An annual percentage rate (APR) represents the sum of the periodic interest rates over the course of one year, but does not account for the effects of compound interest. In order to accurately calculate the interest earned when interest compounds quarterly, you need to compute the annual percentage yield (APY). You receive higher interest returns with quarterly compounding than annual compounding, because the interest you receive after the first quarter begins immediately accruing additional interest for the rest of the year.

1. Divide the annual interest rate by 4 to find the quarterly interest rate. For example, if the annual interest rate equals 4.04 percent, divide 0.0404 by 4 to get a quarterly interest rate of 0.0101.

2. Add 1 to the quarterly interest rate. In this example, add 1 to 0.0101 to get 1.0101.

3. Raise the sum to the fourth power, because interest compounds four times per year. In this example, raise 1.0101 to the 4th power to get 1.041.

4. Subtract 1 from the result to find the annual percentage yield (APY) when interest is compounded quarterly. In this example, subtract 1 from 1.041 to find the APY equals 0.041, or about 4.1 percent.

5. Multiply the APY by the balance of the account to calculate the annual interest paid on the account. For example, if you had a savings account paying 4.04 percent interest, compounded quarterly, with $4,600 in the account, multiply $4,600 by 0.04102 to find you would earn $188.69 in interest over a year.

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