# Effective Interest Rate

The effective interest rate is the interest rate on a loan that is iterated from the nominal interest rate while the rate of interest is the annual compound interest. The effective interest rate is also called effective annual interest rate or Annual Equivalent Rate (AER). Sometimes, it is also called as effective rate.

The effective interest rate is determined in such a way that it is compounded annually. The mathematical presentation of the effective rate is given below:

r = (1+ (i/n))(n) -1

Where,

r stands for the effective annual rate
i stands for the nominal rate
n stands for the number of compounding periods per year

If the frequency of compounding is raised to infinity, the mathematical representation of the effective interest rate will be:

r = e (i)�1 , where e= 2.71828

The concept of compounding terms for the interest rates may cause ambiguous interpretations. The annual cost of interest for two different loans may be incomparable due to two different types of compounding terms. The effective interest rate concept is used in such cases when it makes the comparison between two loans possible by converting any one loan into the equivalent annual rate.

The effective interest rate varies from annual percentage rate in two ways:

• The effective interest rate usually does not comprise one-time charges like front-end fees.
• The effective interest rate is not defined by regulatory authorities or legal authorities.

The use of effective annual interest is varied in nature. Depending on the various circumstances, the effective interest rate can be useful in economic studies. For example, a bank refers to the yield earned from a loan portfolio as its effective yield after assessing the expected losses. Depending on the calculated effective yield, the bank earns income from other fees. This means that the interest that is paid by the borrowers may change considerably depending on the bank’s effective yield. 