3 compound interest, Compound, Interest – Casio SERIES FX-9860G User Manual
Page 377: 3 compound
20070201
7-3-1
Compound Interest
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
F
(
i
) = Formula I
u Formula II ( I% = 0)
Here:
i
(1 + i)
n
(1 + i
× S)[(1 + i)
n
–1
]
=
α
i
(1 + i)
n
(1 + i
× S)[(1 + i)
n
–1
]
=
α
(1+ i)
n
1
=
β
(1+ i)
n
1
=
β
+
(1 + i
× S)[n(1 + i)
–n–1
]+S
–
nFV
(1 + i)
–n–1
i
i
PMT
(1 + i
× S)[1 – (1 + i)
–n
]
F(i)' =
–
[
+S
[1 – (1 + i)
–n
]
]
+
(1 + i
× S)[n(1 + i)
–n–1
]+S
–
nFV
(1 + i)
–n–1
i
i
PMT
(1 + i
× S)[1 – (1 + i)
–n
]
F(i)' =
–
[
+S
[1 – (1 + i)
–n
]
]
PV
+ PMT
× n + FV = 0
PV
+ PMT
× n + FV = 0
PV
= – (PMT
× n + FV )
PV
= – (PMT
× n + FV )
7-3 Compound Interest
This calculator uses the following standard formulas to calculate compound interest.
u Formula I
Here:
PV + PMT
×
+ FV
i
(1 + i)
n
(1 + i)
n
(1 + i
× S)[(1+ i)
n
–1
]
1
= 0
i
=
100
I
%
PV + PMT
×
+ FV
i
(1 + i)
n
(1 + i)
n
(1 + i
× S)[(1+ i)
n
–1
]
1
= 0
i
=
100
I
%
PV
= – (PMT
× + FV × )
β
α
PV
= – (PMT
× + FV × )
β
α
FV
= –
β
PMT
× + PV
α
FV
= –
β
PMT
× + PV
α
PMT
= –
β
PV
+ FV
×
α
PMT
= –
β
PV
+ FV
×
α
n
=
log
{ }
log(1 + i)
(1+ i
× S ) PMT + PVi
(1+ i
× S ) PMT – FVi
n
=
log
{ }
log(1 + i)
(1+ i
× S ) PMT + PVi
(1+ i
× S ) PMT – FVi