Effective Annual Rate Calculator
The EAR is the one honest number behind any quoted rate: what you truly earn — or truly pay — per year once compounding is counted. Convert any nominal rate, at any frequency, up to continuous compounding.
▸ All frequencies, side by side
| Compounded | Times/yr | EAR | Year-1 interest on $100,000 |
|---|
Estimates are for illustration and education only — not financial advice.
Effective annual rate, explained
The effective annual rate answers one question: if all the within-year compounding were rolled into a single annual payment, what rate would that be? The formula is EAR = (1 + r ÷ n)n − 1 for n compounding periods per year, and EAR = er − 1 for continuous compounding — the mathematical ceiling no frequency can exceed.
EAR vs. APY vs. APR
EAR and APY are the same number — "APY" is the banking-product name (deposits), "EAR" the finance-textbook name used for loans, bonds and analysis. APR is the nominal rate before compounding. For savings, banks advertise the flattering APY; for loans, the flattering APR — the EAR is how you see through both.
Why the ceiling exists
Each halving of the compounding interval adds less than the one before, converging to er − 1. At 6% nominal, annual compounding gives 6.000%, monthly 6.168%, daily 6.183% — and continuous only 6.184%. The chart above shows how quickly the bars flatten: past monthly, frequency is marketing, not money.
Where EAR really matters: debt
A credit card quoting 24% APR compounds daily — an EAR of about 27.1%. On loans, the gap between nominal and effective is your true cost. For the savings side of the same math, see the APY calculator, or project a balance over years in the compound interest calculator.
Nominal → effective at a glance
Effective annual rates for common nominal rates. The last column is the ceiling — continuous compounding.
| Nominal | Quarterly | Monthly | Daily | Continuous |
|---|---|---|---|---|
| 3% | 3.034% | 3.042% | 3.045% | 3.045% |
| 6% | 6.136% | 6.168% | 6.183% | 6.184% |
| 9% | 9.308% | 9.381% | 9.416% | 9.417% |
| 12% | 12.551% | 12.683% | 12.747% | 12.750% |
| 24% | 26.248% | 26.824% | 27.115% | 27.125% |
Rounded to three decimals; assumes interest is credited and retained all year.
The effective annual rate formula
The EAR converts any nominal rate into the true annual cost or yield once compounding is taken into account — the only fair way to line up rates quoted at different frequencies.