APR Calculator

Two rates are at work. First, the monthly payment is calculated the ordinary way — on the full loan amount at the stated nominal rate: PMT = P × r ÷ (1 − (1 + r)⁻ⁿ), with r the stated rate ÷ 12 and n the number of months. But the fees are deducted up front, so the amount financed — the money you actually receive — is the loan amount minus the fees. The APR is then the monthly rate i that makes the same payment stream worth exactly that smaller amount: PMT × (1 − (1 + i)⁻ⁿ) ÷ i = amount financed, and APR = i × 12 × 100. There is no closed-form solution for i, so the calculator solves it by bisection: halving a bracket around the rate until the present value matches the amount financed to within 1e-10. With zero fees the amount financed equals the loan amount, and the APR comes out exactly equal to the stated rate — the built-in sanity check.

APR stands for annual percentage rate, and unlike most numbers in a loan offer, it is not the lender’s invention. The federal Truth in Lending Act requires creditors to disclose it, and Regulation Z — the CFPB’s rulebook at 12 CFR Part 1026 — defines it as a measure of the cost of credit expressed as a yearly rate. The interest rate prices only the money you borrow. APR prices the finance charge: under Regulation Z §1026.4, that is any charge payable directly or indirectly by you and imposed by the creditor as an incident to, or a condition of, the extension of credit. Interest is only the largest item inside it.

So what is apr on a loan, in one sentence? It is the interest rate re-measured against the money you actually receive: the payment is calculated on the full loan amount, but the upfront fees come out of your pocket first, so the rate that makes those payments worth exactly what reached you is higher. That is why the APR and the note rate on the same loan are two different numbers, and why the APR is the one that tells the truth about cost.

Counted in APR under Regulation Z: interest; origination and loan fees; discount points; mortgage broker fees; finder’s and assumption fees; and premiums for credit insurance or debt-cancellation cover the creditor requires and sells at closing. Left out: charges you would pay in a comparable cash transaction (the tax, title and registration on a car, for example), application fees charged to every applicant whether or not the loan is made, late fees and default charges, and seller’s points. On loans secured by real estate, §1026.4(c)(7) also leaves out bona fide third-party charges the creditor does not keep — fees for title examination and title insurance, property surveys, document preparation, notary and credit report fees, and amounts deposited into escrow.

You meet this definition on paper, not in advertising. For a mortgage, the APR is disclosed on the Loan Estimate you receive after applying and again on the Closing Disclosure before you sign. For an installment loan, the Truth in Lending disclosure statement prints the APR beside the finance charge, the amount financed and the total of payments — the four numbers this calculator shows. For a credit card, the rates sit in the Schumer box in the application and account agreement. In every case the APR’s legal job is the same: one comparable yearly figure, fees in, so two offers can be judged on the same terms.

One more legal detail explains why a lender’s disclosed APR may differ a hair from your own calculation: for a regular closed-end loan, Regulation Z treats the disclosed APR as accurate if it falls within one-eighth of a percentage point (0.125%) of the true figure. This calculator solves the rate to far tighter precision than the tolerance, so if your result and your disclosure differ by more than a rounding whisker, a fee classification — not the arithmetic — is the reason. On the savings side the mirror concept is APY, and our guide to APY vs APR works through the conversion both ways; the APY Calculator applies the same treatment to deposits.

You can calculate apr for any fixed-rate installment offer with four steps, and only the third needs a computer:

1. Work out the payment on the full loan amount at the stated note rate: PMT = P × r ÷ (1 − (1 + r)⁻ⁿ), with r the note rate ÷ 12 and n the number of monthly payments.
2. Subtract the upfront fees from the loan amount. What is left is the amount financed — the money you actually receive.
3. Solve for the rate i that makes the payment stream worth exactly the amount financed: PMT × (1 − (1 + i)⁻ⁿ) ÷ i = amount financed. There is no closed-form solution — the rate hides inside both a power and a division — so the equation is solved by iteration, narrowing a bracket around i until the present value matches.
4. Annualise: APR = i × 12 × 100. That is the whole apr formula — a payment, a smaller amount received, and the rate that reconciles the two.

Worked example. A personal loan of $15,000 at a stated 9.00% over 48 months carries a $300 origination fee (2% of the loan). Step 1: the payment on the full $15,000 is $373.28 a month. Step 2: you receive $15,000 − $300 = $14,700. Step 3: the monthly rate that makes 48 payments of $373.28 worth exactly $14,700 is 0.8386% — and step 4 annualises it to an APR of 10.06%. Over the term you pay $17,917.23 in total: $2,917.23 of interest plus the $300 fee makes a finance charge of $3,217.23. A two-point fee load has bought a 1.06-point lift in the rate — and run the same four steps with no fee and the solve returns 9.00% exactly, which is how you know the method is honest. The fee ladder on this same loan shows the shape of the effect: a $150 fee gives an APR of 9.53%, the $300 fee gives 10.06%, and doubling the fee to $600 gives 11.16% — each extra dollar of upfront cost raises the rate, and it raises it faster the shorter the term over which it is spread.

