Effective Annual Rate (%)
8.33%
How it works
The Effective Interest Rate Calculator converts a nominal annual interest rate (APR) into the effective annual rate (EAR/APY) that accounts for the frequency of compounding — daily, monthly, quarterly, or continuous. It also converts between APR and APY and calculates the periodic rate.
The distinction between APR and APY is critical for comparing financial products. A savings account advertised at 4.8% APR compounded monthly has an APY of 4.908% — this is the true annual return. A credit card at 24% APR compounded daily has an EAR of 27.11% — this is the true annual cost. Regulators require disclosure of both, but they are easy to confuse.
How to use it: enter the nominal rate and compounding frequency. The calculator returns the effective annual rate (EAR/APY). Or enter the APY and it reverse-calculates the equivalent APR for any compounding frequency.
Formulas: - EAR = (1 + r/n)^n − 1 where r = nominal rate, n = compounding periods per year - Continuous compounding EAR = e^r − 1 - Periodic rate = APR / n
Continuous compounding: the mathematical limit as compounding frequency approaches infinity. A 5% nominal rate with continuous compounding produces an EAR of 5.127%. Used in options pricing, certain financial derivatives, and theoretical models.
Loan comparison: to fairly compare two loans (one quoted as 5.5% monthly compounding vs. one quoted as 5.4% daily compounding), convert both to EAR. The 5.5% monthly compounding (EAR 5.641%) is more expensive than the 5.4% daily compounding (EAR 5.549%).
Privacy: rate conversion runs in the browser.
Frequently Asked Questions
- APR (Annual Percentage Rate) is the nominal rate without compounding — it's what's quoted. APY (Annual Percentage Yield) or EAR (Effective Annual Rate) is the actual rate earned/paid after accounting for compounding. A savings account at 4.8% APR compounded monthly has an APY of 4.908%. Savings products advertise APY (higher); loan products advertise APR (lower).
- Daily compounding maximizes the effective rate for the lender. A credit card at 24% APR with daily compounding has an EAR of 27.11% — significantly higher than 24%. This is why the APR on credit cards is always disclosed separately from the EAR. By law, credit cards must disclose the APR; the EAR is often buried in the fine print.
- Continuous compounding is the mathematical limit as compounding frequency approaches infinity. The EAR formula becomes e^r − 1 instead of (1 + r/n)^n − 1. At 5% nominal rate: annual compounding EAR = 5%, monthly = 5.116%, daily = 5.127%, continuous = 5.127%. The difference between daily and continuous is negligible for practical purposes.
- Convert both to Effective Annual Rate (EAR). Loan A: 5.5% APR compounded monthly → EAR = 5.641%. Loan B: 5.4% APR compounded daily → EAR = 5.549%. Loan B has a lower true annual cost despite the smaller APR difference, because daily compounding added more to Loan A's rate. EAR comparison is the correct apples-to-apples comparison.