# Interest calculation,

Keywords: interest calculation, simple Interest, compound Interest, investment, annuity, interest rates, principal

### Simple Interest

Interest i for the principal P with an interest rates of  r %:

$i=P·\frac{r}{100}$

Interest coefficient q in case the interest rate is r %:

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

Increased value of principal P increased with interest at the interest rate of r %:

$P+i=P·q$

### Compound Interest

Value of principal Pn  after n years with an interest rate of r % in case of starting principal P0:

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

Value of principal Pn  after n years with an amortization rate of r % in case of starting principal P0:

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

Discount value of principal Pn with an interest rate of r %:

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

Increase of annuities a after n years:

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

### Investment

Availabel amount after n years in case of annuity investment a (amount, invested each year),
if the payment is at the beginning of each year:

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

Availabel amount after n years in case of  annuity investment a (amount, invested each year),
if the payment is at the end of  each year:

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

Installment (annuity) of the loan P on an annual basis, if the repayment rate is due at the end of the year:

$A=\frac{P}{100}·\frac{{q}^{n}·r}{{q}^{n}-1}$