15-3-3

Compound Interest

Calculation Formulas

uPV, PMT, FV, n

I

% G 0

PV =

–

α ⋅

PMT –

β ⋅

FV

 

 

 

 

 

 

 

 

 

 

 

γ

 

 

 

 

 

 

 

 

 

 

PMT = –⋅PV –⋅FV

FV = – ⋅ PV – ⋅ PMT

n =I% = 0

log {(1+(1+ iSiS)) ⋅⋅ PMTPMT +– FVPV ⋅⋅ ii}

log (1+ i)
PV = – (PMT ⋅ n + FV )

PMT = – PV + FV n

FV = – (PMT ⋅ n + PV )

n = –

 

PV + FV

 

 

 

 

 

 

 

 

 

PMT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

α = (1+ i ⋅ S ) ⋅

1 – β

 

 

 

 

 

 

 

 

 

 

 

(1+ i ) −n .................

i

 

 

Off (Format tab)

 

 

 

 

 

 

 

ß = {(1+ i) −Intg(n)

............

 

 

 

CI or SI (Format tab)

 

1 ...........................

 

 

 

 

 

 

 

 

Off (Format tab)

γ =

 

(1+ i ) Frac (n)

...........

 

 

 

CI (Format tab)

 

{1+ i ⋅ Frac (n) .......

 

SI (Format tab)

 

0 ............................

 

 

 

 

 

 

 

 

Payment : End (Format tab)

S = {1 ............................

 

 

 

 

Payment : Begin (Format tab)

 

 

 

I% ...............................

 

 

 

 

(P/Y = C/Y = 1)

 

 

100

 

 

 

 

 

 

C/Y

 

 

 

 

 

 

 

 

i =

{(1+

 

 

I%

 

 

 

 

 

 

 

 

)

P/Y

–1..... (Other than those above)

 

100 ⋅ [C/Y ]

 

 

uI%i (effective interest rate)

i (effective interest rate) is calculated using Newton’s Method. γ ⋅ PV + α ⋅ PMT + β ⋅ FV = 0

To I% from i (effective interest rate)

i ⋅ 100 .................................

(P/Y = C/Y = 1)

 

I% = {{(1+ i )

P/Y

 

 

 

–1}⋅C/Y ⋅ 100

 

 

C/Y

(Other than those

above)

Tip

•Interest (I%) calculations are performed using Newton’s Method, which produces approximate values whose precision can be affected by various calculation conditions. Interest calculation results produced by this application should be used keeping the above in mind, or results should be confirmed separately.

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