# Effective Annual Interest Rate

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## Definition of 'Effective Annual Interest Rate'

The effective annual interest rate (EAR), also known as the annual percentage yield (APY), is the interest rate that is actually paid or earned on a loan or investment over a year. It is calculated by taking the nominal interest rate (the interest rate stated on the loan or investment) and compounding it over the number of times per year that interest is paid or compounded.

For example, if you have a loan with a nominal interest rate of 10% that is compounded monthly, the effective annual interest rate would be 10.47%. This is because 10% compounded monthly is the same as 10 / 12 * (1 + 10 / 12)12 = 10.47%.

The effective annual interest rate is important because it gives you a more accurate picture of the true cost of borrowing or investing. The nominal interest rate does not take into account the effects of compounding, so it can sometimes be misleading.

The effective annual interest rate is also used to compare different loans or investments. When you are comparing loans or investments, it is important to compare the effective annual interest rates, not the nominal interest rates.

The effective annual interest rate can be calculated using the following formula:

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

where:

r = the nominal interest rate

n = the number of times per year that interest is compounded

For example, if you have a loan with a nominal interest rate of 10% that is compounded monthly, the effective annual interest rate would be 10.47%. This is because 10% compounded monthly is the same as 10 / 12 * (1 + 10 / 12)12 = 10.47%.

The effective annual interest rate is a useful tool for comparing loans and investments. It gives you a more accurate picture of the true cost of borrowing or investing, and it can help you make better financial decisions.

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