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3 compound interest, Compound, Interest – Casio SERIES FX-9860G User Manual

Page 377: 3 compound

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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