How to use the interest rate calculator
- Enter the amount borrowed, the amount you actually receive and will repay.
- Enter the monthly payment from the loan offer or statement.
- Enter the term as years plus extra months, so the calculator knows the number of payments.
- Read the APR, the monthly and effective annual rates, the total interest and the sensitivity table that shows how the rate moves if the payment were slightly different.
Formula
Amount = payment x (1 - (1 + r)^-n) / r
Solve for the monthly rate r by repeated halving between a lower and an upper bound
APR = r x 12; effective annual rate = (1 + r)^12 - 1
Total interest = payment x n - amount
The loan formula cannot be rearranged to isolate r, so the calculator narrows it down by trying a rate, checking whether the payments are worth more or less than the amount, and halving the gap 300 times. It then checks the answer by computing the payment from the rate it found.
Worked examples
A car loan: you borrow $28,000 and pay $540 a month for 60 months. The rate that makes those payments repay the loan is 5.899% APR, which is 0.4916% a month and a 6.061% effective annual rate. You pay $32,400.00 in total, of which $4,400.00 is interest.
Sensitivity: if the payment were 10% lower at $486.00, the implied rate would be 1.609%. At $567.00 (5% higher) it would be 7.945%. A small change in payment moves the rate a lot, so compare quotes by the exact payment.
Cross-check: a $20,000 loan with a $377.42 payment over 60 months comes out at 4.999%, matching the 5% rate that produces that payment in the loan calculator. A mortgage of $250,000 with a $1,896.20 payment over 360 months is 8.352%.
When you need to solve for the rate
Sometimes the interest rate is the one number you do not have. A dealer may quote only a payment, a private lender may describe a loan in terms of payments, or an old statement may omit the rate. If you know the amount, the payment and the number of payments, the rate is determined, and this tool finds it. Compare it with offers you have been given and ask the lender to explain any large gap.
Why a lender's APR may be higher
This calculator returns the rate of the payment stream itself. A lender's disclosed APR can be higher because fees, such as origination charges, are folded in. If you receive less than you repay, for example you borrow $10,000 but $300 is taken as a fee, enter the amount you actually received. The result will then include the cost of that fee.
The calculation also assumes equal monthly payments and a fully amortizing loan. Interest-only periods, balloon payments and irregular payments need a different method.
What the error messages mean
If your payments add up to less than the amount borrowed, the only matching rate would be negative, so the tool asks you to check the numbers. If the figures imply an APR above 1,000%, it stops instead of showing a rate that is almost certainly a typing mistake. A payment that exactly repays the amount over the term means a rate of 0%.
Assumptions and limits
- A fully amortizing loan with equal payments at the end of every month, and monthly compounding.
- APR here is the monthly rate times 12, the usual quoting convention. The effective annual rate is shown separately.
- Fees, insurance and add-ons are included only if you reduce the amount received to reflect them.
- The final payment is assumed to equal the others. Real loans may adjust the last payment by a few cents.
- Balloon payments, interest-only periods, variable rates and daily accrual are not modeled.
- This is an estimate, not financial advice or a loan disclosure.
Frequently asked questions
How can I find the interest rate if I only know the payment?
You need the amount borrowed, the monthly payment and the number of payments. With those three, exactly one monthly rate makes the payments repay the loan, and this calculator searches for it.
Why does the answer say APR and also effective annual rate?
APR multiplies the monthly rate by 12. The effective annual rate compounds the monthly rate over twelve months, so it is a little higher. On the $28,000 example they are 5.899% and 6.061%.
Why do small payment changes move the rate so much?
Most of each payment repays principal, so the interest part is a small difference between large numbers. Over 60 payments, a $27 change in the monthly payment on $28,000 moves the rate by about two percentage points.
What if the lender charged fees?
Enter only the money you actually received as the amount. The solved rate then includes the effect of the fees, and it will be higher than the note rate, which is how a disclosed APR treats certain charges.