

• Do not throw battery into a ﬁ re, as it may explode.

Page 83

Replacement procedure

1. Turn the power off by pressing . c.

2. Loosen the screw and remove the battery cover.

(see ﬁ g. 1)

3. Remove the used battery using a ball-point

pen or similar object. Do not use a mechanical pencil or any sharp or pointed object to remove the battery. (see ﬁ g. 2)

4. Install a new battery into the battery housing

with the positive side (+) facing up. (see ﬁ g. 3)

5. Replace the battery cover and the screw.

6. Press the RESET switch located on the back of

the calculator with the tip of a ball-point pen or similar object. Do not use an object with a breakable or sharp tip. (see ﬁ g. 4)

• Make sure that the display appears as shown. If not, remove the battery, reinstall, and check the display again.

ﬁ g. 1

ﬁ g. 2

ﬁ g. 3

ﬁ g. 4

000

Automatic power-off function

This calculator will turn its power off automatically if no key is pressed for about 10 minutes.

Priority Levels in Calculations

This calculator performs operations according to the following priority:

1. Functions preceded by their argument (

x, x

3. Implied multiplication of a memory value (2Y, etc.)

4. Functions followed by their argument (sin, cos, etc.)

5. Implied multiplication of a function (2sin 30, etc.)

6. nCr, nPr

7. ×,

8. +, –

9. =, M+, M–, ⇒M, and any other calculation ending instructions

, n!, etc.)

Page 84

Key operation and calculation priority

5 + 2 x . { 30 + 25 x 5 . @ 3 =

• Parenthesized operations take precedence over other operations.

Speciﬁ cations

Calculations: Financial calculations General arithmetic calculations Scientiﬁ c calculations Statistical calculations

Calculation method: D.A.L. (Direct Algebraic Logic) Internal calculations: Mantissas of up to 14 digits Pending operations: 24 calculations, 10 numeric values Power source: 3.0 V …

Lithium battery (CR2032) × 1 Operating life:

• May vary depending on the operating

Operating temperature: 0°C – 40°C (32°F – 104°F) External dimensions: 77 mm (W) × 144 mm (D) × 10.8 mm (H)

Weight: Accessories: Battery

For more information about ﬁ nancial calculators

Visit us on the Internet at: http://sharp-world.com/calculator/

For USA only: This product contains a CR Coin Lithium Battery which contains Perchlorate Material – special handling may apply, California residents, See www.dtsc.ca.gov/hazardouswaste/perchlorate/

(DC)

Approx. 5 years (with 1 hour of daily use)

environment and operation method.

3-1/32” (W) × 5-21/32” (D) × 7/16” (H) Approx. 82.5 g (0.19 lb.) (including battery)

1 (installed), operation

manual, and hard case

Page 85

Index

, 37, 51, 64

+ - x = , ( )

} %

z i g y ! P

; : . &

* / " # $

< > ? @ I J K L O Q R S t ] f

e d h M

j k l m N o p q

s w u

, 11, 15 , 11, 37, 61

, 11, 16, 61 , 23 :, 60, 61 , 16, 62 , 54

, 51 , 11 , 16, 61 , 61 , 61 , 4, 6, 7 , 44, 45, 52 , 4, 6, 7, 15 , 33 , 15, 16, 23 , 22, 28, 33 , 45 , 58 , 12, 19 , 41 , 37, 38 , 39, 66 , 7, 19 , 56 , 37, 64 , 52 , 12 , 49 , 7, 19 , 61 , 11 , 22, 23 , 7, 61 , 22, 23 , 13 , 39, 66 , 61 , 61 , 15 , 11, 16 , 16 , 5, 12, 13 , 63 , 6, 10, 12 , 22, 23 , 62

, 62 , 6 , 6, 12 , 22, 23 , 22, 23

8, 4, 11

, 6, 13

, 22, 23 , 62, 63

, 7, 15

, 6, 8–10

, 7, 15

, 16, 60, 61, 69

;

, 61

% (I/Y), 18, 54, 75

∑

INTEREST, 33, 72

∑

PRINCIPAL, 33, 72 ACCU INT, 44 Amortization calculations,

17, 33–36, 72 AMRT P1, AMRT P2, 12, 33, 77 Angular unit, 8, 9, 61 Annuity due, 7, 22, 28 ANS (last answer memory), 14, 15 APR, 17, 51, 74 Arithmetic calculations, 11 Arithmetic operations (+, –, ×, ÷), 11 Automatic power-off function, 81 BALANCE, 33, 72 Battery replacement, 80, 81 Bond calculations, 17, 18, 44–47, 73 Breakeven calculations, 17, 58, 59, 75

