Annual percentage rate

Annual percentage rate (APR) is the yearly interest rate quoted on a loan or credit card before within-year compounding is applied; compounding it up gives the higher effective annual rate (EAR), the true cost of borrowing.

ByHoang TruongUpdated July 11, 2026

See it move

Loading infographic...

A credit card quotes an APR of 18%, compounded monthly, so the monthly periodic rate is 18% ÷ 12 = 1.5%. Compounding that twelve times gives EAR = (1.015)^12 − 1 ≈ 19.56% — nearly one and a half percentage points above the quoted 18% APR, purely from monthly compounding.

Where it fits

TopicTime Value of MoneyCoreSubjectCorporate FinanceCore

The formula

LaTeX

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

Variables

$E A R$: Effective annual rate (%)
$A P R$: Annual percentage rate (nominal quoted rate) (%)
$m$: Number of compounding periods per year (periods)

Converts a quoted nominal rate (APR) compounded m times a year into the true effective annual rate.

Check yourself

PracticeCORE

A loan is quoted at an APR of 24%, compounded monthly. What is the effective annual rate (EAR), to two decimal places?

Select an answer to check your understanding.