Effective annual rate

The effective annual rate (EAR) is the true annual cost or return after accounting for intra-year compounding. A 12% nominal rate compounded monthly produces an EAR of approximately 12.68%, higher than the stated rate.

ByHoang TruongUpdated July 2, 2026

FrameworkTime value of money

What it is

See it move

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A credit card quotes a nominal rate of 18% a year, compounded monthly across twelve periods. Converting that into an effective annual rate, (1 + 0.18/12) to the twelfth power minus one, gives 19.56%, noticeably higher than the stated 18%. Comparing products on the effective rate, not the nominal one, is the only fair way to judge which genuinely costs or pays more.

The formula

LaTeX

EAR = \left(1 + \frac{r_{nom}}{m}\right)^m - 1

Variables

$E A R$: Effective annual rate: the true annual cost or return after accounting for intra-year compounding
$r_{n} o m$: Stated nominal annual interest rate (as a decimal)
$m$: Number of compounding periods per year

For continuous compounding (m → ∞): EAR = e^(r_nom) − 1. Converting all rates to EAR is the only valid basis for comparing financial products with different compounding frequencies.

Check yourself

PracticeCORE

A savings account pays a nominal annual interest rate of 6%, compounded monthly. What is the effective annual rate (EAR)?

Select an answer to check your understanding.