APR Calculator
A rate with fees attached is not the rate you pay. APR is the rate that reconciles the payments you make with the money you actually received — and it has to be solved for, not added up.
On this page
APR is not the rate plus the fee
The intuitive shortcut is to add the fee percentage to the interest rate. A 3% origination fee on a 7.5% loan gives 10.5%, and that is wrong by a wide margin.
It is wrong because the fee is a one-off charge spread across the life of the loan, not an annual one. On a five-year loan the real APR is closer to 8.8%; on a thirty-year mortgage the same 3% barely moves the rate at all. The shorter the loan, the more a fixed fee costs in rate terms.
What APR actually is
The rate at which the present value of your payments equals the money you actually received. Two figures matter and they are different:
The loan amount is what the note is written for, and it is what the payment is calculated from. The amount financed is what reaches you after the fees deducted at closing. You pay on the first and receive the second, and APR is the rate that reconciles them.
There is no closed-form solution, so it is solved numerically — by bisection, which cannot diverge and converges reliably from a bracketed range. Regulation Z then annualises by multiplying the periodic rate by the number of periods rather than compounding it, which is why the APR and the effective annual rate on this page differ slightly.
A worked example
$28,000 over five years at 8.25%, with a 3% origination fee and $250 of prepaid charges.
The payment is $571.16, calculated on the full $28,000. Fees of $1,090 come off at closing, so $26,910 actually reaches you. Sixty payments of $571.16 total $34,269, and the finance charge — the cost of credit — is $7,359.
Solving for the rate that makes sixty payments of $571.16 equal $26,910 today gives about 9.87%. Against the 8.25% nominal rate, the fees added 1.62 points. The naive shortcut of 8.25% + 3% = 11.25% overstates it by nearly a point and a half.
What APR does and does not compare fairly
APR is the fairest single number for comparing offers of the same term. It is designed for exactly that and it is why lenders are required to disclose it.
Across different terms it misleads. A 15-year and a 30-year mortgage at identical APRs cost very different amounts in total, and the shorter one is far cheaper. Comparing on APR alone would suggest they are equivalent.
APR also assumes you keep the loan to term. Pay off a mortgage after seven years and the closing costs were spread over seven years rather than thirty, so the rate you effectively paid is higher than the disclosed APR — sometimes substantially.
Which fees are in it
That depends on the product. For a mortgage, origination charges and points are included while an appraisal fee generally is not. For a personal loan the origination fee is included. A credit card has no APR of this kind at all, because there is no fixed term or payment schedule — the APR on a card is simply the periodic rate annualised.
Enter the charges your disclosure lists as finance charges. If the calculated APR differs noticeably from the disclosed one, the difference is usually a fee that is or is not included.
What this does not cover
- Variable rates. APR on an adjustable loan assumes an index path and is disclosed under specific rules.
- Credit cards. No fixed term means this calculation does not apply.
- Irregular payments. Balloon payments, interest-only periods, and skipped payments all change the cash flows.
- Early repayment. APR assumes the full term is run.
- Which fees are legally includable. That is a regulatory question and it varies by product.
To compare several offers at once, use the loan comparison calculator, which solves the APR on each.
Frequently asked questions
What is the difference between APR and interest rate?
The interest rate is what accrues on the balance and determines the payment. The APR folds in the fees as well, expressed as an annual rate, so it reflects the whole cost of the credit.
When two offers have the same rate but different fees, the APR is what tells them apart.
Why is my APR higher than my interest rate?
Because fees were charged. Origination fees, points, and prepaid finance charges all reduce the money you receive while leaving the payments unchanged, which raises the effective rate.
If the APR equals the rate exactly, the loan had no includable fees.
Can I just add the fee percentage to the rate?
No, and the error is large. A one-off fee is spread across the life of the loan, so adding it as though it were annual overstates the effect — badly on long loans, less so on short ones.
Solving properly is the whole reason this page exists.
Is a lower APR always the better loan?
At the same term, generally yes. Across different terms, no: a longer loan can have a lower APR and cost far more in total.
Compare APR when terms match, and total cost when they do not.
What is the amount financed?
The loan amount less any finance charges deducted at closing — the money that actually reaches you or the seller.
It appears on Truth in Lending disclosures and is the figure APR is computed against, which is why it is shown separately here.
Does APR account for paying the loan off early?
No. It assumes the loan runs its full term. Paying early spreads the same fees over fewer years, so the rate you actually paid is higher than the disclosure suggests.
This matters most on mortgages, which are very often repaid long before term.
Related calculators
This calculator is provided for general educational and estimation purposes only and is not lending or legal advice. Which charges must be included in APR depends on the credit product and the regulations that govern it. The APR your lender discloses is the one that binds.