APR Calculator

APR exists to answer one question a note rate cannot: what does this loan cost once the fees are counted? The Truth in Lending Act (15 U.S.C. § 1606) and Regulation Z define it as the rate that makes the amount you actually receive equal the present value of the payments you actually make. So the calculation runs in three steps. First, the amount financed: 12 CFR § 1026.18(b) takes the principal and reduces it by prepaid finance charges, so a $12,000 loan with a $600 origination fee finances $11,400. Second, the monthly payment, computed on the full $12,000 at the stated note rate — because the note was written for the full amount and you repay every dollar of it regardless of how the fee was settled. Third, the solve: find the periodic rate i for which amount financed = payment x (1 - (1+i)^-n) / i. There is no closed form for i. Appendix J (b)(9)(ii) says as much, expecting that "calculators or computers will be programmed to carry all available decimals throughout the calculation and that enough iterations will be performed to make virtually certain that the annual percentage rate obtained, when rounded to 2 decimals, is correct." This page runs that iteration entirely in decimal arithmetic, never dropping to floating point, and keeps four decimal places internally before rounding for display. The last step is the one that trips up finance-trained readers. Appendix J (b)(1) annualises the monthly rate by simple multiplication — APR = 12 x i x 100 — a nominal figure, not a compounded one. That is why APR and APY are not comparable: APY on a savings account compounds, APR by regulatory definition does not, and a 12% APR is a genuine 12.68% if you compound it. Which fees count is the whole game, and § 1026.4 draws the line. Finance charges are the ones imposed as an incident to the extension of credit: origination fees, discount points, broker and underwriting fees. Charges for services you would pay for anyway are generally not — appraisal, title insurance, recording fees, property taxes, homeowners insurance. Enter only the first kind. Put a title fee in the box and you will overstate the APR against every quote you are comparing it to. This page also assumes fees are paid at or before closing rather than rolled into the balance; if your lender is financing the fee, enter the larger balance being amortised and leave the fee box at zero. Two consequences follow that people find counterintuitive. APR can never be below the note rate — fees only ever shrink the amount financed, which only ever pushes the solved rate up — and with zero fees the two are identical to the cent. And the lowest APR is not automatically the cheapest loan: APR spreads the upfront fee across the full scheduled term, so a low-APR, high-fee loan is only cheaper if you actually keep it that long. Refinance or pay off a 30-year mortgage in year six and the points you bought were amortised over 360 months you never used. Reg Z also permits tolerance. Under § 1026.22 a disclosed APR on a regular transaction is accurate if it is within one-eighth of one percentage point of the actuarial value, so a small gap between this page and a lender disclosure is expected rather than an error. Use this to compare offers of the same amount and term; use the personal loan calculator when you want the payoff schedule behind the number, or the mortgage calculator when escrow and insurance belong in the picture too.