Question:

# How to calculate effective annual interest rate?

Firstly, the effective annual interest rate is also called effective interest rate, or annual equivalent rate (AER), and is different from the APR - annual percentage rate. In fact, the effective annual interest rate is typically higher than the quoted APR. The following example of how the effective interest rate is calculated will help you understand why.

Let's assume you want to deposit in a bank \$1000. The bank will pay you 10% interest annually. This means that at the end of the year you will receive 10% x \$1000 = \$100 and this rate will turn your \$1000 into \$1100. In this example, the effective interest rate is the same as the quoted interest (10%).

Now let's examine the same example of a stated annual rate of 10% but this time the bank will pay it semi-annually (the compounding will occur twice a year). This means that when the first payment occurs the bank will pay you 5% x \$1000 = \$50. However, at the end of the year, when the second payment occurs, the bank will pay you 5% x \$1050 = \$52.50 and this will turn your \$1000 into \$1102.50 . Thus, for the whole year you would have actually earned \$102.50 and the effective interest rate would be 10.25% (more than the quoted interest of 10%).

Basically, the effective annual interest rate is the annual interest rate that accounts for the effect of compounding.

## Effective Mortgage Interest Rate

In the example above you are depositing money in a bank and naturally the compounding effect is welcomed. However, when it comes to credit card debt, unsecured personal loan, auto loan or mortgage loan you are the one who has to pay interest. And you don't make mortgage payments once a year. Typically, you make your payments on a monthly basis.

Thus, your quoted APR is not the same as your effective annual interest rate. Always ask your lender what the effective interest rate will be or calculate it yourself.

## Effective Annual Interest Rate Formula

So how to calculate effective annual interest rate if you know the nominal interest rate and the number of compounding periods? Here is the formula:

Effective annual interest rate = (1 + R / P)P - 1 ,

where R is the nominal rate and P is the number of compounding periods.

For example, let's assume you have a loan with 8.25% nominal interest. When you make monthly payments (12 compounding periods), your effective annual interest rate will be:

(1 + 0.0825 / 12)12 - 1 = 8.57%

Calculating the effective annual interest rate differs from calculating the nominal rate. The nominal rate is calculated as you multiply the number of periods times the interest for the period. For example, 1% monthly interest times 12 is 12% nominal interest rate.

Calculating annual interest rate is necessary as the interest for different loans can be calculated based on a daily, weekly, monthly or quarterly basis. The effective annual interest rate is used to compare loans with different compounding periods. A loan whose effective rate is based on daily compounding will have significantly higher rate than a loan based on monthly compounding.

You should distinguish simple interest and compound interest (the effective annual interest rate can be referred to as annual compound interest).

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