Take a $30,000 car loan at a stated 7.50% over 60 months, with $450 of lender fees — an origination and processing charge — rolled into the deal. The payment is worked out on the full $30,000, but only $29,550 of it is really working for you:

The payment never changes — fees do not alter what leaves your account each month. What changes is the rate that honestly describes the deal, and it moves from 7.50% to 8.14% because of $450. The apr calculator car test: before you sign, run each dealer’s quote with its fees entered and compare APRs, not note rates — two dealers can quote the same 7.50% and deliver loans well apart in APR once their fees are in. One warning from Regulation Z that cuts the other way: the tax, title and registration on the car are not part of the APR, because you would pay them in a comparable cash purchase too. A documentation fee sits on the line — charged to cash buyers as well, it is excluded; charged only to financed buyers, it is a finance charge and belongs in the solve.

A second installment example shows what the term does to a fee. Borrow $5,000 at a stated 12.00% over just 24 months with a $150 upfront fee. The payment is $235.37, you receive $4,850, and the solve gives an APR of 15.09% — a 3.09-point lift from a fee that is smaller, in dollars, than the car loan’s. The total interest is $648.82 and the finance charge $798.82. The fee is spread over 24 payments instead of 60, so each payment carries more of it; that is the whole mechanism, and it is why short loans with fees deserve the closest APR reading.

Lenders and statements often restate that yearly figure as a monthly periodic rate — simply APR ÷ 12. In that monthly dress, this page doubles as a monthly apr calculator: the $5,000 loan’s 15.09% APR is a monthly rate of 1.2575%, and the 26.99% APR on a credit card is 2.2492% a month. Credit cards actually go one step finer and bill by the day — the FAQ below shows that arithmetic — but the monthly restatement is the quickest sanity check on any statement: multiply the monthly rate by 12 and you should land back on the disclosed APR.

This loan apr calculator needs the offer exactly as a lender states it: the loan amount, the stated interest rate, the term in months, and every upfront fee that comes out of the money you receive. The mortgage mode adds the home price, down payment, points and PMI, because on a home loan the fee side of the ledger is longer. Nothing else is estimated for you — an annual percentage rate calculator is only as honest as its fees field, and leaving a $300 origination fee out of the entry understates the APR just as surely as if the lender had left it out of the disclosure.

Watch what the fees entry does when you change it: the monthly payment does not move at all, because the payment is set by the note rate on the full amount — but the amount financed falls, and the APR climbs. That split is the APR-versus-interest-rate distinction made visible. Used as an apr interest calculator, the tool shows both numbers at once: the interest rate prices the principal, the APR prices the principal and the cost of getting it.

In mortgage mode, two entries deserve care. Points are entered as a percentage of the loan amount — one point is 1% of the loan, $3,200 on a $320,000 loan, paid upfront to buy the note rate down — so enter the dollar cost the lender quotes if the percentage is not stated. PMI is entered as an annual percentage of the loan amount and is charged monthly while you owe more than 80% of the home’s price; it drops off at 80% loan-to-value, and because it is charged over time rather than upfront, the calculator works its total into the APR solve as the results card shows.

To read the answer against a real quote, compare three figures, not one.

If your computed APR lands within an eighth of a point of the lender’s disclosed APR, the two of you agree — that is the Regulation Z tolerance. If the lender’s APR is noticeably lower than yours, a fee you entered is probably one the rules classify as excluded, such as an appraisal or title charge on a home loan; the disclaimer below explains how this calculator treats the fees you enter. And whatever the APR says, check the total finance charge beside it: APR spreads fees across the term, so it can flatter a long loan and punish a short, cheap one. The dollars never flatter anything.

Three more readings sit one click away. The results card also restates the true APR as an APY — the effective annual rate, interest-on-interest counted — so a loan can be held up against a savings account’s APY honestly: the default loan’s 8.86% APR is a 9.23% APY. The early-payoff field in Advanced options answers the question the headline APR assumes away, because APR is worked out as if you keep the loan to term: repay the default loan after payment 12 instead of payment 60 and the same $400 fee spreads across a single year, so the APR you actually paid climbs to 10.28% — even though you hand over $21,477.53 in total, not $24,331.67. And with Credit card picked as the loan type, the calculator drops the fee solve entirely and works the way issuers do, at a daily periodic rate on your average daily balance: 26.99% APR is 0.07395% a day, so a $3,000 balance costs $66.55 over a 30-day cycle — a 30.97% effective annual rate if a balance like it revolved and compounded for a full year.