APR vs. interest rate: what each number means
Key takeaways
04 · ideas- APR always equals or exceeds the stated interest rate
- A 6.5% rate with $3,000 in fees can produce a 6.9% APR
- APR standardizes loan comparisons across lenders
- For short-term loans, fees create very high APRs
Basic level
The essentials · 1 min
Two numbers appear on almost every loan offer: the interest rate and the APR (Annual Percentage Rate). They measure related but different things.
Interest rate: The percentage the lender charges annually on the outstanding balance. This determines your monthly payment.
APR: The interest rate plus most fees and costs, expressed as a single annualized percentage. It reflects the broader cost of borrowing.
Because APR includes origination fees, points, and certain closing costs, it provides a standardized way to compare loans even when fee structures differ across lenders. APR is always greater than or equal to the stated interest rate. If they are equal, the loan has no fees.
Intermediate level
How it applies · 1 min
How APR is calculated
For a mortgage with a $300,000 loan at 6.5% with $4,500 in lender fees:
- The lender effectively disburses $295,500 ($300,000 minus fees)
- But you repay as if you borrowed $300,000 at 6.5%
- The APR solves for the rate on $295,500 that produces the same payments
In this case, APR is approximately 6.78%. A competing lender offering 6.75% with no fees would have APR = 6.75%.
APR on short-term loans
| Loan type | Amount | Fee | Term | Approximate APR |
|---|---|---|---|---|
| Payday loan | $500 | $75 | 2 weeks | ~391% |
| Personal loan | $5,000 | 2% origination | 36 months | ~12.5% |
A $75 fee on a $500 two-week loan equals 15% for two weeks, which annualizes to 391% APR.
Advanced level
The math, step by step · 1 min
The mathematics of APR
APR is the internal rate of return (IRR) of the loan cash flows, annualized. For a loan disbursing net amount D with payments PMT_t at periods t:
Annualizing: APR = 12 \cdot r_{monthly}
Under US Truth in Lending Act (TILA), lenders are required to disclose APR for consumer loans. Not all costs are included — some fees may be excluded depending on loan type and jurisdiction.