APR is the nominal annual rate before compounding. APY is the effective annual yield after compounding. For savings products, APY shows what you actually earn over a year.
Use APY = (1 + APR / n)^n - 1, where APR is written as a decimal and n is the number of compounding periods per year.
Yes. Use APR = n × ((1 + APY)^(1/n) - 1), with APY written as a decimal. For continuous compounding, use APR = ln(1 + APY).
Continuous compounding models interest as if it is applied constantly instead of in fixed periods. For APR to APY, the formula is APY = e^APR - 1.
When interest compounds, each period earns interest on prior interest. The more often interest compounds, the larger the gap between APR and APY.
Use the frequency stated by the bank, exchange, lending product, or DeFi protocol. Daily, monthly, quarterly, and annual compounding can produce different effective yields.
No. APY is a rate convention. Real returns can change due to variable rates, fees, withdrawals, risk, and product terms. For U.S. deposit disclosures, the FDIC Truth in Savings overview defines APY as a rate that reflects interest and compounding.
APR and APY often describe the same product from different angles. The FDIC Truth in Savings overview treats APY as the disclosure rate that reflects interest and compounding for deposit accounts.
"APY is the cleaner comparison metric because it includes compounding. APR is useful, but only tells part of the story."
Match the Disclosure
Use the same compounding frequency stated in the product terms. A daily APY and monthly APY are not interchangeable.
Compare Effective Yield
When comparing accounts or protocols, compare APY to APY. APR can understate the effective return when rewards compound.
Watch Variable Rates
If the underlying rate changes, the projected APY changes too. Treat high APYs as a snapshot, not a promise.
