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324
19-3 Compound Interest Calculations
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
FV= –
β
PMT
u
+ 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 beginning of term
S = 1 assumed for end of term
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