Casio CFX-9970G Manuale utente

Chapter

Financial Calculations

19-1 Before Performing Financial Calculations

19-2 Simple Interest Calculations

19-3 Compound Interest Calculations

19-4 Investment Appraisal

19-5 Amortization of a Loan

19-6 Conversion between Percentage Interest Rate and

Effective Interest Rate

19-7 Cost, Selling Price, Margin Calculations

19-8 Day/Date Calculations

320

19-1 Before Performing Financial Calculations

The Financial Mode provides you with the tools to perform the following types of

financial calculations.

• Simple interest

• Compound interest

• Investment appraisal (Cash Flow)

• Amortization

• Interest rate conversion (annual percentage rate and effective interest rate)

• Cost, selling price, margin

• Day/date calculations

uGraphing in the Financial Mode

After performing a financial calculation, you can use 6(GRPH) to graph the

results as shown below.

• Pressing !1 (TRCE) while a graph is on the display activates Trace, which

can be used to look up other financial values. In the case of simple interest, for

example, pressing edisplays PV, SI, and SFV. Pressing ddisplays the

same values in reverse sequence.

• Zoom, Scroll, Sketch, and G-Solve cannot be used in the Financial Mode.

• In the Financial Mode, horizontal lines are blue and vertical lines are red.

These colors are fixed and cannot be changed.

• The present value is positive when it represents receipt of money, and a

negative value when it represents a payment.

• Note that calculation results produced in this mode should be regarded as

reference values only.

• Whenever performing an actual financial transaction, be sure to check any

calculation results obtained using this calculator with against the figures

calculated by your financial institution.

uSet up screen settings

Note the following points regarding set up screen settings whenever using the

Financial Mode.

• The following graph set up screen settings are all turned off for graphing in the

Financial Mode:Axes, Grid, Dual Screen.

P.6

P.7

321

• Drawing a financial graph while the Label item is turned on, displays the label

CASH for the vertical axis (deposits, withdrawals), and TIME for the horizontal

axis (frequency).

• The number of display digits applied in the Financial Mode is different from the

number of digits used in other modes. The calculators automatically reverts to

Norm 1 whenever you enter the Financial Mode, which cancels a Sci (number

of significant digits) or Eng (engineering notation) setting made in another

mode.

kEntering the Financial Mode

On the Main Menu, select the TVM icon to enter the Financial Mode. When you

do, the Financial 1 screen appears on the display.

Financial 1 screen Financial 2 screen

•{SMPL}/{CMPD}/{CASH}/{AMT}/{CNVT}/{COST}/{DAYS} ... {simple interest}/

{compound interest}/{cash flow}/{amortization}/{conversion}/{cost, selling

price, margin}/{day/date} calculation

Before Performing Financial Calculations 19 - 1

P.6

322

19-2 Simple Interest Calculations

This calculator uses the following formulas to calculate simple interest.

365-day Mode

SI' = n

365× PV × i

SI' = n

360× PV × i

100

i =

100

i =

SI : simple interest

n: number of simple

360-day Mode interest periods

PV : present value

I%: periodic interest rate

SFV: simple future value

SI = –SI'

SFV = –(PV +SI')

Press 1(SMPL) from the Financial 1 screen to display the following input screen

for simple interest calculation.

n ......................number of simple interest periods (days)

I% ................ annual interest rate

PV .................. present value

•{SI}/{SFV} ... calculates {simple interest}/{simple future value}

Example What would the interest amount and principal plus interest be

for a loan of $1,500 borrowed for 90 days at an annual rate of

7.25%?

Use the 360-day mode and two decimal places.

In the set up screen, specify “360” for Date Mode and “Fix2” for Display and then

press J.

Perform the following key operation from the input screen.

jaw

h.cfw

-bfaaw

1(SI)

P.7

P.6

323

Now you can perform the following key operation to return to the input screen and

then display the principal plus interest.

1(REPT) (Returns to the input screen)

2(SFV)

You can also press 6(GRPH) to draw a cash flow graph.

6(GRPH)

The left side is PV, while the right side is SI and SFV. The upper part of the graph

is positive (+), while the bottom part is negative (–).

• V-Window values vary in accordance with simple interest conditions.

Press J(or !6 (G↔T)) to return to the input screen.

Press Jagain to return to the Financial 1 screen.

Simple Interest Calculations 19 - 2

324

19-3 Compound Interest Calculations

This calculator uses the following standard formulas to calculate compound

interest.

uFormula I

PV+PMT

+ FV

i(1+ i)

(1+ i)

(1+ i

S)[(1+ i)

–1]1= 0

i = 100

I％



Here:

PV= –(PMT u+ FV u )

FV= –

PMT

+ PV

PMT= –

PV + FV u

n =

log

{ }

log(1+ i)

(1+ i S ) PMT+PVi

(1+ i S ) PMT–FVi

(

1+i

)

(1+ i

S)[(1+ i)

–1]

(1+ i)

F(i) = Formula I

+ (1+ i S)[n(1+ i)

–n–1

]+S[1–(1+ i)

–n

]

+ FV–n(1+ i)

–n–1

PMT (1+ i S)[1– (1+ i)

–n

]

F(i)'= –

[]

uFormula II (I% = 0)

PV + PMT × n + FV = 0

Here:

PV = – (PMT un + FV )

FV = – (PMT un + PV )

PV : present value

FV : future value

PMT : payment

n:number of compound periods

: annual interest rate

iis calculated using Newton’s Method.

