7-3-2

Compound Interest

FV = – (PMT ⋅ n + PV )

PV + FV

PMT = –

n

PV + FV

n = –

PMT

• 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%

 

[C / Y ]

P/Y : installment

 

 

[P / Y ]

 

periods per year

I%' = {(1+

100 ⋅ [C / Y ] ) –1}⋅100

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%

 

[P / Y ]

 

 

P/Y : installment

I%' =

(1+

)[C / Y ] –1

⋅[C / Y ]⋅100

periods per year

 

 

 

100

 

 

}

C/Y: compounding

periods per year

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

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