How it works
The monthly payment is set by the nominal rate:
M = P · [ r(1+r)^n ] / [ (1+r)^n − 1 ]
APR answers a different question: at what rate i does the stream of payments have a present value equal to what you actually received (loan minus fees)?
M · [ 1 − (1+i)^−n ] / i = P − fees
- P = loan amount; r = monthly nominal rate (annual ÷ 12); n = number of monthly payments
- There's no closed-form solution, so the calculator solves for
iiteratively (bisection) and multiplies by 12
Example
$10,000 loan, $300 in fees, 6% interest, 36 months:
- Monthly payment: $304.22
- Total interest over 3 years: $951.90
- APR: 8.06% — nearly two points above the advertised 6%
Set fees to $0 and the APR drops back to exactly 6%. Fees hit short loans hardest: the same $300 on a 12-month loan would push the APR far higher, because you spread the fee over far fewer payments.
What this calculator does not include
It treats fees as a single upfront amount deducted from the proceeds. Recurring costs — annual fees, mortgage insurance, escrowed taxes — are not folded in, and the model assumes every payment is made on schedule. Lenders compute APR under their own disclosed assumptions, so treat this as an apples-to-apples comparison tool rather than a legal disclosure.
FAQ
What is the difference between interest rate and APR?
The interest rate is the cost of borrowing the principal alone. APR spreads the lender's fees across the life of the loan and expresses them as an annualized rate, so it reflects the true cost of the money you actually receive.
Why is APR higher than the interest rate?
Fees reduce what you effectively receive: you repay interest on the full loan amount, but the fees come out of it upfront. In the example, a $10,000 loan at 6% with a $300 fee has an APR of about 8.06% — nearly two points higher.
If a loan has no fees, is APR the same as the interest rate?
Yes. With zero fees, the amount you receive equals the amount you repay interest on, so the APR equals the nominal interest rate.