Casio ALGEBRA FX 2.0 Plus Manuel utilisateur

Financial Calculation (TVM)

2-1 Before Performing Financial Calculations

2-2 Simple Interest

2-3 Compound Interest

2-4 Cash Flow (Investment Appraisal)

2-5 Amortization

2-6 Interest Rate Conversion

2-7 Cost, Selling Price, Margin

2-8 Day/Date Calculations

2-9 Depreciation

2-10 Bonds

2-11 TVM Graph

Chapter

20010101

2-1 Before Performing Financial Calculations

kTVM Mode

On the Main Menu, select the TVM icon.

Entering the TVM Mode displays the Financial screen like the one shown below.

Financial 1 screen Financial 2 screen

•1(SMPL) .... Simple interest

•2(CMPD) ... Compound interest

•3(CASH) .... Cash flow (investment appraisal)

•4(AMT) ...... Amortization

•5(CNVT) .... Interest rate conversion

•6(g)1(COST) ... Cost, selling price, margin

2(DAYS) ... Day/date calculations

3(DEPR) ... Depreciation

4(BOND) ... Bonds

5(TVMG) ... TVM (compound interest simulation) graph

2-1-1

Before Performing Financial Calculations

* The above shows the ALGEBRA

FX 2.0 PLUS screen.

20010101

kSET UP Items

uPayment

•{BGN}/{END}........ Specifies {beginning of the period} / {end of the period} payment

uDate Mode

•{365}/{360}......... Specifies calculation according to a {365-day} / {360-day} year

uPeriods/YR. (Bond)

•{Annual}/{SEMI}... Indicates an {annual} / {semi-annual} period

Note the following points regarding SET UP screen settings whenever using the Financial

Mode.

•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). Axis

labels do not appear on the TVM graph.

•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.

kGraphing in the TVM Mode

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

below.

•Pressing 1(TRACE) 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 e

displays PV, SI, and SFV. Pressing ddisplays the same values in reverse sequence.

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

•Whether you should use a positive or a negative value for the present value (PV) or the

purchase price (PRC) depends on the type of calculation you are trying to perform.

•Note that graphs should be used only for reference purposes when viewing TVM Mode

calculation results.

•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.

2-1-2

Before Performing Financial Calculations

20010101

2-2 Simple Interest

This calculator uses the following formulas to calculate simple interest.

uFormula

365-day Mode

SI' = n

365 × PV × i

SI' = n

360 × PV × i

100

i =

100

i =

SI :interest

n:number of interest

360-day Mode periods

PV :principal

I%:annual interest

SFV :principal plus interest

SI = –SI'

SFV = –(PV +SI')

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

interest.

1(SMPL)

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

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

PV ............................... principal

After configuring the parameters, press one of the function keys noted below to perform the

corresponding calculation.

•1(SI) ....... Simple interest

•2(SFV) ... Simple future value

2-2-1

Simple Interest

20010101

• An error (Ma ERROR) occurs if parameters are not configured correctly.

Use the following function keys to maneuver between calculation result screens.

•1(REPT) ... Parameter input screen

•6(GRPH) ... Draws graph

After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation

results along the graph.

Each press of ewhile trace is turned on cycles the displayed value in the sequence:

present value (PV) →simple interest (SI) →simple future value (SFV). Pressing dcycles

in the reverse direction.

Press ito turn off trace.

Press iagain to return to the parameter input screen.

2-2-2

Simple Interest

20010101

2-3 Compound Interest

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 ×+ FV ×)

FV= –

PMT ×

+ P

PMT= –

PV + FV ×

n =

log

{ }

log(1+ i)

(1+ i S ) PMT+PVi

(1+ i S ) PMT–FVi

(

1+ i

)

(1+ i ×

S)[(1+ i)n–1]

(1+ i)n

F(i) = Formula I

+ (1+ i S)[n(1+ i)–n–1]+S

[

–

nFV(1+ i)–n–1

PMT (1+ i S)[1– (1+ i)–n]

F(i) = –

[

+S [1–(1+ i)–n]

]

uFormula II (I% = 0)

PV + PMT × n + FV = 0

Here:

PV = – (PMT × n + FV )

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 end of term

S= 1 assumed for beginning of term

2-3-1

Compound Interest

20011201

20010101

FV = – (PMT × n + PV )

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.

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.

2-3-2

Compound Interest

I%' = I%

(1+ ) –1

[C / Y ]

[P / Y ]

100 × [C / Y ]

{ }

×100

20011101

20010101

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

compound interest.

2(CMPD)

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

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

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

of savings)

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

Important!

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.

2-3-3

Compound Interest

20010101

After configuring the parameters, press one of the function keys noted below to perform the

corresponding calculation.

•1(n) ............ Number of compound periods

•2(I%).......... Annual interest rate

•3(PV) ......... Present value (Loan: loan amount; Savings: balance)

•4(PMT) ....... Payment (Loan: installment; Savings: deposit)

•5(FV) .......... Future value (Loan: unpaid balance; Savings: principal plus interest)

•6(AMT) ....... Amortization screen

•An error (Ma ERROR) occurs if parameters are not configured correctly.

Use the following function keys to maneuver between calculation result screens.

•1(REPT) ..... Parameter input screen

•4(AMT) ....... Amortization screen

•6(GRPH) .... Draws graph

After drawing a graph, you can press 1(TRACE) to turn on trace and read calculation

results along the graph.

Press ito turn off trace.

Press iagain to return to the parameter input screen.

2-3-4

Compound Interest

20010101

2-4 Cash Flow (Investment Appraisal)

This calculator uses the discounted cash flow (DCF) method to perform investment appraisal

by totalling cash flow for a fixed period. This calculator can perform the following four types

of investment appraisal.

•Net present value (NPV )

•Netfuture value (NFV )

•Internal rate of return (IRR)

•Pay back period (PBP)

A cash flow diagram like the one shown below helps to visualize the movement of funds.

CF0

CF1

CF2CF3CF4

CF5CF6

CF7

With this graph, the initial investment amount is represented by CF0. The cash flow one year

later is shown by CF1, two years later by CF2, and so on.

Investment appraisal can be used to clearly determine whether an investment is realizing

profits that were originally targeted.

uNPV

NPV = CF0+ + + + … +

(1+ i)

CF1

(1+ i)2

CF2

(1+ i)3

CF3

(1+ i)n

CFn

i = 100

I %

n: natural number up to 254

uNFV

NFV =NPV × (1 + i )

uIRR

0 = CF

+ + + + … +

(1+ i)

In this formula, NPV = 0, and the value of IRR is equivalent to i×100. It should be noted,

however, that minute fractional values tend to accumulate during the subsequent

calculations performed automatically by the calculator, so NPV never actually reaches

exactly zero. IRR becomes more accurate the closer that NPV approaches to zero.

2-4-1

Cash Flow (Investment Appraisal)

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