APY Calculator
Free to use, with no sign up. Your entries stay in this browser; calculations run on your device.
Result
APY = 100[(1 + r/n)^n − 1]. r = nominal annual rate / 100; n = equal compounding periods per year. Illustration balance = 1000 × (1 + r/n)^n, with no deposits.
OpenStax Contemporary Mathematics: compound interest explains the principal formula. Contributions sum the same growth formula from each deposit time. Modeled APY assumes a constant nominal rate and equal compounding periods over one year. US Truth in Savings Act / Regulation DD, Appendix A: APY = 100[(1 + interest/principal)^(365/days) − 1]; the expression above is its one-year, fixed-rate specialization. Actual account disclosures can use different day counts and account terms.
Worked example: $1,000 at a nominal 5% compounded monthly for one year grows to $1,051.16. APY = 100[(1 + 0.05/12)^12 − 1] ≈ 5.1162%. At a nominal 10% compounded twice a year, APY = 100[1.05² − 1] = 10.25%.
Modeled APY uses a constant nominal annual rate and 1–365 equal compounding periods per year. Enter the nominal rate, not an already effective APY. Contributions are off. The balance table is a fixed $1,000 illustration over one year in USD; principal does not affect this modeled APY. Fees, changing rates and account-specific day counts are excluded. This is not an inverse APY-to-APR solver or an account disclosure certification.
Arithmetic only; not financial advice.
Underlying engine: Compound Interest Calculator. Related calculators: Investment Calculator, CD Calculator, Simple Interest Calculator.
How to use this tool
Enter the nominal annual rate as a percentage and compounding periods per year: 1 annual, 4 quarterly, 12 monthly or 365 daily. Select Calculate for modeled APY; deposits are disabled.
Frequently asked questions
Is nominal annual rate the same as APY?
No. APY includes compounding. This page computes modeled APY from the nominal rate and equal compounding periods over one year.
Does the principal change modeled APY?
No. With a fixed rate and equal compounding periods, principal cancels from the yield formula. The page uses a fixed $1000 one-year balance illustration with no contributions.
Can I convert APY back to APR?
No. This page only computes APY from a nominal annual rate. Actual account disclosures may use different day counts, fees or changing rates.