Finance
The true annual cost of a loan including upfront fees — solved from the monthly payment, not approximated.
Monthly payments, no early repayment. Results update as you type. All calculations run locally in your browser.
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First the monthly payment at the nominal rate: PMT = P × i ÷ (1 − (1 + i)−n), where P is the loan amount, i is the monthly nominal rate, and n is the number of payments. APR is then the monthly rate r that makes the present value of those payments equal the amount actually received (P − fees): (P − fees) = PMT × (1 − (1 + r)−n) ÷ r. The nominal APR is 12 × r; the effective APR is (1 + r)12 − 1. The page solves for r by bisection, not by an approximation formula.
$10,000 at a 6% nominal rate over 36 months with $300 of upfront fees: the monthly payment is 10,000 × 0.005 ÷ (1 − 1.005−36) = $304.22, and $304.22 × 36 = $10,951.90 is repaid in total. The borrower actually receives 10,000 − 300 = $9,700, and the monthly rate that discounts 36 payments of $304.22 back to $9,700 is 0.6714%, so the nominal APR is 12 × 0.6714% = 8.06% (8.36% effective). The $300 fee lifts the true cost from 6% to 8.06% — that gap is exactly what APR exists to reveal.
This page assumes fixed monthly payments, a fixed nominal rate, and a single upfront fee deducted from the amount received. It does not model variable rates, balloon payments, early-repayment penalties, ongoing monthly charges, or fees paid separately rather than deducted — each of those changes the APR. Lenders' disclosed APRs follow jurisdiction-specific rules about which charges count; this page's figure is a transparent calculation from the four inputs shown, not a lender disclosure. If fees are zero, APR equals the nominal rate (effective APR is slightly higher because of monthly compounding).
Because APR spreads the fees across the loan as well as the interest. In the example, $300 of fees on a $10,000 loan lifts the cost from 6% to 8.06%. A loan with a lower rate but heavy fees can easily cost more than a higher-rate loan with no fees.
Nominal APR is 12 times the monthly rate (8.06% here). Effective APR compounds that monthly rate over a year ((1 + r)12 − 1 = 8.36%). Lenders usually quote the nominal figure; the effective figure is what compounding actually costs.
Compare APRs for loans of the same term and structure — it is the only figure that includes fees. Monthly payments alone hide fees, and a longer term can look cheaper per month while costing far more overall.
Then the amount received equals the loan amount, the solving rate equals the nominal monthly rate, and nominal APR equals the nominal rate. The effective APR is still slightly higher because interest compounds monthly.
With the same fees, a shorter term raises APR: the same $300 is spread over fewer payments, so each payment carries more fee cost. That is why small short loans often show startling APRs.
It should be close if the inputs match and the lender counts the same charges. If it differs, check which fees the lender included or excluded, and whether the rate is fixed — a variable rate makes any single APR figure an estimate.
Results are estimates only and do not constitute professional advice.