Mortgage payment formula, worked example, and costs to check
This calculator estimates the regular monthly principal-and-interest payment for a fixed-rate, fully amortizing mortgage. First, the amount financed is the home price minus the down payment. The payment formula uses that principal, the monthly interest rate, and the total number of monthly payments.
The formula
M = P × r ÷ [1 − (1 + r)−n]. Here, P is the amount borrowed, r is the annual interest rate divided by 12 and then by 100, and n is the loan term in years multiplied by 12. At a zero interest rate, the payment is simply P ÷ n.
Worked example
For a $350,000 home with a $70,000 down payment, the estimated loan principal is $280,000. At a fixed 6.5% annual rate over 30 years, the estimated principal-and-interest payment is about $1,769.79 per month. Over 360 payments, that is about $637,124.57 in principal and interest, including about $357,124.57 in interest. The displayed monthly amount is rounded; totals are calculated using the unrounded payment.
What this estimate leaves out
- Property taxes and homeowners insurance, whether paid monthly or separately.
- Private mortgage insurance (PMI), homeowners-association dues, and other recurring housing costs.
- Up-front closing costs, lender fees, repairs, utilities, and changes to escrow amounts.
Compare the full payment and fees shown in lenders’ official estimates, not just the principal-and-interest figure. The Consumer Financial Protection Bureau explains fixed-rate mortgage payments, and its Loan Estimate guide explains how to review additional costs.
Tips for accurate results
Enter the home price, down payment, rate, and term to see the principal-and-interest payment. Then add estimated property taxes, homeowners insurance, and any mortgage insurance or association dues to get a more realistic monthly cost.
Common mistakes and limits
The result is an estimate, not a loan offer. Rates change daily, and lenders consider credit, income, and debts. Closing costs, moving costs, and ongoing maintenance are separate and often significant, so budget for them in addition to the monthly payment.
Learn more: How mortgage payments are calculated.