How Mortgage Calculations Work: Formulas, Escrow & Amortization
Calculating a mortgage payment involves more than simply dividing the purchase price by the number of months in the loan term. Because lenders charge interest continuously on the outstanding principal balance, each monthly payment is governed by an amortization formula that balances interest and principal reduction over time.
The Standard Amortization Formula
In the United States, mortgage loans compound monthly. The monthly principal and interest payment (M) is calculated using the following standard formula:
Where:
- P: The loan principal (Home purchase price minus down payment).
- r: The monthly interest rate (Annual interest rate divided by 12).
- n: The total number of monthly payments (Loan term in years multiplied by 12; e.g., 360 months for a 30-year mortgage).
Understanding PITI: What Your Real Monthly Cost Includes
First-time homebuyers frequently overlook that the principal and interest payment is only a portion of the monthly bill. Most lenders require an escrow account that collects one-twelfth of your annual property taxes and homeowners insurance each month. When you add homeowners association (HOA) fees and private mortgage insurance (PMI), your actual monthly outlay—frequently called PITI—can be 20% to 40% higher than the base loan payment.
Private mortgage insurance (PMI) is required by conventional lenders whenever your down payment is less than 20% of the home's purchase price (an initial loan-to-value ratio greater than 80%). On a $340,000 loan, PMI typically costs between $150 and $250 each month until you accumulate sufficient equity.
How Amortization Schedules Shift Over Time
In the early years of a 30-year fixed mortgage, the vast majority of each monthly payment goes toward interest, while only a small slice reduces the loan balance. For example, during month one of a $340,000 loan at 6.75%, $1,912.50 of your $2,205.23 payment goes purely to interest, while just $292.73 goes toward equity. By year 20, that proportion flips dramatically. Making extra principal payments early in the loan has a disproportionately powerful compounding effect by bypassing future interest cycles entirely.