APY to APR Converter – Calculate Effective Annual Rate Online

APR (Annual Percentage Rate) is the nominal interest rate without considering the effect of compounding within the year. APY (Annual Percentage Yield), also known as the Effective Annual Rate (EAR), accounts for compound interest and reflects the true annual return. APY is always greater than or equal to APR when compounding occurs more than once per year. For example, a 5% APR compounded monthly yields an APY of approximately 5.116%.

To convert APY to APR, use the formula: APR = n × ((1 + APY)^1/n − 1), where n is the number of compounding periods per year. For continuous compounding, the formula is APR = ln(1 + APY). Our calculator handles both discrete and continuous compounding automatically.

The more frequently interest is compounded, the higher the APY for a given APR. Daily compounding produces a higher APY than monthly compounding, which in turn is higher than quarterly compounding. Continuous compounding represents the theoretical maximum—where interest is compounded infinitely many times per year. The difference becomes more pronounced at higher interest rates.

APY is higher than APR (when compounding occurs more than once per year) because of the compounding effect. With compounding, you earn interest on previously earned interest. APR ignores this effect, while APY captures it. The only case where APY equals APR is when compounding occurs exactly once per year (annual compounding). This is why financial institutions often advertise APY for savings accounts—it appears more attractive to depositors.

Continuous compounding is the mathematical limit where interest is calculated and added to the principal an infinite number of times per year. The formula for continuous compounding is APY = e^APR − 1, where e ≈ 2.71828 (Euler's number). While no bank offers truly continuous compounding, it represents the theoretical upper bound of compound interest and is widely used in financial mathematics and derivatives pricing.

Banks typically use APY for deposit products (savings accounts, CDs, money market accounts) to show the actual earning rate including compounding. They use APR for lending products (mortgages, credit cards, personal loans) as required by Truth in Lending regulations. Understanding both metrics helps consumers make informed comparisons—a loan with a lower APR but more frequent compounding could actually cost more than one with a slightly higher APR but less frequent compounding.

Yes, APY and APR are equal only when compounding occurs exactly once per year (annual compounding, n = 1). In this case, there is no intra-year compounding effect, so the nominal rate equals the effective rate. For any compounding frequency greater than 1 (semi-annual, quarterly, monthly, daily, or continuous), APY will always exceed APR.