Enter a nominal annual rate and choose a compounding schedule, including continuous, to see the effective annual rate.
How to Use the EAR Calculator
Enter the nominal annual rate and pick a compounding schedule from the dropdown — Annually, Semiannually, Quarterly, Monthly, Daily, or Continuous. The effective annual rate updates immediately, alongside the nominal rate for reference.
Effective Annual Rate and Annual Percentage Yield are the same calculation wearing two different labels — EAR is the term finance and economics texts use, APY is what shows up on a bank's marketing page. Both measure what a nominal rate actually delivers once compounding is applied within the year.
Discrete Compounding
EAR = (1 + rate÷100÷n)ⁿ − 1n is set by the dropdown: 1 for annual, 2 for semiannual, 4 for quarterly, 12 for monthly, 365 for daily. A 6% nominal rate compounded monthly comes out to roughly 6.17% EAR — the extra 0.17 points is pure compounding, not a different underlying rate.
The Continuous Limit
Continuous compounding is what happens as n grows without bound — infinitely frequent compounding, which sounds exotic but reduces to a clean closed form:
EAR = e^(rate÷100) − 1At 6% nominal, continuous compounding gives about 6.18% — barely above the monthly figure. This is the mathematical ceiling: no compounding schedule, however frequent, pushes the EAR any higher than the continuous case for a given nominal rate.
What EAR Is Actually For
Use it to compare two rates quoted with different compounding schedules on equal footing — a 5.9% rate compounded daily and a 6.0% rate compounded annually aren't obviously ranked until both are converted to EAR and set side by side. Quoted nominal rates alone can rank loans or accounts backwards.