Loan Interest Rate Calculator

How it works

A fixed-rate loan ties together four numbers: the amount borrowed, the interest rate, the number of monthly payments and the payment. Know any three and the fourth is fixed. This calculator finds either the rate or the number of payments.

Solving for the rate has no direct formula. The calculator searches for the monthly rate at which the standard loan payment formula gives exactly your payment, then multiplies by 12 to state it as an annual rate, the way lenders and spreadsheets' RATE function do. Use it to check what a dealer or lender quote really costs when you were told only the payment.

Solving for the term uses the inverse of the payment formula. The answer is rarely a whole number of months, so the last payment is smaller than the others; the calculator shows that final payment and the total you will pay.

Formula

r = monthly rate        n = number of payments        M = payment
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
Rate:  solve the formula above for r (bisection); annual rate = 12 × r
Term:  n = −ln(1 − P × r ÷ M) ÷ ln(1 + r)        (n = P ÷ M when r = 0)
payments = n rounded up; final payment = balance after the others × (1 + r)
total interest = total of payments − P

Example

An $8,000 loan repaid with 48 monthly payments of $200 carries an annual interest rate of 9.242% (a monthly rate of 0.770%). The payments total $9,600, so $1,600 is interest. This is the example in Microsoft's documentation for the Excel RATE function, which gives 9.24%.

Going the other way, a $20,000 loan at 6% with $400 monthly payments takes 58 payments: 57 of $400 and a final one of $272.27. That totals $23,072.27, of which $3,072.27 is interest.

Assumptions and limitations

• The rate is fixed and compounds monthly, payments are equal and made at the end of each month, and the loan fully amortizes.
• The annual rate shown is the monthly rate × 12 (a nominal rate, as on a loan disclosure), not the effective annual rate with compounding.
• Fees are not included. If a fee was taken out of the money you received, enter the amount you actually received as the loan amount to see the rate including the fee; the APR on a loan disclosure is computed that way.
• This is an estimate for planning. It is informational and educational and not financial, tax or legal advice.

Frequently asked questions