(symbol), 8, 20 Calculation ranges, 78, 79 Calculator layout, 6 Calendar range, 44, 47, 52 Cash flow data, 12, 37–40, 76 Cash flow diagrams, 21 Chain calculations, 60 COMP (symbol), 7, 20 Compound interest, 21, 54–56, 75 Constant calculations, 60 Conversion between APR and EFF, 17, 51 COST, 56, 75 COST (PV), 18, 48, 74 Cost/sell/margin/markup calculations,

17, 56, 57, 75 COUPON (PMT), 18, 44, 73, 76 CPN/Y (N), 18, 44, 77 Cursor key, 6, 13 C/Y, 18, 22, 72, 77 Date format, 10, 44, 47, 52 Day and date calculations,

17, 18, 52–54, 74 Day-count method (ACT/360), 44, 52 DAYS, 52, 53, 75 DB, 9, 48, 74 DB (I/Y), 18, 48, 74 Decimal place, 8, 9, 63 DEG, 8, 9, 61, 78 Delete key, 12 DEPRECIATE, 48 Depreciation calculations,

17, 18, 48–50, 74 Depreciation method, 9, 48

Page 86

Discounted cash flow analysis,

17, 18, 37–43, 72 Display layout, 7 Display notation, 8 EFF, 17, 51, 74 ENT (symbol), 7, 20 Entering dates, 47 Entering numbers, 11 Error, 14, 76–78 EXP, 64 Financial calculations, 17, 18, 72 FIXED, 58, 75 FLO_A (FLOAT A), FLO_B (FLOAT B), 7, 9 Floating point, 8, 9 Formulas, 72–75 FV, 18, 22, 72 GRAD, 8, 9, 61, 78 Independent memory (M), 8, 12, 14, 15 Insert mode, 13 INV, 64 IRR, 40, 41, 72, 77 I/Y, 18, 22, 72, 77 LIFE (N), 18, 48, 74 LINE, 64 Listed financial variables, 12, 14, 15, 18, 19 LOG, 64 M (symbol), 8 MARGIN, 56, 75 MARK UP, 56, 75 M-D-Y 1, M-D-Y 2, 18, 44, 52, 73, 75 Memory clear key, 5, 12, 13 Modify function, 63 N, 18, 22, 72 NET_PV, 40 NEW PRC (FV), 18, 54, 75 NORMAL mode, 10, 17, 60 NPV, 40, 41, 72 OLD PRC (PV), 18, 54, 75 Ordinary annuity, 7, 22, 28 Overwrite mode, 13 Payment period (payment due), 22, 28 Percent change/compound interest calculations, 17, 18, 54–56, 75 PERIODS (N), 18, 54, 75 Playback function, 13 PMT, 18, 22, 72 PRICE, 58, 75 PRICE (PV), 18, 44, 45, 73, 76 Priority levels in calculations, 81, 82 PROFIT, 58 PV, 18, 22, 72 PWR, 64 P/Y, 18, 22, 72, 77 QUAD, 64 QUANTITY, 58 RAD, 8, 9, 61, 78 Random coin, 62 Random dice, 62 Random functions, 62–63

Random integer, 63 Random numbers, 62 RATE (I/Y), 18, 40, 72 RBV, 48, 74 RDV, 48, 74 REDEMPT (FV), 18, 44, 73, 76 RESET switch, 5, 12, 81 Resetting the calculator, 5 SALVAGE (FV), 18, 48, 74 SCI, 7, 8 Scientific calculations, 60–63 Scientific notation, 8, 9, 11, 63 SD, 64 SELL, 56, 75 SET UP menu, 8–10 SL, 9, 48, 74 Specifications, 82 START MONTH, 48, 74, 77

(symbol), 8, 10, 64 STAT (statistics) mode, 10, 64 Statistical calculations, 10, 64–71 Statistical data, 12, 64–67, 76 Statistical variables, 12, 14, 16, 68 Symbol, 7 SYD, 9, 48, 74 TAB, 7, 8 Temporary memory (A-H, X-Z), 12, 14, 15 TVM (time value of money) solver,

17, 22–32, 72 TVM variable, 12, 14, 15, 18, 19, 22 VARIABLE, 58, 75 YEAR, 12, 48, 77 YIELD (I/Y), 18, 44, 45, 73, 76, 77

Page 87

Page 88