APR Calculator: True Yearly Cost of a Loan
Enter the loan amount, the fees you pay to get it, the stated yearly rate and the term to find the APR.
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Formula
The monthly payment M is found from the loan amount P, the stated monthly rate and the term n months, as in a standard loan. The borrower receives P − fees. The APR is 12 × i, where i is the monthly rate that satisfies:
P − fees = M × (1 − (1 + i)^−n) ÷ i
There is no closed form for i, so the calculator finds it numerically. With no fees i is the stated monthly rate, so the APR equals the stated rate.
Worked example
10,000 at 6% a year over 36 months with 300 in fees:
M = 304.22a month- The borrower receives 10,000 − 300 = 9,700
- Solving
304.22 × (1 − (1 + i)^−36) ÷ i = 9,700givesi = 0.6715%a month - APR = 12 × 0.6715% = 8.06%, which is 2.06 points above the stated rate
Frequently asked questions
What is APR?
The annual percentage rate is the yearly cost of a loan as a percentage, counting the interest and upfront fees. It lets you compare loans with different fees on one scale.
How is APR calculated here?
The payments are based on the full loan amount, but you only receive the amount minus fees. The APR is the monthly rate i that makes the payments worth that smaller sum, times 12. For 10,000 at 6% over 36 months with 300 fees, the payment is 304.22 and the APR is 8.06%.
Why is the APR higher than the interest rate?
Because fees are paid up front, you borrow less than you repay interest on. With no fees the APR equals the stated rate. In the example above, 300 of fees add 2.06 points.
Will this match my lender's APR?
It may differ slightly. Rules for which charges count, and whether APR is shown as a nominal or an effective yearly rate, vary by country and lender. This uses the nominal rate (monthly rate × 12).