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Interest Rate Calculator

Find the annual interest rate of a loan from the amount borrowed, the monthly payment and the term, plus the effective annual rate and total interest.

  • Free, no sign-up
  • Runs in your browser
  • Finance
Loan details
Enter years, months or both. For example 4 years and 6 months is 54 payments.

How to use the interest rate calculator

Enter the loan amount, the fixed monthly payment and the term in years, months or both. Press Calculate to see the annual interest rate, the effective annual rate, the total of all payments and the total interest. A yearly summary below shows how much interest and principal you pay each year and the remaining balance.

This is useful when a lender or seller quotes only a monthly payment, for example for a car or a store financing offer, and you want to know the rate hidden in it.

Annual rate and effective rate

  • The annual interest rate is the nominal rate compounded monthly, the way most loan rates and APRs are quoted: the monthly rate times 12.
  • The effective annual rate includes the effect of monthly compounding: (1 + monthly rate)^12 − 1. It is always a little higher than the nominal rate when the rate is above zero.

The calculator does not include fees, so if a loan has an origination fee, its true APR is higher than the rate shown here.

The method

There is no direct formula for the rate, so the calculator solves the standard loan payment equation, payment = amount × r / (1 − (1 + r)^−n), for the monthly rate r numerically. A higher rate always means a higher payment, and the answer must lie between 0 and payment / amount, so the calculator halves that range again and again (bisection) until it is accurate to the limit of the computer's precision. This method always finds the answer when one exists.

Two special cases are handled:

  • If the payments add up to exactly the loan amount, the rate is 0%.
  • If they add up to less than the loan amount, no positive rate exists and the calculator tells you the minimum payment for a 0% loan.

Worked example

A loan of 200,000 repaid at 1,199.10 a month for 30 years works out to an annual rate of 5.999992%, shown as 6.000%. The effective annual rate is about 6.168%. The 360 payments total 431,676, so the total interest is 231,676.

Good to know

  • Results are estimates based on equal monthly payments. Real loans can differ because of fees, rounding of payments and the exact day count a lender uses.
  • A payment rounded up by a cent can move the rate in the third or fourth decimal place.
  • Very high results (above 1,000% a year) are treated as an input mistake.

Frequently asked questions

Is the result the same as the APR?

It matches the APR only when the loan has no fees. APR also spreads fees and some other charges over the loan, so a loan with fees has an APR higher than the interest rate this calculator finds from the payment alone.

Why is the effective annual rate higher?

Interest is charged monthly and each month's interest is based on the remaining balance. Compounding 12 times a year makes the effective yearly cost slightly higher than the nominal rate. At 6% nominal, the effective rate is about 6.168%.

Why does it say no positive rate exists?

If the monthly payment times the number of payments is less than the loan amount, the loan would never be repaid with interest. Check the payment and the term; the message shows the payment needed for a 0% loan.

Can I enter a term in months only?

Yes. Leave the years empty and enter the months, for example 54 for 4 years and 6 months. You can also combine both fields; they are added together.