Casio fx9860G 7-3Compound Interest, (1+, (1+, PMT, PMT, F(i), PMT = –, (1+ i)n, uFormula, (1 + i)n, i(1+ i)n, i(1 + i)n, PV + FV ⋅ β, uFormula II (I% = 0)

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 =	I %
		+ FV
	i(1 + i)n		(1 + i)n
					100

Here:

PV = – (PMT ⋅ α + FV ⋅ β )

FV = – PMT ⋅ α + PV

β

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

PV : present value

FV : future value

PMT : payment

n: number of compound periods

I% : annual interest rate

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–1uFormula II (I% = 0)

PV + PMT ⋅ n + FV = 0

Here:

PV = – (PMT ⋅ n + FV )

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