S= 0 assumed for beginning of term

S= 1 assumed for end of term

325

PMT = –PV + FV

PMT

n = – PV + FV

• A deposit is indicated by a plus sign (+), while a withdrawal is indicated by a

minus sign (–).

uConverting between the nominal interest rate and effective

interest rate

The nominal interest rate (I% value input by user) is converted to an effective

interest rate (I%') when the number of installments per year (P/Y) is different from

the number of compound interest calculation periods (C/Y). This conversion is

required for installment savings accounts, loan repayments, etc.

I%' = I%

(1+ ) –1

[C / Y ]

[P / Y ]

100 × [C / Y ]

{ }

×100

P/Y: installment

periods per year

C/Y: compounding

periods per year

When calculating n, PV, PMT, FV

The following calculation is performed after conversion from the nominal interest

rate to the effective interest rate, and the result is used for all subsequent

calculations.

i = I%'÷100

When calculating I%

After I% is obtained, the following calculation is performed to convert to I%'.

I%' = I%

(1+ ) –1

[C / Y ]

[P / Y ]

100

{ }

×[C / Y ]×100

P/Y: installment

periods per year

C/Y: compounding

periods per year

The value of I%' is returned as the result of the I% calculation.

Press 2(CMPD) in the Financial 1 screen to display the input screen for

compound interest calculation.

n..................... number of compound periods

I% ................... annual interest rate

PV .................. present value (loan amount in case of loan; balance in case

of savings)

Compound Interest Calculations 19 - 3

326

19 - 3 Compound Interest Calculations

PMT ............... payment for each installment (payment in case of loan;

deposit in case of savings)

FV .................. future value (unpaid balance in case of loan; principal plus

interest in case of savings)

P/Y.................. installment periods per year

C/Y................. compounding periods per year

Inputting Values

A period (n) is expressed as a positive value. Either the present value (PV) or

future value (FV) is positive, while the other (PV or FV) is negative.

Precision

This calculator performs interest calculations using Newton’s Method, which

produces approximate values whose precision can be affected by various

calculation conditions. Because of this, interest calculation results produced by

this calculator should be used keeping the above limitation in mind or the

results should be verified.

kCompound Interest Examples

This section shows how compound interest calculations can be used in a variety

of applications.

uSavings (standard compound interest)

Input Condition: Future value is greater than present value.

Formula Representation of Input Condition: PMT = 0

|PV| < |FV|

Example Calculate the interest rate required to increase a principal of

$10,000 to $12,000 in three years, when compounding is

performed semiannually.

Perform the following key operation from the input screen.

d*bcw(Input n= 3 ×12.)

-baaaaw(PV = –10,000)

bcaaaw(FV = 12,000)

cw(Semiannual compounding)

2(I%)

327

Now you can press 6to draw a cash flow graph.

6(GRPH)

The left side is PV, while the right side is FV. The upper part of the graph is

positive (+), while the bottom part is negative (–).

uInstallment savings

Input Condition: Future value is greater than the total of payments.

Formula Representation of Input Condition:

PMT and FV have different signs (positive, negative) when PV = 0.

–FV < n×PMT when FV > 0

–FV > n×PMT when FV < 0

Example Calculate the interest rate required to have a $2,500 balance in

an installment savings account in two years when $100 is

deposited each month and interest is compounded semiannu-

ally.

Perform the following key operation from the input screen.

c*bcw(Input n= 2 ×12.)

aw(PV = 0)

-baaw(PMT = –100)

cfaaw(FV = 2,500)

bcw(Monthly installment)

cw(Compounding every six months)

2(I%)

uLoans

Input Condition: Total of payments is greater than loan amount.

Formula Representation of Input Condition:

PMT and PV have different signs (positive, negative) when FV = 0.

–PV > n×PMT when PV > 0

–PV < n×PMT when PV < 0

Compound Interest Calculations 19 - 3

328

Example Calculate the interest rate required to repay a $2,300 balance

on a loan in two years paying back $100 per month, when

interest is compounded monthly.

Perform the following key operation from the input screen.

c*bcw(Input n= 2 ×12.)

cdaaw(PV = 2,300)

-baaw(PMT = –100)

aw(FV = 0)

bcw(Monthly installment)

(Monthly compounding)

2(I%)

uLoan when final installment is greater than other installments

Input Condition: Total of equal amount payments is greater than the difference

between the loan amount and final payment amount.

Formula Representation of Input Condition:

PV,PMT, FV do not equal zero.

PV + FV > – n×PMT when FV > PV

PV + FV < – n×PMT when FV < PV

Example Calculate the interest rate required to repay a $2,500 balance

on a loan in two years (24 installments) paying back $100 per

month and a final $200 installment, when interest is com-

pounded monthly.

Perform the following key operation from the input screen.

c*bcw(Input n= 2 ×12.)

cfaaw(PV = 2,500)

-baaw(PMT = –100)

-caaw(FV = –200)

bcw(Monthly installment)

(Monthly compounding)

2(I%)

19 - 3 Compound Interest Calculations

The value you input for P/Y (the

number of installment periods per

year) is also automatically input for

C/Y (the number of compounding

periods per year). You can input

another value for C/Y if you want.

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