How APR is calculated
Regulation Z defines the APR as “a measure of the cost of credit, expressed as a yearly rate” [2]. Under the actuarial method, the unpaid balance grows by the finance charge earned each period and falls by each payment; the APR is the periodic rate times the number of periods in a year [3]. Here that means finding the monthly rate at which the payments, discounted back, equal the amount financed.
Amount financed = P × (1 − (1 + i)^−n) ÷ i, APR = 12 × i
P = monthly payment (worked out from the loan amount and interest rate), n = number of payments, i = monthly rate. Amount financed = loan amount − prepaid finance charges. Finance charge = total of payments − amount financed.
Example: a loan with a fee
$10,000.00 at 7% for 36 months, with $300.00 in prepaid finance charges.
- Payment: $308.77 a month
- Amount financed: $10,000.00 − $300.00 = $9,700.00
- Total of payments: $308.77 × 36 = $11,115.75; finance charge: $11,115.75 − $9,700.00 = $1,415.75
- The monthly rate that makes 36 payments of $308.77 equal $9,700.00 gives an APR of 9.07%, about 2.07 points above the interest rate.
Example from Regulation Z
Appendix J works through an iteration with $1,000.00 financed and 36 monthly payments of $33.61, and states an APR of12.83% [3]. This calculator’s method gives 12.8256% on the same numbers. It also matches the five examples in Appendix J for monthly, semimonthly, quarterly and weekly payments to the stated two decimals.
The legal tolerance for a disclosed APR is 1/8 of a percentage point, 0.125 points [2]. Differences of a few hundredths of a point are normal.
Questions
What is the difference between APR and interest rate?
The CFPB says the interest rate “does not reflect fees or any other charges,” while the APR is a broader measure, so “your APR is usually higher than your interest rate” [1]. With no fees at all, the two are the same.
Which fees go in the “prepaid finance charges” box?
Only charges that count as finance charges and are paid up front out of the loan, such as points or an origination fee. Not every closing cost qualifies. Your lender’s Loan Estimate or Truth in Lending disclosure lists them; use those figures.
What is the amount financed?
The loan amount less prepaid finance charges. Regulation Z’s official interpretation gives an example: a $2,500 loan with a $40 fee paid at closing gives an amount financed of $2,460 [4].
How accurate does a lender’s APR have to be?
As a general rule an APR is accurate if it is “not more than 1/8 of 1 percentage point above or below” the correct rate (a quarter point for irregular transactions) [2]. That is why a lender’s figure can differ slightly from this page.
Why might my lender’s APR differ?
This calculator is for a fixed rate, equal monthly payments and a full first month. Odd first periods, adjustable rates, irregular payments, and different treatment of some fees all change the result. Your disclosure is the figure that counts.
How is APR computed?
By the actuarial method in Regulation Z: find the monthly rate at which the payments, discounted back, equal the amount financed, then multiply by 12 [3].