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

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.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

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.