The formula
Payment = P × i ÷ (1 − (1 + i)−n), using the note rate divided by payments per year. Amount financed = loan − prepaid finance charges. The APR is u × m, where u is the periodic rate that solves PV of payments at u = amount financed, and m is the number of payment periods in a year.
Source
Regulation Z (12 CFR part 1026): section 1026.22 defines the APR, permits the actuarial method and sets the accuracy tolerances; Appendix J gives the equations and instructions for the actuarial method.
When to use it
Use it to compare loan offers with different fees, to understand why a quoted APR differs from the rate, or to test a rate in a loan confirmation or covenant file.
Limits
This tool handles one advance, equal payments and regular periods. It does not model irregular first periods, balloon payments, adjustable rates, mortgage insurance or the detailed rules in 12 CFR 1026.4 on which charges are finance charges: whatever you enter as a prepaid finance charge is treated as one. Disclosure APRs for regulated consumer loans must be computed by the lender's compliance process. Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What is APR?
Regulation Z defines the annual percentage rate as a measure of the cost of credit expressed as a yearly rate. It ties the amount and timing of the funds the borrower receives to the amount and timing of the payments, so up-front charges raise it above the note rate.
Why is the APR higher than the interest rate?
Prepaid finance charges, such as points or an origination fee, reduce the money the borrower actually gets while the payment is still computed on the full loan. The same payments on a smaller amount financed mean a higher yearly cost. With no prepaid charges and regular payments, APR equals the note rate.
How is APR calculated?
Under the actuarial method, find the periodic rate at which the present value of all payments equals the amount financed, then multiply by the number of periods in a year. There is no closed form, so the tool solves it numerically.
How accurate does a disclosed APR have to be?
Under 12 CFR 1026.22(a), a disclosed APR is treated as accurate if it is within one-eighth of one percentage point above or below the correctly computed rate. For irregular transactions, with multiple advances or irregular payment periods or amounts, the tolerance is one-quarter of a point.
Does Regulation Z cover business loans?
Regulation Z applies to consumer credit. Credit extended primarily for business, commercial or agricultural purposes is outside it, so a commercial lender is not bound to disclose an APR this way. Business lenders sometimes quote an all-in rate anyway, and this tool will compute one from the cash flows you enter.
Runs in your browser. The figures you type are not sent to CORAA or stored. Check the result against your firm's methodology before relying on it.