How mortgage payments are calculated
A fixed-rate mortgage is paid back in equal monthly installments. Each payment covers that month's interest first, and whatever is left reduces the balance. Because interest is charged on the remaining balance, early payments are mostly interest and later payments are mostly principal. The chart above shows that shift year by year.
The formula
The monthly principal and interest payment M is:
M = P × r / (1 − (1 + r)^−n)- P is the amount borrowed: the home price minus the down payment.
- r is the monthly interest rate: the annual rate divided by 12 and by 100. 6.5% a year is 0.065 / 12 ≈ 0.005417 a month.
- n is the number of monthly payments: years × 12.
For a $320,000 loan at 6.5% over 30 years, r = 0.005417 and n = 360, which gives a payment of about $2,022.62. If the rate is 0%, the formula breaks down and the payment is simply P / n.
What else goes into the monthly bill
Lenders often collect property tax and homeowners insurance with the mortgage and hold them in an escrow account. Together with principal and interest this is called PITI. Turn on the extra costs above to include them, along with any HOA fees. Things this calculator does not include:
- Private mortgage insurance (PMI): may be required for a conventional loan with a down payment below 20%. Its cost and cancellation rules vary. See the CFPB explanation of PMI.
- Adjustable rates: an ARM's payment changes when the rate resets. The figures here assume the rate stays fixed for the whole term.
- Closing costs and points, which are paid up front rather than monthly.
Shorter term or lower payment?
For the same loan amount and positive interest rate, a 15-year term has a higher monthly payment and lower total interest than a 30-year term. Switch between the term buttons to compare the figures. This calculator assumes a fixed rate and scheduled payments; it does not model extra principal payments or lender-specific fees.
