APR Calculator

What the APR measures

The interest rate on a loan decides the monthly payment. It says nothing about the fees you pay to get the loan — an origination fee, discount points, a broker fee. Two loans at 9% can cost very different amounts if one charges $750 up front and the other nothing.

The annual percentage rate folds those fees into a single yearly rate. The US Truth in Lending rules (Regulation Z) define it as a measure of the cost of credit that relates what you receive, and when, to what you pay back, and when. In practice:

• The amount financed is the money you actually get to use: the loan balance minus the fees paid to obtain it (the prepaid finance charges).
• Your payments are still worked out from the stated rate on the full balance.
• The APR is the rate at which those payments are worth exactly the amount financed. Because you repay more than you effectively received, the APR is higher than the stated rate whenever there are fees.

That is the difference from the loan calculator, which only shows the payment and interest at the stated rate. Use this page when you are comparing offers with different fees, or checking the APR on a disclosure.

How the APR is calculated

First the payment, from the stated monthly rate r on the balance P:

Then the monthly rate i that makes the payments worth the amount financed A:

P

loan balance the payment is based on (plus the fees, if they are added to the loan)

r

stated annual interest rate ÷ 12

n

number of monthly payments

M

monthly payment, rounded to the cent (the last payment absorbs the rounding)

A

amount financed: P minus the upfront fees

i

the monthly rate being solved for

This is the actuarial method in Appendix J of Regulation Z: the rate for one unit period (here a month) multiplied by the number of unit periods in a year. There is no closed-form answer, so the calculator solves it numerically — Newton’s method, protected by bisection so it always converges — to far more precision than the rule requires. Regulation Z treats a disclosed APR as accurate within 1/8 of a percentage point for a regular loan like this one.

Because the APR is 12 × the monthly rate, it does not include compounding within the year. The effective annual rate, (1 + i)¹² − 1, does, and is shown alongside for comparison with yields quoted as an APY.

Worked example

A lender offers $25,000 over 5 years at 9% and charges a $750 (3%) origination fee, taken out of the loan proceeds.

1. Amount financed: $25,000 − $750 = $24,250 — the money you actually receive
2. Monthly payment on the full $25,000 at 0.75% a month for 60 months: $518.96 (the last payment is $518.89)
3. Total of payments $31,137.53, so the finance charge is $31,137.53 − $24,250 = $6,887.53 ($6,137.53 of interest plus the $750 fee)
4. The monthly rate that discounts those 60 payments to $24,250 is 0.859247%, so the APR is 10.311% — about 1.31 points above the stated rate
5. Effective annual rate: (1.00859247)¹² − 1 = 10.812%

If the same $750 were added to the loan instead, you would borrow $25,750, pay $534.53 a month and the APR would be 10.272%. With no fee at all the APR equals the 9% interest rate.

As a check against the Federal Reserve’s published APR tables for Regulation Z: their example of a $65.11 finance charge on $332.20 financed over 24 monthly payments gives 17.81% here, which the tables round to the nearest quarter point, 17¾%.

Using the APR to compare loans

• Compare offers for the same term. Fees are spread over the life of the loan, so the same fee raises the APR of a short loan more than a long one. On the example above, the APR on a 2-year term would be noticeably higher than on the 5-year term.
• If you repay early, fees cost more than the APR suggests. The APR assumes you keep the loan for the full term. Paying it off or refinancing sooner spreads the same fee over fewer months.
• Which fees count. The APR includes finance charges — interest, points, origination and similar lender fees. Costs you would pay in a cash deal, and on mortgages some third-party charges such as title fees or an appraisal, are left out of the finance charge by the rules. Enter only the charges your lender lists as prepaid finance charges.
• APR is not APY. On savings, the APY includes compounding. The loan APR does not; the effective annual rate shown here is the loan equivalent of an APY.

Limits of this calculator

• The first payment is assumed exactly one month after the loan starts. A longer or shorter first period changes the APR slightly; Regulation Z has separate equations for that case.
• Payments are monthly and level. Adjustable rates, balloon payments and interest-only periods are not modelled.
• Mortgage insurance and other charges that recur with the payment are part of a lender’s finance charge but are not included here.