Formulas

                                       Interest calculation

Simple interest

I = i.t.PV

FV = PV + I è PV*(1+i*t) ….. (no effect of previously paid interest, typically Money Market,
securities with lifetime < 1 year)

Commercial discount (interest is payed ahead)

D = d*t*FV

PV = FV – D è FV*(1-d*t) (short time securities, T-bills, Promissory note)

i = d/(1+d) è d = i/(1-i)

Compound interest

PV for 1st year… = PV + I[1]

PV for 2nd year… = (PV + I[1]) + I[2] ,… è PV*(1+i)*(1+i)

PV for 3rd year... =( (PV +  I[1]) + I[2]) + I[3 ]

.

.

PV for nth year… =PV*(1+i)^n


Interest period < 1 year è PV*(1+i/m)^m

Effective interest rate

i[e] = (1+i/m)^m-1

Combined interest (When the whole time is not integer)

FV = PV*(1+i)^n*(1+i*R)

Where t = n + R, n ϵ Z and R < 1 Interest period

Continues interest (Interest period is in every moment, if m within one year goes to infinity)

FV=PV*e^^(f*t)  , … f = ln(i[e]+1), consequently  = e^ ^f- 1

Real interest^

… we consider the effect of inflation, then it must be true

PV*(1+i[r]) = PV*(1+i[n]) /(1+π) è i[r] =*(1+i[n]) /(1+π) – 1

Tax, FV after tax

FV=PV*(1+i*(1-T))^n

Note: The tax period is not always the same like the interest period! In most cases the tax period
is one year.

PV …………………………………………Present value

FV …………………………………………Future value

I    …………………………………………Interest (Amount)

D   …………………………………………Discount (Amount)

i    …………………………………………Interest rate

d   …………………………………………Commercial discount

n   …………………………………………Number of Interest periods

t   …………………………………………Time

R  …………………………………………Remaining time

T  …………………………………………Tax rate

f  …………………………………………Interest intensity