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Interest Rate Calculator

Know the payment but not the rate? Enter the amount you borrow, how long you pay, and the monthly payment to find the interest rate built into the deal.

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How to use the interest rate calculator

  1. Enter the loan amount: the cash you actually borrow.
  2. Enter the loan term in years or months.
  3. Enter the monthly payment the lender or seller quoted.
  4. Read the annual interest rate, the effective annual rate and the total interest. The table shows how the rate changes if the payment were a little higher or lower.

This is useful when a dealer or store quotes only "$400 a month for 60 months" and you want to know what rate that really is.

How the rate is found

The payment formula links four numbers: loan amount, rate, term and payment. Knowing any three gives the fourth, but the rate can't be isolated with algebra, so it has to be found by trial.

P = M × (1 − (1 + i)^−n) ÷ i P = loan amount, M = monthly payment, n = number of payments, i = monthly rate Annual rate = 12 × i Effective annual rate = (1 + i)^12 − 1

The right-hand side is the present value of the payments: what they are worth today at a monthly rate i. A higher rate makes it smaller. The calculator uses bisection: it tries a rate halfway between a low and a high guess, keeps the half that contains the answer, and repeats until the present value matches the loan amount to a fraction of a cent.

Two cases have no positive answer. If the payments add up to exactly the loan amount, the rate is 0%. If they add up to less, no rate can work, because even an interest-free loan would need more, and the calculator says so.

Worked example

The defaults are $20,000 repaid at $400 a month for 5 years (60 payments):

  • Total paid: $400 × 60 = $24,000, so the interest is $4,000
  • Try 7%: the payments are worth $20,200.80 today, more than $20,000, so the rate is higher
  • Try 8%: they are worth $19,727.37, less than $20,000, so the rate is lower
  • Narrowing down gives a monthly rate of 0.61834%, which is 7.42% a year
  • Check: at 7.42%, 400 × (1 − 1.0061834^−60) ÷ 0.0061834 = $20,000.05
  • Effective annual rate: 1.0061834^12 − 1 = 7.68%

How the payment changes the rate

The same $20,000 over 60 months, at different payments:

Monthly payment Total interest Annual rate
$350 $1,000 1.94%
$375 $2,500 4.73%
$400 $4,000 7.42%
$425 $5,500 10.01%
$450 $7,000 12.50%
$500 $10,000 17.27%

Each extra $25 a month adds roughly 2.5 to 2.8 percentage points here. Small differences in a quoted payment hide big differences in the rate, so it pays to work it out.

Interest rate, APR and effective rate

The rate this calculator finds is the nominal annual rate, the figure lenders quote, which is 12 times the monthly rate. The effective annual rate shows the cost with monthly compounding included and is always a little higher. Neither one counts fees. If you paid an origination fee or the dealer added charges to the loan, enter the cash you actually received as the loan amount, or use the APR calculator to fold the fees in.

Frequently asked questions

Can I find the rate without a calculator?

Not exactly, because the formula can't be rearranged for the rate. You can bracket it by hand: compute the payment at two guesses with the payment calculator and narrow the gap. The calculator does the same thing about 200 times in a split second.

Why does the calculator say no rate fits?

Your payments add up to less than the amount borrowed. On $20,000 over 48 months at $400, you would repay only $19,200, which would need a negative interest rate. Check that the term and payment are right and that the amount excludes any down payment.

Is a 0% result real?

Yes, if the payments exactly equal the loan amount. Promotional "0% financing" deals work this way. Check whether you gave up a cash rebate to get the 0% offer, because the lost rebate is a hidden cost.

Does the rate include fees?

No. It is the rate built into the payment on the amount you enter. If fees were deducted from the money you received, enter the smaller amount you actually got to see the higher, fee-inclusive rate.

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Results are estimates for educational purposes and are not financial, tax or legal advice. See our disclaimer.