Annuity

Annuity is a type of repayment, which is constant over the time. Th annuity payment consists of two parts – the interest and the amortization. The ratio of the interest to amortization is gradually decreasing.

To calculate the annuity we use the following formula:

$S = U \\cdot {{q^n \\cdot (q - 1)} \\over {q^n - 1}}$

S – annuity repayment
U – borrowed sum of money
q – q = 1 + interest_rate_per_time_period
n – number of time periods (time)

Example

We borrow 200 000$ in the bank for 5 years, payable monthly, with interest rate $15\\%$ per year. Find the monthly annuity payment.

Number of periods (months):
$n = 5 \\cdot 12 = 60$

We pay per month (we have to divide the annual interest rate):
$q = 1 + {{0.15} \\over {12}} = 1.0125$

We substitute into the formula:
$S = 200 000 \\cdot {{1.0125^{60} \\cdot (1.0125 - 1)} \\over {1.0125^{60} - 1}} = 4757.98$

We will pay 4758$ per month.

Borrowed sum of money:
Annual interest rate (%):
Total duration of the loan:
Length of the payment period:

Example

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