Interest calculation,

Simple interest

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

k = T \cdot \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 \cdot q

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

T_{n} = T_{0} \cdot {(1 + \frac{p}{100})}^{n}

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

T_{n} = T_{0} \cdot {(1 - \frac{p}{100})}^{n}

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

T_{0} = T_{n} \cdot {(\frac{100}{100 + p})}^{n}

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

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

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

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