# Annual percentage rate

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Financial maths - interest rates.

(APR).

A legally defined consistent basis for quoting and comparing retail rates of interest payable.

Similar to the effective annual rate (EAR).

It is designed to enable borrowers to compare different borrowing deals on a consistent basis.

In particular, lenders may be tempted to present finance offerings to retail investors to make them sound cheap.

Quoting the APR basis can reveal how expensive some of the offerings are in reality.

Converting periodic interest rate to Annual Percentage Rate

APR = (1 + r)n - 1

Where:

APR = annual percentage rate

r = periodic interest rate

n = number of times the interest calculation period fits into a calendar year

Example 1: APR from monthly periodic rate of 2%

Interest is payable on a credit card at a rate of 2% per month, compounded once per month under usual market conventions.

What is the annual percentage rate?

Periodic interest of r = 2% (= 0.02) is charged per month.

The equivalent annual percentage rate is calculated from (1 + r).

1 + r

= 1 + 0.02

= 1.02

n = 12, the number of times interest is compounded per year

APR = (1 + r)n - 1

APR = 1.0212 - 1

APR = 26.8%.

Out of this total, the amount relating to interest on the original principal - simple interest - is 12 months x 2% per month = 24%.

The rest of the total of 26.8% is the additional amount due to compounding - interest on interest.

Example 2: Credit card interest at monthly rate of 3%

Interest is payable on a credit card at a rate of 3% per month, compounded once per month under usual market conventions.

What is the annual percentage rate?

Periodic interest of r = 3% (= 0.03) is charged per month.

The equivalent annual percentage rate is calculated from (1 + r).

1 + r

= 1 + 0.03

= 1.03

n = 12, the number of times interest is compounded per year

APR = (1 + r)n - 1

APR = 1.0312 - 1

APR = 42.6%.

Out of this total, the amount relating to interest on the original principal - simple interest - is 12 months x 3% per month = 36%.

The rest of the total of 42.6% is the additional amount due to compounding - interest on interest.