# Effective Annual Interest Rate - Explained

What is an Effective Annual Interest Rate?

# What is an Effective Annual Interest Rate?

An effective annual interest rate, also known as annual equivalent rate, effective rate, and effective interest rate, is a return that is earned on investments, loans, or other financial assets during a stipulated period of time. The rate differs from the stated annual percentage rate because of compounding of interest.

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## How Does an Effective Annual Interest Rate Work?

The effective rate of return often differs from the nominal return. This is because interest earned is calculated (compounded) on a monthly, bi-monthly, semi-annual, or annual basis. Suppose investment A has 10% return compounded monthly, and investment B has 10.1% compounded semi-annually. To determine which investment is more attractive and pays more return over the given time period, the effective interest rate can be used to assess which investment is more profitable. The effective interest can be calculated by using the following formula; = (1+i/n) ^n-1 i = annual interest fee n = number of compounding years The nominal interest rate in an interest rate stated on the face value of financial instruments. The nominal interest rate in the above example is 10% for investment A and 10.1% for investment B. An effective interest rate can be calculated by applying the above formula. EAR for investment A would be: 10.47% = (1 + (10% / 12)) ^ 12 - 1 And EAR for investment B would be: 10.36% = (1 + (10.1% / 2)) ^ 2 - 1 From the above example, it can be seen that the investment has a higher nominal interest rate but it has a lower effective rate of investment due to fewer compounding period.