Interest Rate Calculator
Enter a loan amount, the fixed monthly payment and the term in months, and the calculator finds the annual interest rate that payment implies. Use it to check the rate behind a quoted payment or to compare two offers that quote payments instead of rates.
Annual Interest Rate
6.01%
Total Paid
$432,000.00
Total Interest
$232,000.00
How to use the Interest Rate Calculator
- Enter your numbers in the Interest Rate Calculator above.
- The result updates as you type, so there is no button to press.
- Change any value to see how the result moves.
The interest rate solver
M = P · r / (1 − (1 + r)^−n) Annual rate = r × 12 Total paid = M × n · · · Total interest = M × n − P
P is the loan amount, M the monthly payment, n the number of months and r the monthly rate. No algebra can solve this formula for r, so the calculator searches for it. The payment grows as the rate grows, and it is never less than the first month's interest, P × r. The rate therefore lies between 0 and M ÷ P, and the calculator halves that range until it pins r down. If the payments add up to exactly the loan amount, the rate is 0%. If they add up to less, no rate repays the loan and the calculator says so. It takes amounts from 0.01 to 1 trillion and terms from 1 to 1,200 whole months, and it refuses rates above 1,000% a year as a likely typo.
Worked example
A $20,000 loan repaid at $400 a month over 60 months implies an annual rate of 7.42%. You pay $24,000 in total, of which $4,000 is interest. At $450 a month the rate is 12.50%, with $27,000 paid and $7,000 of interest. The fields start at a $200,000 loan, $1,200 a month and 360 months, which comes to 6.01%.
Frequently asked questions
Why solve for the rate instead of the payment?
Some lenders and dealers quote a monthly payment without a rate. If you know the amount borrowed, the payment and the number of payments, this calculator shows the rate they imply, so you can compare it with other offers or check an existing loan.
Is this the APR?
No. The calculator returns the monthly rate times 12, an interest rate. The Consumer Financial Protection Bureau describes the APR as the interest rate plus points, broker fees and other charges you pay to get the loan, so on a loan with fees the APR is higher. To see what upfront fees do to the rate, enter the loan amount minus the fees. The same payments on a smaller amount give a higher rate.
Can I use this for credit cards?
Not directly, because a credit card's minimum payment changes with the balance. It works only for a fixed payment over a fixed number of months.