APR vs APY
APR is the annual interest rate without compounding effects; APY includes compounding and is always equal to or higher than APR for the same nominal rate.
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APR stands for Annual Percentage Rate. APY stands for Annual Percentage Yield. Both express interest as an annual percentage, but APR ignores intra-year compounding while APY includes it. For the same nominal rate, APY is always greater than or equal to APR, with the gap growing as compounding becomes more frequent. Lenders typically advertise APR; banks typically advertise APY.
How it works
APR is the simple annualized interest rate: a 12% APR on a credit card means roughly 1% per month, ignoring compounding effects on a balance. APY converts the same scenario to its true annualized return assuming the interest compounds. If a savings account pays 5% APR compounded monthly, the APY is approximately 5.12%. The compounding frequency drives the gap: daily compounding produces a slightly higher APY than monthly, which is higher than annual. The APR-to-APY conversion is: APY = (1 + APR/n)^n - 1, where n is the number of compounding periods per year.
Why it matters
APR understates the true cost of borrowing or true return on saving when compounding happens within the year. On a savings product, a higher APY beats a higher APR if compounding frequency differs. On a loan, the APR usually includes some fees but excludes compounding effects, so the effective cost can be higher than the headline rate. When comparing two products, always compare like to like: APR to APR or APY to APY, not one to the other.
Example
Two savings accounts: Account A advertises 5.00% APR compounded monthly, Account B advertises 4.95% APY. Convert A to APY: (1 + 0.05/12)^12 - 1 = 5.116%. Account A’s effective return is 5.116%, slightly better than Account B’s 4.95%. On the borrowing side: a credit card with 24% APR compounded daily has an effective APY of about 27.1%, which is what a balance left unpaid actually costs you over a year.
Common mistakes
- Comparing an APR loan offer to an APY savings offer head to head
- Ignoring compounding frequency when products advertise the same APR
- Forgetting that credit card APR understates the cost of revolving balances
- Treating advertised APY as a guarantee instead of a current rate
- Not noticing when a product switches from APR to APY language in fine print