What is the effective annual rate formula?

EAR = (1 + i ÷ m)m − 1, where i is the nominal annual rate and m the number of compounding periods per year. For continuous compounding, EAR = ei − 1.

Is EAR the same as APY?

Yes. Both measure the rate earned over a year including compounding. APY is the term used for deposit accounts.

Why is the effective rate higher than the nominal rate?

Because interest earned in early periods itself earns interest in later periods of the year.

How do I compare two loans with different compounding?

Convert both to an effective annual rate and compare those. The lower EAR is the cheaper loan.

Effective Annual Rate (EAR) Formula

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Effective Annual Rate (EAR) Calculator

The effective annual rate is the interest rate you actually earn or pay over a year once compounding is taken into account. A loan quoted at 12% a year with monthly compounding charges 1% a month, and 1% a month compounded twelve times is 12.68% a year, not 12%. EAR is the number that makes offers with different compounding frequencies comparable.

Formula

EAR = (1 + im)^m − 1 continuous: EAR = eⁱ − 1

Where

EAR: effective annual rate: the rate actually earned or paid over one year
i: nominal (stated) annual rate, as a decimal
m: number of compounding periods per year

Calculator

Nominal annual rate (i) (%)

Compounding

Result and step-by-step solution

Effective annual rate

12.6825%

A nominal 12% compounded monthly is equivalent to 12.6825% compounded once a year.

Rate per compounding period
im = 0.1212 = 0.01
Compound for one year
(1 + 0.01)¹² = 1.12682503
Subtract 1
EAR = 1.12682503 − 1 = 12.6825%

How to use the formula

The formula divides the nominal annual rate i by the number of compounding periods m, compounds that periodic rate m times and subtracts 1. As m grows the EAR rises, but by less and less; the limit, continuous compounding, is eⁱ − 1. The calculator includes that option, so you can see that 12% compounded daily (12.747%) is already very close to continuous (12.750%).

EAR is the same quantity that savings accounts advertise as APY. Use this page when you are comparing loans, credit cards or investments quoted with different compounding; use the APR to APY or APY to APR pages when converting quoted consumer rates.

Frequently asked questions

What is the effective annual rate formula?: EAR = (1 + i ÷ m)^m − 1, where i is the nominal annual rate and m the number of compounding periods per year. For continuous compounding, EAR = eⁱ − 1.
Is EAR the same as APY?: Yes. Both measure the rate earned over a year including compounding. APY is the term used for deposit accounts.
Why is the effective rate higher than the nominal rate?: Because interest earned in early periods itself earns interest in later periods of the year.
How do I compare two loans with different compounding?: Convert both to an effective annual rate and compare those. The lower EAR is the cheaper loan.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.