The annual percentage yield (APY) is a percentage that reflects the total amount of interest paid on an account. The APY is used together with the Annual Percentage Rate (APR) to calculate the total return on investment (ROI).
If the balance is compounded annually, then the APY and APR will be the same figure. However, if an account pays compound interest, the APY will be higher than the APR figure.
The APY calculation formula is the following:
APY = [(1 + Interest Rate / # of Compounding Periods)^Number of Compounding Periods] – 1
Example APY and APR Calculation
John has a savings account with interest compounding quarterly. The stated APR is 2% per year. John funds the account with $100,000 on January 1, 2023, and wants to calculate how much interest income he will have by the end of the year. If the account compounded interest annually, the interest would simply be $2,000 ($100,000 times 2%).
Given the account compounds quarterly(i.e., 4 times per year), John must calculate the APY using the following formula:
APY = ((1 + 0.06 / 4)^4) – 1
APY = 0.02015
APY = 2.015%
The end-of-the-year account value is $102,015, which means John earned $2,015 of interest income.