Investment calculators
APY to APR converter.
Turn an annual percentage yield into the nominal rate that produced it, or the other way round, for any compounding frequency.
APY = (1 + APR/n)n − 1 and APR = n[(1 + APY)1/n − 1], where n is compounding periods per year. Continuous compounding: APY = er − 1.
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Result
Worked example: a 12-month CD
A CD advertises 4.00% compounded monthly. Here n = 12, so APY = (1 + 0.04/12)12 − 1 = 4.0742%. On $10,000, one year of interest is about $407.42, not the $400.00 that 4.00% alone would suggest. Going the other way, a savings account that pays a 5.00% APY with monthly compounding has a nominal rate of 12 × [(1.05)1/12 − 1] = 4.8889%. Daily compounding changes the same 4.00% to a 4.0808% APY; continuous compounding gives e0.04 − 1 = 4.0811%.
Formulas and sources
APY is the effective one-year yield. The U.S. Truth in Savings regulation (Regulation DD) defines it as APY = 100[(1 + Interest/Principal)365/Days in term − 1], with the official examples $61.68 on $1,000 for 365 days = 6.17% and $30.37 on $1,000 for a 182-day CD = 6.18% (12 CFR Part 1030, Appendix A, Part I, as read 2026-09-30). The converter's formulas are the same relationship with interest expressed through a nominal rate compounded n times a year, solved for either side; the code reproduces both official examples in the test suite. The continuous case is the limit as n grows without bound, er − 1.
What this does not cover
Conversion is exact for a full-year term and a fixed rate. It ignores fees, tax, rate changes and partial-year terms, and a loan or credit card APR follows different disclosure rules. If an account states only an APY, it already includes compounding and needs no conversion.
Frequently asked questions
Is APY higher than APR?
For the same account, yes whenever interest compounds more than once a year, because interest earns interest. At annual compounding they are identical.
Which compounding frequency should I pick?
The one in your account terms. Many savings accounts and CDs compound daily or monthly. If the terms quote only an APY, you do not need to convert.
Does this APR match a loan or credit card APR?
Not necessarily. This page converts a nominal deposit rate to its effective yield; loan APRs follow separate rules and can include fees.
Disclaimer
Educational only. Rates on real accounts can change and may be subject to fees and tax; check your account disclosure.