User manual - financial

6
3. Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
uu
uu
uFormula I
PV+PMT u + FV
i(1+ i)
n
(1+ i)
n
(1+ i u S)[(1+ i)
n
–1] 1
= 0
i =
100
I％

Here:
PV= –(PMT u + FV u )
β
α
F
V= –
β
PMTu + PV
α
PMT= –
β
PV + FV u
α
n =
log
{ }
log(1+ i)
(1+ i S ) PMT+PVi
(1+ i S ) PMT–FVi
i
(
1+ i
)
n
(1+ i u S)[(1+ i)
n
–1]
=
α
(1+ i)
n
1
=
β
F(i) = Formula I
+ (1+ i S)[n(1+ i)
–n–1
]
+S [1–(1+ i)
–n
] – FV • n(1+ i)
–n–1
ii
PMT
(1+ i S)[1– (1+ i)
–n
]
F(i)= –
[
]
uu
uu
uFormula II (I% = 0)
PV + PMT × n + FV = 0
Here:
PV = – (PMT u n + FV )
FV = – (PMT u n + PV )
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