How the rate is found
A loan of L repaid by n equal monthly payments of P at a monthly rate r satisfies the equation below. Given L, P and n, the calculator searches for the r that makes it true, then multiplies by 12 for the annual rate.
P = L × r ÷ (1 − (1 + r)^−n)
r = monthly rate (annual rate ÷ 12), n = number of monthly payments. If the payments exactly repay the loan (P × n = L), r = 0.
Example: a car loan
A $25,000.00 loan repaid with 60 payments of $483.15.
- Total paid: $483.15 × 60 = $28,989.00
- Total interest: $28,989.00 − $25,000.00 = $3,989.00
- The monthly rate that makes the equation work is about 0.4988%, so the annual rate is 5.985%, which is 5.99% to two decimals.
Example: a 0% loan
$12,000.00 repaid with 24 payments of $500.00.
- 24 × $500.00 = $12,000.00, exactly the loan, so there is no interest: 0%.
Questions
What is the difference between an interest rate and an APR?
The CFPB explains that “the interest rate is the cost you will pay each year to borrow the money” and does not include fees, while the APR also reflects other charges, so “your APR is usually higher than your interest rate” [1]. This page finds the interest rate. For the APR with fees, use the APR calculator.
Why can’t the rate just be calculated with a formula?
The payment formula can be written either way round, but not rearranged to give the rate directly. So the calculator searches for the rate that makes the payment come out right. It narrows the range step by step and shows how many steps it took and how close the result is to your payment.
What if my payments add up to less than the loan?
No interest rate can fit, because even a 0% loan needs payments that add up to the loan. The calculator says so and shows the smallest payment that would work.
What payment should I enter for a mortgage?
Only the principal-and-interest part. If your payment also includes items such as property taxes or insurance, take those out first, or the rate will come out too high.
What do the monthly, annual and effective rates mean?
The monthly rate is what is charged each month. The annual rate is that times 12, the usual way loans quote it. The effective annual rate shows what 12 months of compounding adds up to, which is a little higher.
Does this work for credit cards?
Only for loans with a fixed payment and a set term. Credit card payments change from month to month, so use the debt payoff calculator instead.