# Interest calculation,

## Simple interest

Simple interest k with p % anulal interest rate on amount T (capital, deposit, loan, principal amount):

$k=T·\frac{p}{100}$

Interest factor q at anual interest rate p %:

$q=\frac{100+p}{100}=1+\frac{p}{100}$

The value of amount T increased by p % interest:

$T+k=T·q$

## Compound interest

Tn - The increased value of initial capital T0  over n years at an annual interest rate of p [%] :

${T}_{n}={T}_{0}·{\left(1+\frac{p}{100}\right)}^{n}$

Tn - The amortized value of initial capital T0 over n years with annual amortization rate of p [%]:

${T}_{n}={T}_{0}·{\left(1-\frac{p}{100}\right)}^{n}$

The annual discounted value of Tn by p [%]::

${T}_{0}={T}_{n}·{\left(\frac{100}{100+p}\right)}^{n}$

The increased value of the annuity a (savings intended for a unit period) over n years:

${S}_{n}=\frac{100·a}{p}\left({q}^{n}-1\right)$

## Annuity, loan

The increased value of the annuity a at the end of the n - th year, if the payment is due at the beginning of each year:

${S}_{n}=aq·\frac{\left({q}^{n}-1\right)}{q-1}$

The increased value of the annuity a at the end of the n - th year, if the payment is due at the end of each year:

${S}_{n}={S}_{n}^{*}=a·\frac{\left({q}^{n}-1\right)}{q-1}$

The annual installment of the T loan repayment (annuity), if the repayment is due at the end of each year:

$A=\frac{T}{100}·\frac{{q}^{n}·p}{{q}^{n}-1}$
Keywords: interest calculation, simple Interest, compound Interest, investment, annuity, interest rates, principal