📊 EAR Calculator

The effective annual rate is what a nominal rate truly earns or costs after compounding within the year. An 8 percent nominal rate compounded monthly is not 8 percent; it is (1 + 0.08/12)^12 - 1 = 8.30 percent. The 0.30-point gap is interest earning interest, and it is why lenders quote nominal rates while the true cost runs higher.

How to Use This Calculator

Enter the nominal annual rate and the compounding frequency. The calculator returns the EAR, the compounding bonus over nominal, and what $10,000 grows to in one year at the effective rate.

The Formula

More frequent compounding always raises the EAR, but with diminishing returns: the jump from annual to monthly matters far more than from monthly to daily. In the limit of continuous compounding, EAR approaches e^nominal - 1. Regulators know this, which is why US savings disclosures use APY, essentially the EAR, so banks cannot hide behind compounding games.

Worked Example

Nominal 8 percent, monthly compounding: EAR = (1 + 0.08/12)^12 - 1 = 8.2999 percent, shown as 8.300 percent. The compounding adds 0.300 points. On $10,000 that is $8,300 of a year's growth versus $8,000 at simple annual compounding, a $30 difference. Daily compounding would give 8.328 percent, only 0.028 points more than monthly, showing how quickly the gains flatten.

EAR vs APR vs APY

Where EAR Decides

Credit cards disclose APR but charge daily periodic rates, so the effective rate on carried balances exceeds the stated APR; that gap is pure EAR math. Mortgages with monthly compounding versus Canadian-style semi-annual compounding differ in EAR even at identical nominal rates. And when a savings account advertises 4.5 percent compounded daily against a competitor's 4.55 percent compounded monthly, the EAR settles it: 4.60 versus 4.65 percent. Small gaps, real dollars.

Common Mistakes

Comparing nominal rates across different compounding frequencies is the classic error; always convert to EAR first. Confusing APR with EAR on loans ignores fees, which APR includes and EAR does not. For the fee-inclusive picture use our APR calculator, for converting between frequencies our equivalent rate calculator, and for long-run growth our compound interest calculator.

Where EAR Hides in Disclosures

Truth in Lending requires APR disclosure, but the EAR often lurks beneath it. Credit card statements show a nominal APR while interest accrues daily, so the effective rate on a carried balance runs a few tenths higher than the disclosed number. Over a year of revolving $10,000 at 24.99 percent APR, the daily compounding adds roughly $150 beyond what the nominal rate implies. The disclosure is legal and the math is real; both can be true at once.

Mortgage disclosures handle this better: the APR on a Loan Estimate already folds in most fees, and monthly compounding is standard, so the gap between APR and EAR is small. The trap is comparing a monthly-compounding US mortgage with a semi-annual-compounding Canadian one at the same nominal rate. The Canadian loan's EAR is lower by about 0.1 percent, a genuine saving hidden in compounding convention.

For savers, the tables turn: banks must disclose APY, which is the EAR, so the compounding games favor you. A 4.60 percent APY compounded daily beats a 4.60 percent nominal rate compounded monthly, and the disclosure tells you so plainly. Whenever a product's disclosure leads with the nominal rate, reach for this calculator; whenever it leads with APY, the work is already done.

Investment ads exploit the same gap in reverse, quoting nominal yields that look competitive until converted. A bond fund advertising a 6 percent distribution yield with monthly payouts delivers about 6.17 percent effective, a genuine bonus, while a 6 percent yield paid annually delivers exactly 6. Whenever two products quote different compounding frequencies, convert both to EAR before comparing; the nominal figures are not on the same scale.

EAR and the Rule of 72

The Rule of 72 estimates doubling time as 72 divided by the rate, but it works properly only with the effective rate. At 8 percent nominal compounded monthly, the rule using 8 gives 9.0 years; using the 8.30 percent EAR gives 8.7 years, which matches the actual math. The difference is small for one doubling and meaningful over a lifetime of compounding, which is exactly when precision matters most.

The same correction applies to tripling (Rule of 114) and quadrupling (Rule of 144). Whenever compounding is more frequent than annual, substitute the EAR for the nominal rate in every shortcut formula. The shortcuts were derived for effective rates; feeding them nominal rates quietly understates every long-horizon result.

Estimates for planning only, not financial advice.