APY (Annual Percentage Yield) is the real annual return a savings rate produces once compounding is factored in — the number that lets you compare a 5.00% daily-compounding rate against a 5.05% monthly-compounding rate apples-to-apples. This calculator converts a stated rate to APY (or the reverse) and projects real dollar earnings on a deposit.
Quick answer: Nominal rate + compounding frequency → APY (or the reverse: target APY → required rate), plus projected dollar earnings on a deposit.
Forward: APY = (1 + r/n)^n − 1 Reverse: r = n × ((1 + APY)^(1/n) − 1) r = nominal annual rate (decimal) n = compounding periods per year Projected earnings = deposit × ((1 + APY)^years − 1)
Assumptions
Equivalent APY ≈ 5.13%. Projected 1-year earnings on $10,000 ≈ $513.
Required nominal rate ≈ 4.89%. Monthly compounding needs a slightly lower stated rate than daily to reach the same APY, since it compounds less often.
APY (Annual Percentage Yield) is the effective annual return including the effect of compounding, while the interest rate (or 'nominal rate') is the base rate before compounding. Because compounding means you earn interest on previously earned interest within the year, APY is always equal to or slightly higher than the nominal rate — the more frequent the compounding, the bigger the gap.
Federal Reserve Regulation DD (Truth in Savings Act) requires banks to disclose APY specifically so consumers can compare accounts on equal footing — a bank compounding monthly at a lower nominal rate could actually pay less than one compounding daily at a slightly lower rate, and APY normalizes that difference into one comparable number.
The gap between daily and annual compounding at typical savings rates (4-5%) is usually well under a quarter of a percentage point of APY — meaningful for large balances over long periods, but rarely the deciding factor between two accounts. The nominal rate itself matters far more than the compounding frequency; always compare the APY, not the raw rate, across banks.
No — APY (Annual Percentage Yield) describes what you EARN on a deposit and includes compounding. APR (Annual Percentage Rate) describes what you PAY on a loan or credit card and, for most consumer loans, does not include the compounding effect the same way. They answer different questions and aren't directly comparable.
The formula APY = (1 + r/n)^n − 1 is exact for fixed-rate accounts with a constant compounding schedule — which covers the vast majority of savings accounts, money market accounts, and CDs. Variable-rate accounts (where the rate can change during the year) will see their actual realized APY diverge from this exact math if the rate moves.