APR vs APY: How to Calculate the Yield You Actually Earn

APR, the annual percentage rate, is the simple stated interest rate for a year before any compounding is considered. APY, the annual percentage yield, is what you actually earn once interest is added to your balance and then earns interest itself. Whenever interest compounds more than once a year, the APY is higher than the APR.

This distinction matters most when comparing savings accounts, certificates of deposit, and money market accounts. Two accounts can advertise the same APR yet pay different real returns because one compounds daily and the other only monthly. Comparing by APY puts every account on equal footing, which is exactly why United States regulations require banks to disclose APY on deposit accounts.

The math is straightforward. APY equals one plus the periodic rate raised to the number of periods, minus one. In symbols, APY equals the quantity one plus r divided by n, all raised to the power n, minus one, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year.

For example, a 5 percent APR compounded monthly uses r equal to 0.05 and n equal to 12. The result is about 5.116 percent APY. Compounded daily with n equal to 365, the same 5 percent APR yields about 5.127 percent. The gaps look small on paper but grow with larger balances and longer time horizons, which is the whole point of compounding.

Each time interest compounds, the interest earned so far is folded into the principal so future interest is calculated on a slightly larger base. More frequent compounding means the balance grows in smaller but more numerous steps, and those steps add up. Daily compounding beats monthly, which beats quarterly, which beats annual, for the same stated rate.

There is a ceiling, though. As compounding frequency increases toward infinity, the yield approaches continuous compounding, calculated as e raised to the rate minus one. For a 5 percent rate that continuous limit is about 5.127 percent, barely above daily compounding. In practice the jump from annual to daily captures nearly all the benefit, and pushing beyond daily adds almost nothing.

The calculator works entirely in your browser with no account or upload required. Give it the nominal rate and how often interest compounds, and it returns the effective annual yield so you can compare offers honestly. Results are estimates for planning and do not account for fees, taxes, or promotional rate changes.

When a bank advertises a rate, check whether the headline number is the APR or the APY, because the APY will always look more attractive. For deposit accounts in the United States, the disclosed APY is the fair comparison figure. For loans and credit cards, lenders quote APR, and there the direction of your interest is reversed: more frequent compounding works against you.

Keep in mind that these calculations assume a fixed rate for the full year. Promotional or teaser rates that expire, tiered rates that depend on your balance, and variable rates that track a benchmark can all change your actual yield. Treat any single APY figure as an estimate, and for significant financial decisions consider speaking with a qualified financial professional.