APY / APR Converter

APR (annual percentage rate) is the nominal rate before compounding. For this converter it equals the periodic rate times the number of periods per year. APY (annual percentage yield) is the effective annual return once compounding is applied. A savings account quoting a 5% APR compounded monthly has an APY of about 5.116%, the extra fraction being the interest you earn on your own interest over the year.

APR is the right comparison for loans and mortgages. US law (Regulation Z, the Truth in Lending Act) requires lenders to disclose it so you can compare offers on equal footing. For deposit products like savings accounts and CDs, use APY instead: the Truth in Savings Act requires banks to advertise it, and it reflects what you actually earn. Comparing a loan's APR to a savings account's APY is an apples-to-oranges mistake.

Continuous compounding is the theoretical limit where interest compounds every instant. The formulas simplify to APY = e^APR - 1 and APR = ln(1 + APY). In practice, daily compounding (365 periods per year) sits so close to continuous that the gap is a fraction of a basis point. Continuous compounding shows up in academic finance and options pricing, but is rare in retail banking products.

Because each compounding period credits interest on the already-accumulated balance, not just the original principal, so that reinvested interest earns its own return. The gap widens with more frequent compounding: at 6% APR, monthly compounding gives 6.168% APY, while daily compounding gives 6.183% APY. APR and APY are equal only when there is exactly one compounding period per year (annual compounding).

Only when the rate is negative. For any positive rate with discrete compounding, APY is strictly greater than APR. At a rate of zero, or with annual compounding (n = 1), the two are exactly equal. Negative rates are mathematically valid in this converter (a savings rate below zero is unusual but not impossible), and the same formulas hold as long as the APY stays above -100%.