Annual Percentage Rate (APR) — Definition, Formula & Examples
Annual Percentage Rate (APR) is the yearly interest rate charged on borrowed money or earned on an investment, expressed as a single percentage. It gives you a standardized way to compare loans or credit cards that may have different compounding periods or fee structures.
The Annual Percentage Rate is the nominal interest rate per year applied to a loan or investment, calculated by multiplying the periodic interest rate by the number of compounding periods in one year. In regulated lending contexts, APR also incorporates fees and costs to represent the true annual cost of credit.
Key Formula
Where:
- = Interest rate per compounding period (as a decimal or percentage)
- = Number of compounding periods per year
How It Works
Lenders often quote a monthly or daily interest rate, so APR converts that rate into an equivalent yearly figure. To find the APR from a periodic rate, multiply the rate per period by the number of periods in a year. For example, a monthly rate of 1.5% gives an APR of . Note that APR does not account for the effect of compounding within the year — that role belongs to APY (Annual Percentage Yield). When comparing two loans, the one with the lower APR generally costs less, assuming similar terms.
Worked Example
Problem: A credit card charges 1.5% interest per month on unpaid balances. What is the APR?
Identify the periodic rate and periods: The monthly rate is 1.5%, and there are 12 months in a year.
Multiply to find APR: Multiply the monthly rate by the number of months.
Answer: The credit card has an APR of 18%.
Why It Matters
Understanding APR is essential when comparing auto loans, mortgages, or credit cards. A lower APR can save thousands of dollars over the life of a loan. Personal finance and business courses rely on APR calculations as a foundation for evaluating borrowing costs.
Common Mistakes
Mistake: Confusing APR with the effective annual rate (APY/EAR), which includes compounding.
Correction: APR is a simple (nominal) rate — it does not reflect compounding. The effective annual rate is always equal to or higher than the APR when compounding occurs more than once per year. Use the formula for the effective rate.