Interest calculation,

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

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

i = P \cdot \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 \cdot q

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

P_{n} = P_{0} \cdot {(1 + \frac{r}{100})}^{n}

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

P_{n} = P_{0} \cdot {(1 - \frac{r}{100})}^{n}

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

P_{0} = P_{n} \cdot {(\frac{100}{100 + r})}^{n}

Increase of annuities a after n years:

S_{n} = \frac{100 \cdot a}{p} (q^{n} - 1)

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} = a q \cdot \frac{(q^{n} - 1)}{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 \cdot \frac{(q^{n} - 1)}{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} \cdot \frac{q^{n} \cdot r}{q^{n} - 1}