Mortgage Payment Calculator

How it works

Your loan is the home price less your down payment. The standard loan payment formula turns that loan, the monthly interest rate and the number of payments into a level principal-and-interest payment that clears the balance on the last month.

Lenders usually collect property tax and homeowners insurance with the payment and hold them in escrow, so one twelfth of each annual bill is added. HOA dues are paid to the association, not the lender, but they are part of what the home costs you each month, so they are added too.

With less than 20% down, a conventional lender requires private mortgage insurance (PMI). It is charged as a yearly percentage of the original loan, split into monthly installments. Under the Homeowners Protection Act it must end automatically once the balance is scheduled to fall to 78% of the home's original value, and no later than the midpoint of the loan; the year table shows when that happens on your schedule.

Formula

loan = price × (1 − down % ÷ 100)
r = rate ÷ 100 ÷ 12        n = years × 12        (rate up to 50%)
P&I = loan × r × (1 + r)^n ÷ ((1 + r)^n − 1)     (loan ÷ n when r = 0)
PMI = loan × PMI rate ÷ 100 ÷ 12     when loan > 80% × price
balance_k = P&I × (1 − (1 + r)^−(n − k)) ÷ r     (the payments still due)
PMI stops after the first payment k with balance_k ≤ 78% × price (k ≤ n ÷ 2)
total = P&I + property tax ÷ 12 + insurance ÷ 12 + PMI + HOA
total interest = P&I × n − loan

Example

A $400,000 home with 10% down is a $360,000 loan. At 6.5% for 30 years the principal and interest are $2,275.44 a month. Add $400.00 of property tax ($4,800 a year), $150.00 of insurance ($1,800 a year) and $150.00 of PMI (0.5% of the loan a year) for a total of $2,975.44.

PMI ends after payment 109, in year 10, when the scheduled balance first drops to 78% of $400,000 ($312,000); by then you will have paid $16,350.00 of PMI. Over 30 years the interest comes to $459,160.16.

Assumptions and limitations

• The interest rate is fixed for the whole term, payments are monthly at the end of each month, and the loan fully amortizes.
• Property tax, insurance and HOA dues are held at the amounts you enter; in practice they usually rise over time.
• PMI is modelled as a level percentage of the original loan for borrower-paid monthly PMI and ends at 78% of the price under the Homeowners Protection Act. You may be able to ask your servicer to cancel it earlier, at 80%, and FHA and VA loans use different insurance rules (see the mortgage insurance calculator).
• The home's original value is taken to be the price. Closing costs, points and lender fees are not included unless you add them to the price.
• Payments are not rounded to the cent, so a lender's figures can differ by a few cents.
• This is an estimate for planning, not financial, tax or legal advice. Your lender's Loan Estimate is the authoritative figure.

Frequently asked questions