Compound Interest

uWhen calculating PV, PMT, FV, n

I%  0

α= (1 + i ⋅ S) ⋅

PV =

– α ⋅ PMT – β ⋅ FV

 

 

 

I% = 0

PV = – (PMT ⋅ n + FV )

 

 

 

 

 

 

 

 

 

 

γ

 

 

 

 

 

 

 

 

 

 

PMT = –  PV –  FV

 

PMT = –

PV + FV

 

 

n

 

 

 

FV = – PV –

PMT

 

FV = – (PMT ⋅ n + PV )

 

 

PV + FV

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n = –

 

 

log {

(1

+ iS )

⋅ PMT – FV ⋅ i

}

 

PMT

 

 

 

 

 

 

 

 

 

 

(1

+ iS )

⋅ PMT + PV ⋅ i

 

 

 

 

 

 

n =

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

log (1 + i)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 – β

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i

 

 

 

 

 

 

 

 

 

 

 

 

When “Odd Period” is “Off”

 

When “Odd Period” is “CI”

 

 

When “Odd Period” is “SI”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 =

(1 + i) –n

 

 

 

(1 + i) –Intg (n)

 

 

 

 

 

; =

1

 

 

 

 

(1 + i) Frac (n)

 

 

 

1 + i × Frac (n)

 

 

 

 

 

 

 

 

 

 

When “Payment Date” is “End”

 

When “Payment Date” is “Begin”

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S =

0

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

When P/Y = C/Y = 1

 

 

When P/Y  1 and/or C/Y  1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I%

 

 

 

 

 

 

I%

 

 

 

C/Y

 

i =

 

 

 

(1 +

 

 

)

P/Y

– 1

100

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

100 ⋅ [C/Y ]

 

 

 

 

 

 

 

 

 

 

 

 

 

uWhen calculating I%

i (effective interest rate) is calculated using Newton’s Method.

; × PV + ( × PMT +  × FV = 0

I% is calculated from i using the formulas below:

 

When P/Y = C/Y = 1

When P/Y  1 and/or C/Y  1

 

 

 

 

 

 

P/Y

I% =

i ⋅ 100

((1 + i )C/Y

–1)⋅ C/Y ⋅ 100

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.

Cash Flow

NPV = CF0 +

CF1

 

+

CF2

+

CF3

+ … +

CFn

( =

=%

, n: natural number up to 80)

 

 

(1+ i)

 

 

(1+ i)2

 

(1+ i)3

 

 

(1+ i)n

 

100

 

NFV = NPV ⋅ (1 + i )n

 

 

 

 

 

 

 

 

 

 

 

IRR is calculated using Newton’s Method.

 

 

 

0 = CF0 +

CF1

+

CF2

+

CF3

+ … +

CFn

 

 

 

 

 

 

 

(1+ i)n

 

 

 

 

(1+ i)

(1+ i)2

(1+ i)3

 

 

 

 

Chapter 11: Financial Application

183