To calculate a mortgage payment, use the formula: M = P[r(1+r)^n]/[(1+r)^n-1], where M = monthly payment, P = principal loan amount, r = monthly interest rate (annual rate ÷ 12), and n = total payments (years × 12). Input values for P, annual interest rate, and loan term to compute M. For example, a $300,000 loan at 4% over 30 years yields a $1,416.35 monthly payment.

This formula combines principal amortization and interest compounding. The numerator calculates monthly interest plus principal repayment, while the denominator accounts for the declining loan balance over time. Data from the Federal Housing Finance Agency (FHFA) shows U.S. average mortgage rates ranged from 3.6% to 7.0% between 2020-2023, significantly impacting payment amounts. A 1% rate increase on a $300,000 loan raises the monthly payment by ~$100. Loan terms also affect affordability; a 15-year term at 4% reduces monthly payments to $2,222.80 but saves $93,000 in total interest compared to 30 years. Lenders typically require a down payment (3.5%-20%), which reduces principal and interest calculations. For instance, a 20% down payment on $300,000 lowers the principal to $240,000, decreasing the monthly payment by ~$283. These calculations help buyers assess affordability and align with guidelines like the 28/36 rule, where monthly payments should not exceed 28% of gross income, and total debt ≤36%. Historical data from the U.S. Census Bureau indicates 68% of first-time buyers used mortgages in 2022, emphasizing the importance of accurate payment estimates.