APR Calculator
A loan's stated rate ignores the fees withheld from your proceeds. The APR — computed here by the actuarial method behind US Regulation Z — is the rate on the money you actually receive.
The rate on the money you actually receive
Sign a $10,000 note and you may receive $9,800 — the lender withheld a $200 fee — yet your payments are calculated as if you held the full ten thousand. The APR exists to expose that gap: it is the rate at which your payment stream is worth precisely what landed in your hands. US Regulation Z prescribes the actuarial method used here.
Amount financed = Σ payments ÷ (1 + i)months, solved for i · APR = i × 12
Example: $10,000 at a stated 12% for 12 months: payment $888.49. With $200 withheld, amount financed $9,800 — and the APR that equates the payments to $9,800 is 15.85%. Nearly four points of the loan's price were in the fee, invisible in the stated rate.
Why the law bothers
Without a standardized APR, every lender would quote the number that flatters its own fee structure and comparison would be theater. With one, a loan at 11% plus heavy fees must stand next to a clean 13% loan and lose on the record. Quote-shopping works only because this number exists.
How this is calculated
The payment is computed from the note amount at the stated rate. The APR is then solved by bisection: find the monthly rate i whose present value of those payments equals the amount financed (note − fees withheld); APR = i × 12 × 100. This is the actuarial method of Regulation Z Appendix J for a regular installment transaction. Fees paid separately in cash, rather than withheld, enter the real-world APR computation slightly differently — here they are treated as withheld, the conservative and common case.
Frequently asked questions
Is APR the same as the interest rate?
Only when a loan has no fees. The interest (note) rate prices the balance; the APR prices the transaction — balance, fees and all. With fees, APR is always higher.
Why is mortgage APR so much higher above the rate?
Mortgage APR sweeps in points, origination and many closing costs, so the gap over the note rate is wide — often half a point or more. It is the most honest single number in a Loan Estimate.
Does APR include every cost?
No — it includes finance charges as defined by regulation. Some third-party costs (appraisal in some cases, title, government recording) sit outside it. It is a standardized approximation, not a total-cost audit — the loan-comparison calculator does that job.
Can APR be lower than the stated rate?
Essentially never on a standard loan with fees withheld. If a quote shows it, suspect an error or an unusual structure such as a lender credit large enough to offset all fees.
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