Quick answer
An APR calculator works out the true annual cost of a loan including its fees. A $20,000 loan at a 9% interest rate with $800 of upfront fees has payments of $415.17 a month over 5 years — but because you only receive $19,200, the APR is 10.76%. The 1.76-point gap between rate and APR is what the fees cost you, and it is why APR is the only fair comparison between loans.
How the APR Calculator works, step by step
Enter the loan amount, the stated interest rate, the term and every upfront cost: origination fees, documentation and processing charges, and any prepaid finance charges. The calculator computes the payment from the stated rate on the full amount, then solves for the rate that equates those payments with the net amount you actually receive — that rate is the APR.
The shorter the loan, the harder fees bite. The same $800 of fees adds about 1.76 points to a 5-year loan's APR but about 4.1 points on a 2-year loan and 7.77 points on a 12-month loan, because the fee is spread over fewer payments. On a 30-year mortgage, the same fees dilute to less than half a point.
Use APR to compare, then check the total repayment as a sanity check — two loans with the same APR but different terms cost very different amounts in total interest. APR is a rate, not a price tag: the example loan's total cost is $5,710 (interest $4,910 plus $800 of fees), and a competing 10% loan with no fees would cost $5,496 in total despite the higher headline rate.
The APR equation has no closed-form solution, so the calculator solves it by iteration: it tests monthly rates, discounts the payment stream back to the present, and narrows in on the rate whose present value equals the amount received. That is the same mathematics a lender's disclosure system runs under Regulation Z, which defines which charges count as finance charges.
Watch what APR leaves out. It captures lender and broker fees and most prepaid finance charges, but some third-party costs (certain title, appraisal or notary fees, depending on the loan type) sit outside it, and late fees and other contingent charges are excluded by definition. Read the full fee schedule alongside the APR, especially on mortgages where the Loan Estimate separates lender fees from other closing costs.
The formula
Payment is set by the note rate: Payment = Amount × [r(1 + r)^n] ÷ [(1 + r)^n − 1]. APR is the monthly rate i solving: Amount − fees = Payment × [1 − (1 + i)^(−n)] ÷ i, annualised as i × 12. The equation has no closed form; the calculator solves it by iteration (bisection).
Worked example — try it on the calculator above
Worked example: $20,000 at 9% with $800 of fees, 60 months
Payment on $20,000 at 9% over 60 months: $415.17. Fees of $800 are withheld, so the amount you effectively borrow is $19,200 while the payments are unchanged. Solving for the rate that discounts 60 payments of $415.17 back to $19,200 gives a monthly rate of about 0.90%, an APR of 10.76%. The same $800 of fees on a 24-month loan would push the APR to 13.10%, and on a 12-month loan to 16.77%. A competing loan at 10% with no fees would be cheaper despite the higher headline rate — the comparison APR exists to catch.
Frequently Asked Questions
Why is APR higher than the interest rate?
APR includes most upfront finance charges spread over the loan's life, while the interest rate does not. The two are equal only on a fee-free loan. US law (the Truth in Lending Act and Regulation Z) defines which charges count as finance charges, and lenders must disclose the resulting APR before you sign — compare that disclosed figure across offers.
Does APR include every cost of the loan?
No. It captures lender and broker fees and most prepaid finance charges, but some third-party costs (certain title, appraisal or notary fees, depending on the loan type) sit outside it, and late fees and other contingent charges are excluded by definition. Read the full fee schedule alongside the APR, especially on mortgages where the Loan Estimate separates lender fees from other closing costs.
Why do credit cards quote APR differently?
Card APR is simply the annualised interest rate — there are no origination fees to fold in, and annual fees are not included in card APR. It is a purchase or cash-advance rate applied to average daily balances. That is why a card's 22% APR and a loan's 11% APR are not quite the same species of number, even though both describe interest cost.
Is the lowest APR always the best loan?
For identical amounts and terms, yes. Across different terms, not necessarily: a 5-year loan at 10% APR costs less total interest than a 7-year loan at 9% APR, because you pay it for two fewer years. Decide the term from your monthly budget first, then choose the lowest APR within that term, and confirm with the total repayment figure.
Estimates, not advice. This calculator provides educational estimates based on the inputs you enter and the assumptions shown on this page. It is not financial, tax or investment advice, and it cannot see your full situation. Verify important figures against official sources, and consider a qualified professional for decisions about your own money. See our Disclaimer and Methodology.