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20050401
7-3 Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
uu
uu
u Formula I
PV+PMT × + FV
i(1+ i)
n
(1+ i)
n
(1+ i ×
S)[(1+ i)
n
–1] 1
= 0
i =
100
I %
Here:
PV= –(PMT ×
+ FV ×
)
β
α
FV= –
β
PMT × + P
V
α
PMT= –
β
PV
+ FV ×
α
n =
log
{ }
log(1+ i)
(1+ i × S ) PMT+PVi
(1+ i × S ) PMT–FVi
i
(
1+ i
)
n
(1+ i ×
S)[(1+ i)
n
–1]
=
α
(1+ i)
n
1
=
β
F(i) = Formula I
+ (1+ i × S)[n(1+ i)
–n–1
]+S
–
nFV(1+ i)
–n–1
ii
PMT
(1+ i × S)[1– (1+ i)
–n
]
F(i)'= –
[
+S [1–(1+ i)
–n
]
]
uu
uu
u Formula 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
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
7-3-1
Compound Interest