Every fixed-rate mortgage payment is computed with the same amortization formula:
M = P × [ r(1 + r)n ] / [ (1 + r)n − 1 ]
- M — the monthly principal-and-interest payment;
- P — the loan amount (purchase price minus your down payment);
- r — the monthly interest rate: the annual rate divided by 12;
- n — the number of payments: the term in years multiplied by 12.
Take a $250,000 loan at 4.5% for 30 years. The monthly rate is 0.045 / 12 = 0.00375 and the number of payments is 360, so the payment comes to $1,266.71. Over the life of the loan you would pay about $206,000 in interest — more than 80% of the amount you borrowed, which is why the term and the rate matter so much.
The principal-and-interest payment is only part of the bill. Lenders typically collect 1/12 of the annual property tax and homeowner’s insurance with each payment, plus PMI if your down payment is below 20% and any HOA fees your community charges.
You do not need to run the formula by hand — the mortgage calculator does it instantly, shows the full amortization schedule, and tells you the exact month your PMI ends.