Convert a nominal interest rate into Annual Percentage Yield (APY) based on how often it compounds. See your true annual yield and the real interest earned on any balance — for savings, CDs & HYSAs.
Annual Percentage Yield
APY (Annual Percentage Yield) is the real rate of return you earn on savings in one year once compounding is included. The nominal rate (APR) ignores compounding, so APY is always equal to or higher than the stated rate. The formula is APY = (1 + r ÷ n)n − 1, where r is the nominal annual rate and n is the number of compounding periods per year. A 5% rate compounded daily yields an APY of about 5.13%.
Banks advertise savings accounts and CDs in APY because it's the honest, comparable figure — it already bakes in how often interest is added. When comparing high-yield savings accounts (HYSAs) or certificates of deposit, always compare APY to APY. The more frequently an account compounds (daily beats monthly beats annually), the higher the APY for the same nominal rate, though the difference is small at typical rates.
APY = (1 + r/n)ⁿ − 1. It reflects interest-on-interest, so it's always ≥ the nominal APR.
Banks quote savings & CDs in APY. Always compare APY to APY across accounts — never APY vs APR.
Daily compounding yields slightly more than monthly or annual for the same rate — but the gap is small.
Annual percentage yield expresses what a nominal interest rate actually earns once compounding is taken into account, which makes it the only fair basis for comparing savings products. Two accounts quoting 5% are not equivalent if one compounds daily and the other annually. US banks are required by the Truth in Savings Act to disclose APY precisely so that consumers can compare like with like. The counterpart on the borrowing side is APR, which works the opposite way — it adds fees into a rate rather than adding compounding — so APY and APR are not symmetrical despite the similar names.
APY = (1 + r/n)^n − 1Continuous compounding: APY = e^r − 1Reverse: r = n × [ (1 + APY)^(1/n) − 1 ]where:
Assumptions: APY assumes the rate holds for a full year and interest stays in the account. Variable-rate savings accounts can change the rate at any time, so a quoted APY is a snapshot rather than a promise.
The same headline rate, compounded four different ways, on a $10,000 deposit.
Result5% nominal = 5.13% APY compounded daily
The whole range from annual to continuous is only 12.7 basis points, or $12.71 on $10,000. Compounding frequency is worth checking but is far less important than the rate itself — a bank offering 5.1% annually beats one offering 5.0% daily.