7-3-1

Compound Interest

7-3 Compound Interest

This calculator uses the following standard formulas to calculate compound interest.

uFormula I

PV+PMT ⋅

(1+ i ⋅ S)[(1+ i)n–1]

1

= 0

 

I %

 

+ FV

 

i =

 

 

i(1+ i)n

 

(1+ i)n

 

100

Here:

PV= –(PMT ⋅ α + FV ⋅ β )

PMT ⋅α + PV

PV : present value

FV : future value

PMT : payment

FV= –

β

n

: number of compound periods

I%

: annual interest rate

PMT= –

PV + FV ⋅ β

α

 

{(1+ i ⋅ S ) PMT–FVi }

log

(1+ i ⋅ S ) PMT+PVi

n =

log(1+ i)

α = (1+ i ⋅ S)[(1+ i)n–1]i(1+ i)n

β= 1 (1+ i)n

i is calculated using Newton’s Method.

S = 0 assumed for end of term

S = 1 assumed for beginning of term

F(i) = Formula I

 

 

F(i)'=

PMT

[–

(1+ i ⋅ S)[1– (1+ i)–n]

+ (1+ i ⋅ S)[n(1+ i)–n–1]

i

i

 

 

 

+S [1–(1+ i)–n]]– nFV(1+ i)–n–1

uFormula II (I% = 0)

PV + PMT ⋅ n + FV = 0

Here:

PV = – (PMT ⋅ n + FV )

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