Lenders and banks advertise a "nominal" or "stated" annual rate, but that number understates what you actually earn or pay whenever interest compounds more than once a year. The Effective Annual Rate (EAR) — also called APY on the savings side — restates any nominal rate as the true annual rate you'd need under annual compounding to get the same result.
The Formula
EAR = [(1 + Nominal/100/n)^n − 1] × 100 Continuous compounding: EAR = (e^(Nominal/100) − 1) × 100
n is the number of compounding periods per year. As n grows large (compounding more and more often), the formula approaches the continuous-compounding case, which is the theoretical ceiling for how high the effective rate can go at a fixed nominal rate.
Why EAR Is Always ≥ the Nominal Rate
When n = 1 (annual compounding), EAR equals the nominal rate exactly — there's only one compounding event per year, so nothing compounds within the year. For any n greater than 1, interest earned in an earlier period starts earning its own interest before the year is out, which is why EAR climbs above the nominal rate. The more frequently interest compounds, the bigger that gap gets — though, as the table above shows, the jump from monthly to daily to continuous is small compared to the jump from annual to monthly.
A Worked Example
A credit card advertises "6% APR, compounded monthly." Plugging into the formula: EAR = (1 + 0.06/12)^12 − 1 = (1.005)^12 − 1 ≈ 0.06168, or about 6.17%. That's the rate you're actually paying annually, not the 6% headline figure — a small but real difference that compounds (literally) if you carry a balance for years.
Frequently Asked Questions
Q: Is EAR the same thing as APR?
A: No. APR is generally the nominal rate plus certain fees, without necessarily reflecting intra-year compounding. EAR (or APY) specifically reflects the effect of compounding frequency. Two loans with identical APRs can have different EARs if they compound at different frequencies.
Q: Why would a nominal rate ever be higher than EAR?
A: It can't, mathematically — EAR is always greater than or equal to the nominal rate at any positive rate and any compounding frequency of 1 or more. If you see a quoted "effective rate" lower than the nominal rate, double check whether it's actually a different metric, like a rate net of fees or taxes.
Q: What does "continuous compounding" mean practically?
A: No real account compounds literally every instant, but continuous compounding is a useful mathematical limit and shows up in options pricing and some theoretical finance. In practice, daily compounding gets you extremely close to the continuous result.
Q: Which frequency should I compare loans by?
A: Always compare EAR (or APY), not the nominal rate — it's the only number that puts loans or deposits with different compounding schedules on equal footing.
Disclaimer: This calculator and guide are for educational purposes only and should not be considered financial advice. Always consult with a qualified financial advisor before making borrowing or investment decisions. Past performance does not guarantee future results, and all investments carry risk.