User manual - Chapter 2 Financial Calculation (TVM)

20010101
2-3 Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
uu
uu
uFormula 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
uFormula 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
2-3-1
Compound Interest
20011201