Effective Annual Rate (EAR) Calculator
Convert a nominal interest rate to the Effective Annual Rate (EAR) for any compounding frequency, and compare EAR across all compounding periods.
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How to use this calculator
r = nominal annual rate, n = number of compounding periods per year. For continuous compounding: EAR = e^r − 1.
- 1
Enter the nominal annual interest rate as stated on the financial product.
- 2
Select the compounding frequency — how often interest is applied to the balance.
- 3
The EAR shows the true annual return after accounting for compounding.
- 4
Use the comparison table to see how EAR changes across different compounding frequencies.
Frequently asked questions
What formula does this tool use?
This tool uses EAR = (1 + r ÷ n)^n − 1, where r is the nominal annual rate as a decimal and n is the number of compounding periods per year. For the continuous option it uses EAR = e^r − 1. The result is multiplied by 100 and shown with four decimal places.
How many periods does each frequency use?
The figures built into this tool are 365 for daily, 52 for weekly, 12 for monthly, 4 for quarterly, 2 for semi-annual and 1 for annual. There are no 360-day or 365.25-day variants, so a lender that quotes on a different day-count basis will not match to the last digit.
Do I enter 12 or 0.12 for 12%?
Enter 12. The field is a percentage and is divided by 100 inside the tool. At 12% compounded monthly the EAR is 12.6825%; at 24% compounded monthly it is 26.8242%.
What is the Monthly Equivalent Rate row?
It is (1 + EAR)^(1 ÷ 12) − 1, the single monthly rate that compounds to the EAR over twelve months. With monthly compounding it simply equals the nominal rate ÷ 12, so 12% shows 1.0000%. With annual compounding at 8% it is lower, 0.6434%, because only one yearly step is applied.
Is EAR the same as APY?
For interest earned, yes: both express a nominal rate with compounding included as a single annual figure. The calculator does not add fees, minimum balances or promotional periods, so a quoted APY or APR from a provider may include elements that this formula does not.
What happens at 0% or a negative nominal rate?
A 0% rate returns 0.0000% for every frequency. Negative rates run through the same formulas and give a negative EAR.
How much does compounding more often add?
Less each time. At 12% the EAR rises from 12.0000% annually to 12.3600% semi-annually, 12.5509% quarterly and 12.6825% monthly, then only to 12.7475% daily, against 12.7497% for the continuous limit. The tool shows all of these side by side whichever frequency you choose.
Effective annual rate: how compounding changes a quoted rate
Nominal rate in, yearly equivalent out
A nominal rate is quoted per year but compounded in smaller steps, so the interest you actually accrue over twelve months is higher than the headline. EAR converts the pair of nominal rate and frequency into the single yearly rate that would produce the same growth with one annual step. That makes offers with different compounding directly comparable.
Worked example: 12% compounded monthly
Each month earns 1.0000% (12 ÷ 12), and 1.01 raised to the twelfth power is about 1.1268, so the EAR is 12.6825%, which is 0.6825 percentage points above the nominal 12%. For comparison, the continuous-compounding figure for the same 12% is 12.7497%. A second example, 5% compounded daily, gives 5.1267% against 5.1271% for continuous compounding.
Frequency, rate and EAR together
The table lists runs with other combinations. It shows that the gap between nominal and effective rates widens with the nominal rate itself, so 24% monthly adds almost three points while 5% daily adds about one-eighth of a point. The annual row confirms that with one period per year the two rates are identical.
| Nominal rate | Compounding | EAR |
|---|---|---|
| 12% | Monthly | 12.6825% |
| 5% | Daily | 5.1267% |
| 6% | Continuous | 6.1837% |
| 24% | Monthly | 26.8242% |
| 8% | Annually | 8.0000% |
| 0% | Monthly | 0.0000% |
Why the comparison list is useful
The last result row lists EAR at every frequency for the nominal rate you entered. Reading across it shows the diminishing effect of compounding more often: most of the gain arrives by monthly compounding, and moving to daily adds little. When two products quote the same nominal rate, the one that compounds more often has the higher effective rate, but only slightly if both are already monthly or finer.
What EAR does not cover
EAR covers compounding only. It leaves out account fees, tax on interest, changes in the rate over time and the effect of inflation, and it assumes a constant rate for the full year. Use the output as an illustration of how the inputs interact when you compare quoted rates, not as a forecast of what an account will pay. The comparison row always lists the same six frequencies, so you can read off a differently compounded quote without re-entering anything: at 12%, the monthly entry is 12.6825% and the weekly entry 12.7341%.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →