APY calculator

What is APY?

Annual percentage yield — the interest you actually earn in a year, with compounding included. Banks must quote it on savings accounts and CDs under the Truth in Savings Act.

How do I convert APR to APY?

APY = (1 + APR ÷ n)ⁿ − 1, with n the number of compounding periods a year. 5% compounded monthly is an APY of 5.116%; compounded daily, 5.127%.

Why is APY higher than the rate?

Because interest earns interest. The more often it compounds, the bigger the gap — but it is small at ordinary rates.

Which should I compare between banks?

APY — it puts accounts with different compounding on the same footing. For loans, compare APRs, which include certain fees.

How much will I earn in a year?

Balance × APY: $10,000 at 5.116% APY earns about $511.62 in a year if nothing is added or withdrawn.

Why does my bank show a slightly different APY?

Banks round the APY to the nearest hundredth of a percentage point, so 5.116% appears as 5.12%, and Regulation DD treats a disclosed figure as accurate if it is within 0.05 percentage point of the calculated one. The bank also uses the actual number of days in the term, and it may base a leap year on 366 days.

How is APY figured for a CD that is not one year long?

Regulation DD uses the interest earned over the term: APY = 100 × [(1 + interest ÷ principal)^(365 ÷ days in term) − 1]. If $10,000 earns $240 over a 180-day term, that is 2.4% for the term, and the APY is 4.93%. It assumes the interest stays in the account until the end.

How the conversion works

The page takes a nominal annual rate and the number of times a year interest is added, n. Each period earns the rate ÷ n, and after n periods the balance has grown by (1 + rate ÷ n)ⁿ, so APY = (1 + rate ÷ n)ⁿ − 1. Going the other way, rate = n × [(1 + APY)^(1/n) − 1]. Regulation DD defines APY from the interest actually earned, as in the CD question above, and assumes the principal and interest stay on deposit for the whole term. Under Regulation DD the interest rate itself is the annual rate paid without compounding.

Worked example: $10,000 at 5%

Compounded yearly, the APY equals the rate, 5.000%, and the account earns $500.00. Compounded quarterly it is 5.095%. Compounded monthly, each month adds 5 ÷ 12 = 0.4167%, the balance grows by 1.05116 over the year, and the APY is 5.116%: $511.62 of interest. Compounded daily, 365 times a year, the APY is 5.127% and the interest $512.67. Daily instead of monthly compounding adds $1.05 a year on this balance. In the other direction, an account advertised at 4.50% APY and compounded monthly pays a nominal rate of 4.410%.

Common mistakes

Do not set a savings APY beside a loan APR: one is what a deposit earns with compounding, the other is the cost of credit with certain fees included. Do not read APY as a promise for a year if the rate is variable, since the figure holds only while the rate does. It also leaves out early-withdrawal penalties, which the FDIC points out when it recommends comparing APYs, so check the penalty on any CD before picking the highest number. Finally, APY assumes no deposits or withdrawals; if you add money every month, project the balance with the compound interest calculator rather than multiplying by the APY.

Sources: Regulation DD (Truth in Savings), 12 CFR Part 1030, Appendix A (the APY formula and its assumptions) and 12 CFR 1030.2(c) (definition, rounding and tolerance), as summarized in the FDIC Consumer Compliance Examination Manual, VI-3; FDIC consumer news, “Savings Are Great for Short-Term Goals Too”. To project a balance with deposits, use the compound interest calculator; to price a certificate, the CD calculator; to see what inflation takes back, the real return calculator.

Estimates for planning only — not financial advice. Your bank's disclosures decide. How we check our calculators.