EAR Calculator
Calculate the Effective Annual Rate (EAR) of a nominal interest rate, and compare it across compounding frequencies
By Waqar Mushtaq · Last updated:
The Effective Annual Rate (EAR) — also called the effective interest rate or annual equivalent rate — is the true annual return or cost of a rate once compounding within the year is factored in. Two loans or savings products can advertise the same nominal rate but compound at different frequencies, which means they don't actually cost (or pay) the same amount — EAR is what makes them comparable on equal terms.
Effective Annual Rate Formula
O(1) calculationi = nominal annual rate (as a decimal), n = compounding periods per year
Continuous compounding (the limit as n approaches infinity)
The nominal (stated) annual rate i gets divided across n compounding periods, and because interest earned (or charged) in one period itself earns interest in the next, compounding more frequently pushes the effective rate above the nominal rate.
For example, an 18% nominal rate compounded monthly gives an EAR of (1 + 0.18/12)^12 - 1 ≈ 19.56% — nearly 1.6 percentage points higher than the advertised 18%, purely from monthly compounding. The more frequently a rate compounds (daily vs. monthly vs. annually), the bigger this gap gets, though it converges toward continuous compounding rather than growing without bound.
When n = 1 (annual compounding), EAR equals the nominal rate exactly, since there's only one compounding period and nothing to compound within the year.
Use Cases
Comparing loan or credit card offers
Two lenders quoting the same nominal APR but compounding monthly vs. daily aren't offering the same deal — converting both to EAR shows which one actually costs more over a year.
Comparing savings and CD rates
Banks often advertise a nominal rate alongside a separately-stated APY; EAR is the same calculation, letting you verify the advertised yield or compare accounts that only publish a nominal rate.
Understanding why "18% APR" costs more than 18% a year
Credit cards typically compound daily. Converting the stated APR to its EAR reveals the true annual cost of carrying a balance, which is meaningfully higher than the sticker rate.
Frequently Asked Questions
What is the difference between EAR and APR?
APR (Annual Percentage Rate) is the nominal, stated rate before accounting for compounding within the year. EAR (Effective Annual Rate) applies the compounding, so it reflects the true annual cost or yield. EAR is always greater than or equal to the nominal rate for a given rate, and the two are only equal when compounding happens once a year.
Is EAR the same thing as APY?
Yes — EAR and APY (Annual Percentage Yield) use the identical formula. "EAR" is more commonly used for borrowing/lending contexts (loans, credit cards) and "APY" for savings and deposit accounts, but both describe the same effective, compounding-adjusted annual rate.
Why does compounding frequency matter so much?
Interest earned or charged in each period is added to the balance before the next period's interest is calculated, so more frequent compounding means interest starts earning (or costing) interest sooner. The effect is largest going from annual to monthly compounding, and grows more slowly after that, converging toward the continuous-compounding limit.
Methodology
The formula above is implemented as a standalone module covered by unit tests, so its worked examples are re-checked on every change to the site. It is verified against the authoritative sources listed below.
Not financial advice. This calculator is a general informational tool and cannot account for your individual circumstances. See the terms of use.
Maintained by Waqar Mushtaq. Spotted a result that looks wrong? Report it and it becomes a failing test.