Compound Interest - Casio CFX9850GBPLUS User Manual

7-3 Compound Interest

This calculator uses the following standard formulas to calculate compound interest.
u Formula I
PV + PMT PV + PMT
Here:
PV = – (PMT PV = – (PMT
FV = – FV = –
PMT = – PMT = –
n = n =
= =
= =
F i
( ) = Formula I
F(i)' = F(i)' =
u Formula II ( I % = 0)
PV + PMT n + FV = 0 PV + PMT n + FV = 0
Here:
PV = – (PMT n + FV ) PV = – (PMT n + FV )
Compound Interest
(1 + i S) (1+ i) (1 + i S) (1+ i)
i(1 + i) i(1 + i)
+ FV + FV
PMT PMT + PV + PV
PV + FV PV + FV
{ {
(1+ i S ) PMT – FVi (1+ i S ) PMT – FVi
log log
(1+ i S ) PMT + PVi (1+ i S ) PMT + PVi
log(1 + i) log(1 + i)
n n
(1 + i S) (1 + i) (1 + i S) (1 + i) –1 –1
n n
i(1 + i) i(1 + i)
1 1
n n
(1+ i) (1+ i)
(1 + i S)[1 – (1 + i) (1 + i S)[1 – (1 + i)
PMT PMT
– –
i i
– –
–n –n
+S 1 – (1 + i) +S 1 – (1 + i)
7-3-1
n n
–1 –1
+ FV + FV
n n
(1 + i) (1 + i)
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
} }
–n –n
] ]
+ (1 + i S) n(1 + i) + (1 + i S) n(1 + i)
i i
–n–1 –n–1
nFV(1 + i) nFV(1 + i)
20070201
1 1
I % I %
= 0 = 0
i = i =
n n
100 100
–n–1 –n–1
+S +S