APR Calculator

How it works

Your payment is set by the loan amount and the note rate. But points and lender fees paid at closing mean you walk away with less than the loan amount while still making the full payments. The amount you effectively receive is the amount financed.

The APR is the yearly rate at which your payments exactly repay the amount financed. It is found by the actuarial method that the Truth in Lending Act's Regulation Z prescribes, the same method lenders use, and it is higher than the note rate whenever there are upfront finance charges. Because fees are spread over the term, the same fees raise the APR more on a short loan than on a long one.

A short-term loan with a flat fee, such as $15 for every $100 borrowed for two weeks, has no stated rate at all. Its APR is the fee as a share of the amount borrowed, scaled up to a year: $15 per $100 for 14 days is 15% × 365 ÷ 14, about 391%.

Formula

installment:  r = rate ÷ 12,  payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
amount financed = P − P × points − fees
APR = 12 × i, where payment × (1 − (1 + i)^−n) ÷ i = amount financed
finance charge = payment × n − amount financed
flat fee:  APR = (fee per $100 ÷ 100) × 365 ÷ days

Example

A $200,000, 30-year loan at 6% has a payment of $1,199.10. With 2 points ($4,000) and $1,500 of lender fees, the amount financed is $194,500. Paying $1,199.10 for 360 months to repay $194,500 is an APR of 6.26%; the finance charge is $237,176.38 on total payments of $431,676.38.

Borrowing $500 for 14 days at $15 per $100 costs a $75 fee, and you repay $575. The APR is 0.15 × 365 ÷ 14 = 391.07%.

Assumptions and limitations

• The interest rate is fixed and payments are equal and monthly, the first one a month after closing. Odd first periods, mortgage insurance and adjustable rates are not modelled, so a lender's disclosed APR may differ slightly.
• Every fee you enter is treated as a finance charge paid at closing. Under Regulation Z some closing costs, such as title insurance and appraisal fees on a mortgage, are not finance charges; leave those out.
• A flat-fee loan is repaid in one payment at the end. Renewing or rolling it over is a new loan with another fee.
• This is an estimate for planning, not financial, tax or legal advice. The APR on the lender's Truth in Lending disclosure is the legal figure.

Frequently asked questions