Fixed-rate loan formula and worked example
For a fixed-rate installment loan with equal monthly payments, each payment covers the interest accrued for the month and repays some principal. Early payments generally include more interest because the balance is higher; as principal falls, the interest portion falls too.
Payment formula
M = P × r ÷ [1 − (1 + r)−n], where P is the amount borrowed, r is the annual interest rate divided by 12 and by 100, and n is the number of monthly payments. With a zero rate, the payment is P ÷ n.
Worked example
A $15,000 loan at a fixed 7.5% annual rate over 36 months has an estimated payment of about $466.59 per month. The scheduled payments total about $16,797.36, including roughly $1,797.36 in interest. This illustration assumes the stated rate is applied monthly and there are no additional fees.
What to compare before borrowing
A real loan may include an APR that reflects certain fees, an origination charge, late fees, or other terms that this calculator does not model. A lower monthly payment is not automatically a lower total cost: compare the annual percentage rate (APR), term, fees, and total amount repaid in the lender’s disclosures. For home loans specifically, the CFPB Loan Estimate guide explains how to compare loan costs.
Tips for accurate results
Enter the principal, the annual interest rate, and the number of months or years, then check the payment, total interest, and total repaid. Try adding a small extra payment to see how much sooner the loan ends and how much interest you avoid.
Common mistakes and limits
The payment assumes a fixed rate and equal payments. Variable-rate loans, fees, insurance, and late charges change the real cost. Compare offers using the APR and the total repaid, not only the monthly amount.
Learn more: Loan interest, APR and the real cost of borrowing.