Effective Interest Rate Calculator
Convert a nominal annual interest rate into the effective annual rate (EAR), also called the annual percentage yield (APY). Enter the stated rate and compounding frequency — monthly, quarterly, daily, or continuous — and the calculator returns the true annualized cost or yield after compounding is applied. Useful for comparing loans, savings accounts, bonds, and any other instrument where the compounding period differs from the stated rate period.
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Why the compounding period changes everything
A 6% nominal rate compounded monthly is not the same as 6% compounded annually. With monthly compounding, interest accrues on interest twelve times per year. The result is an effective rate of 6.168% — about 17 basis points higher than the stated rate. That gap widens as compounding frequency increases and as the nominal rate rises.
For savings and investments, higher compounding frequency benefits you: daily compounding on a savings account returns more than monthly compounding at the same APR. For debt, higher compounding frequency works against you: a credit card with a 22.99% APR compounded daily costs slightly more than 22.99% compounded monthly, though most card issuers use daily compounding in their billing cycle.
When comparing two financial products — a loan, a CD, a savings account — always compare effective annual rates, not nominal rates. A 5.9% rate compounded daily beats a 6.0% rate compounded annually for a borrower, but loses for a saver. The EAR standardizes the comparison.
Continuous compounding
Continuous compounding is the theoretical limit as compounding frequency approaches infinity. The effective annual rate under continuous compounding is e^r − 1, where e is Euler’s number (approximately 2.71828) and r is the nominal rate. At 6%, continuous compounding yields an EAR of about 6.184% — only marginally higher than daily compounding (6.183%), which is why daily compounding is a close practical substitute in most financial products.
Continuous compounding appears in options pricing (Black-Scholes), bond duration math, and theoretical finance. In practice, no retail bank or lender compounds continuously — daily is the highest frequency you’ll encounter in standard consumer products.
EAR vs APY vs APR
APR (Annual Percentage Rate) is a regulatory disclosure figure used in lending. Under the Truth in Lending Act, APR includes fees and costs beyond interest, expressed as a single annualized rate — but it does not account for compounding within the year. APY (Annual Percentage Yield) is the same concept as EAR: it reflects the actual annual return after compounding. Savings accounts advertise APY; mortgages advertise APR. This calculator computes EAR/APY from a nominal rate and compounding frequency.