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.
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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
Variables
- Effective annual rate (%)
- Annual percentage rate (nominal quoted rate) (%)
- 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.