Effective Interest Rate Calculator
The effective interest rate (EAR) converts a nominal annual rate into the true annual rate after compounding. The formula is EAR = (1 + i/n)^n - 1, where i is the nominal rate and n is the number of compounding periods per year. This allows you to compare loans or savings accounts that use different compounding conventions on a fair, apples-to-apples basis. A 12% nominal rate compounded daily is slightly more expensive than 12% compounded monthly.
Effective interest rate formula
EAR = (1 + i/n)^n - 1
Where i is the nominal annual rate (as decimal) and n is the number of compounding periods per year. For continuous compounding: EAR = e^i - 1. The premium over nominal = EAR - i (as percentages).
Why compounding frequency matters
At a 12% nominal rate, monthly compounding gives EAR = 12.68%, daily compounding gives EAR = 12.75%, and annual compounding gives EAR = 12.00% exactly. The difference grows with the nominal rate: at 24% nominal, monthly compounding gives EAR = 26.82%, nearly 3 percentage points above nominal. When comparing loan offers with different stated rates and compounding frequencies, always convert to EAR for a fair comparison.
Frequently asked questions
What is the effective annual interest rate?
The effective annual interest rate (EAR or EFF%) is the real annual return or cost of a loan after accounting for compounding within the year. It is always greater than or equal to the nominal rate. EAR = (1 + i/n)^n - 1.
How does effective rate differ from APR?
APR (Annual Percentage Rate) under Regulation Z is a specific legal disclosure for consumer loans that includes fees and uses a specific calculation method. The effective interest rate calculated here is a mathematical conversion of nominal rate to account for compounding, without fee adjustments.
What is continuous compounding?
Continuous compounding is the theoretical limit as compounding frequency approaches infinity. The EAR under continuous compounding is e^i - 1, where e is Euler's number and i is the nominal rate. This is the maximum possible effective rate for a given nominal rate.
Why do lenders use monthly compounding?
Monthly compounding (n=12) is standard for most US consumer loans, mortgages, and credit cards because it aligns with monthly billing cycles. Daily compounding (n=365) is common for some savings accounts. The difference in effective rate between the two is small but measurable.
Does the CFPB require disclosure of the effective rate?
The CFPB requires APR disclosure under Regulation Z, which approximates the effective cost including fees. The effective rate from pure compounding conversion is a mathematical concept used for comparison, not a specific TILA disclosure field.
Official sources
- CFPB Regulation Z (Truth in Lending): 12 CFR Part 1026.
- Federal Reserve: Consumer Credit (G.19 Release).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.