How it works
APR is the number that settles an argument between two loan offers. A lender can advertise a low interest rate and still make a loan expensive by charging an origination fee, because the fee comes out of the money that reaches you while leaving every payment unchanged. The APR folds that fee back into a single annual rate, so the two offers can be compared like for like. This calculator solves for it directly. You supply the loan amount, the upfront fees, the monthly payment the lender quoted, and the term in months. It computes the amount financed — the loan minus the prepaid fees, which is what actually lands in your account — then finds the one monthly rate at which the present value of the entire payment stream equals that smaller figure. Multiply by twelve and you have the APR. The direction of the effect is the whole point, and it is easy to get backwards. Fees shrink the amount financed but leave the payments untouched, so a fee always pushes the APR above the interest rate. On the defaults — a $20,000 loan, $800 of fees, and a $420 payment over 60 months — only $19,200 reaches you, yet you still repay $25,200. The rate that reconciles those two numbers is 11.27%. Remove the fee and the identical payment stream implies 9.50%, so the $800 charge is worth 1.77 percentage points of APR on its own. That gap is the fee restated in the same units as the interest rate, which is precisely why APR is the only figure worth comparing. The tool does not guess your interest rate, and that is deliberate. It takes the payment as an input, because the payment is what a lender actually quotes — printed on the offer, or derivable from it — and solving from a known payment avoids stacking one model's assumptions on top of another's. If you only know the rate and the term, compute the payment first and enter it here. The engine will refuse the inputs if your payments total less than the amount financed, or if the fees meet or exceed the loan amount, since neither case has a meaningful APR. Term length changes how much a fixed fee hurts, and by more than most borrowers expect. The same $800 fee on the same 6% $20,000 loan adds 4.05 percentage points over 24 months (5.95% → 10.00%), 2.76 points over 36 months (5.95% → 8.71%), and 1.71 points over 60 months (6.04% → 7.75%). A fee is a fixed cost spread across the payments, so the fewer payments there are, the more each one must carry. A short loan with a heavy fee can easily cost more than a longer loan with a higher headline rate. Two things the APR does not capture. It is built from the finance charge as Regulation Z defines it, so charges outside that definition — late fees, prepayment penalties and some third-party costs — never enter the number CFPB on APR. And it assumes you hold the loan to term: repay early and the fee has already been paid, so the effective cost of the months you actually used is higher still. The summary separates the two cost figures people conflate — total interest of $5,200 is what the principal costs, while the total cost of borrowing of $6,000 adds the fee on top.
Formula
Amount financed = loan - upfront fees <-- what actually reaches you
APR = 12 x r, where r solves:
SUM over m = 1..N of payment / (1 + r)^m = amount financed
Total you repay = payment x term months
Total interest = total repaid - loan amount
Total cost of borrowing = total repaid - amount financed (= interest + fees)
Worked example - $20,000 loan, $800 fees, $420/month, 60 months
Amount financed = 20,000 - 800 = $19,200
Total repaid = 420 x 60 = $25,200
APR = PV(420 for 60m) = 19,200 = 11.27%
Total interest = 25,200 - 20,000 = $5,200
Cost of borrowing = 25,200 - 19,200 = $6,000
Same payment, no fee = 9.50%
So the $800 fee adds 11.27 - 9.50 = 1.77 percentage points
The same $800 fee on the same 6% $20,000 loan, by term
24 months payment $886 -> 5.95% no fee, 10.00% with fee (+4.05 points)
36 months payment $608 -> 5.95% no fee, 8.71% with fee (+2.76 points)
60 months payment $387 -> 6.04% no fee, 7.75% with fee (+1.71 points)
Tips
- Compare APR, never the interest rate. Two offers with the same rate and different fees have different APRs, and for the same term and payment structure the lower APR is always the cheaper loan.
- A no-fee loan's APR equals its interest rate. If the quoted APR sits above the quoted rate, the difference is the fee — read that gap as a cost, not a rounding artefact.
- Negotiate the fee, not just the rate. Because the fee enters the APR at full weight, waiving the $800 origination fee in the example above removes 1.77 points from the cost of borrowing.
- Watch short terms. The same $800 fee costs 4.05 points over 24 months but only 1.71 over 60 — a fee-heavy short loan can win on rate and still lose on APR.
- Remember what APR excludes: late fees, prepayment penalties and charges outside Reg Z's finance charge. If you expect to repay early, model the fee separately rather than trusting the APR alone.
Frequently asked questions
- What is APR on a loan?
- The annual percentage rate is the true yearly cost of borrowing once prepaid fees are folded into the rate. On the defaults a $20,000 loan with $800 of fees and a $420 payment over 60 months carries an APR of 11.27%, against 9.50% for the identical payment stream with no fee.
- How is APR different from the interest rate?
- The interest rate prices the money alone. The APR adds the prepaid fees, spreading them across the term as if they were extra interest. A low rate with heavy fees can carry a higher APR — and cost more — than a higher rate with no fees, which is why comparing rates alone is a mistake.
- Why does adding a fee raise the APR?
- Because the fee reduces the amount that actually reaches you while leaving every payment unchanged. You repay the same $25,200 having received only $19,200 instead of $20,000, so the rate that reconciles the two cash flows must be higher. The APR is precisely the rate that captures that difference.
- Why do I enter the monthly payment instead of the interest rate?
- Because the payment is the figure a lender actually quotes, and solving from a known payment avoids stacking assumptions. If you only know the rate and the term, compute the payment first — for $20,000 at 6% over 60 months that is $386.66 — and enter it here to see what the fee does to the true cost.
- What does Net amount you receive mean?
- It is the loan amount minus the upfront fees — the money that genuinely reaches your account. On the defaults it is $19,200 from a $20,000 loan, and it is the figure the APR is solved against. If your fees ever meet or exceed the loan amount, the calculator returns an error rather than a meaningless rate.
- What is a good APR?
- It depends on the loan and your credit, but the comparison rule is universal: for the same term and payment structure, the lower APR is the cheaper loan. On the defaults an $800 fee on a 60-month loan lifts a 6% rate to 7.75%; the same fee over 24 months lifts it to 10.00%. Compare APRs across at least three lenders before signing.
- Does APR include every cost of the loan?
- No. It is built from the finance charge as Regulation Z defines it, so late fees, prepayment penalties and some third-party charges sit outside the number, and it assumes you hold the loan to term. A loan repaid early has already paid its fee, making the effective cost of the months used higher than the APR implies.
- Why did the calculator return an error?
- Two cases are rejected. If your payments total less than the amount financed, the inputs are internally inconsistent — the payment or term is wrong. If the fees meet or exceed the loan amount, nothing meaningful reaches you and the APR is undefined. Correct either figure and the rate will solve.