Effective Annual Rate Calculator

The effective annual rate is the true annual yield on a deposit or investment once compounding is counted. A nominal 6% compounded monthly produces 6.1678%, not 6%, because each month's interest earns interest in the months that follow. For US deposit accounts the same figure is disclosed as the APY under Regulation DD.

APR is the nominal rate before compounding; APY is the effective annual rate after it. They are linked by APY = (1 + APR/n)^n - 1, where n is the compounding periods per year, so at the same nominal rate more frequent compounding gives a higher APY. Banks must disclose the APY on deposit accounts under Regulation DD because it compares directly across compounding schedules.

For discrete compounding, EAR = (1 + r/n)^n - 1, with r the nominal annual rate as a decimal and n the periods per year. At 6% monthly: (1.005)^12 - 1 = 6.1678%. For continuous compounding, EAR = e^r - 1: at 6%, e^0.06 - 1 = 6.1837%. The table under the chart shows the EAR at every frequency for the rate you enter.

Yes, for standard US deposit accounts. Regulation DD (12 CFR Part 1030, Appendix A) defines the APY with the same formula as EAR. The names differ by context: EAR is the general-finance term, APY the US disclosure term for deposits, and AER (annual equivalent rate) the UK term. All use the same calculation.

It depends on the compounding frequency: nominal = n x ((1 + APY)^(1/n) - 1). Monthly: 12 x ((1.05)^(1/12) - 1) = 4.8889%. Daily: 365 x ((1.05)^(1/365) - 1) = 4.8793%. Continuous: ln(1.05) = 4.8790%. Choose "Target EAR / APY → Nominal rate" at the top of the calculator to solve it for any APY and frequency.

Each compounding event applies the periodic rate to a balance that includes all earlier interest, so more frequent compounding means interest starts earning interest sooner. At 5% nominal: annually 5.0000%, quarterly 5.0945%, monthly 5.1162%, daily 5.1267%, continuously 5.1271%. On $100,000, daily rather than monthly compounding at 5% adds about $10.56 a year.

It is the limit of compounding as the frequency becomes infinite: EAR = e^r - 1. At 6% nominal it gives 6.1837%, the highest effective rate possible for that nominal rate. No retail bank compounds continuously — daily is as frequent as deposit accounts get — but continuous rates are standard in finance theory, from option pricing to bond mathematics.

Higher than the advertised APR. Credit cards state a nominal APR and usually compound daily on a carried balance. A 24.99% APR compounded daily is an effective annual rate of (1 + 0.2499/365)^365 - 1 = 28.38%; compounded monthly it would be 28.06%. Paying the statement balance in full within the grace period avoids interest on purchases altogether.

No. A mortgage or car-loan APR is a Truth in Lending disclosure that adds certain fees and points to the note rate, spread over the term (Regulation Z). It is not a compounding conversion. Mortgage interest is charged monthly on the remaining balance and paid each month, so the APR is above the note rate because of fees, not compounding.

It is higher whenever interest compounds more than once a year, and equal only with annual compounding. At 6%: annually 6.00%, monthly 6.17%, daily 6.18%, continuously 6.18%. The gap widens with the rate — at 20%, daily compounding gives 22.13%. For a positive rate, the EAR is never below the nominal rate.

Use =EFFECT(nominal_rate, periods_per_year): =EFFECT(0.06, 12) returns 0.061678, or 6.1678%. The reverse is NOMINAL: =NOMINAL(0.05, 12) returns about 4.889%, the nominal rate that gives a 5% APY with monthly compounding. Both work in Google Sheets. For continuous compounding use =EXP(rate)-1.

Take the twelfth root, not a twelfth. The monthly rate equivalent to a 5% APY is (1.05)^(1/12) - 1 = 0.4074%; dividing gives 5% / 12 = 0.4167%, which overstates it because each month's interest compounds over the remaining months. A daily rate works the same way: (1 + APY)^(1/365) - 1.