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Mortgage Payoff Calculator

Find how long to pay off your mortgage.

How it is calculated

The tool solves the loan formula for time. With balance P, annual rate converted to a monthly rate r = rate ÷ 1200 (the rate is entered as a percent, so 6 means 6%) and fixed monthly payment M: n = −ln(1 − r × P ÷ M) ÷ ln(1 + r) months. Months are rounded up to the next whole payment, and years are n ÷ 12 with one decimal.

It assumes interest compounds monthly on the remaining balance and that you pay the same amount each month. If the payment does not exceed the first month's interest, r × P, the balance never falls and the tool returns no result. The rate must be above zero. Escrow for taxes and insurance should be left out of the payment, since it does not reduce the balance. Rate changes on adjustable loans are not modelled.

Worked example

Balance 200000, rate 6% a year, payment 1500 a month.

Monthly rate: 6 ÷ 1200 = 0.005. First-month interest: 0.005 × 200000 = 1000, so 500 of each early payment reduces the balance. Then 1 − 0.005 × 200000 ÷ 1500 = 0.33333, and n = −ln(0.33333) ÷ ln(1.005) ≈ 220.27, rounded up to 221 months. In years: 220.27 ÷ 12 ≈ 18.4.

Try this example →

Common mistakes

  • Entering the rate as a decimal. Type 6 for 6%, not 0.06, otherwise the tool reads it as 0.06% and the payoff looks far too quick.
  • Including escrow (property tax and insurance) in the payment. Only principal and interest pay the loan down.
  • Using the original loan amount instead of the current balance. The tool counts the time remaining from the balance you enter.
  • Using a payment that only just covers interest. At 200000 and 6%, a payment of 1000 returns no result and 1000.01 gives about 192 years.
  • Expecting the answer to include extra payments or later rate changes. It assumes the same payment and rate until the balance is zero.

Sources

About this calculator

This calculator works out how many months remain on a loan by solving the standard amortization formula for time: n = −ln(1 − i·P/M) / ln(1 + i), where P is the current balance, i is the monthly interest rate, and M is the fixed monthly payment. Because interest is charged on the outstanding balance each period, the same payment amount pays off a loan faster once the balance is smaller — which is why extra principal payments shrink the payoff time by more than their dollar amount might suggest.

Homeowners deciding whether to make extra payments, borrowers comparing refinance offers with different rates and terms, and financial planners projecting when a mortgage will be paid off all use this calculation. It's the same math lenders use internally to build amortization schedules, just solved for payoff time instead of monthly payment.

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Comments (1)

  • Editorial team

    Use it to see what a slightly larger payment does. On a 200,000 balance at 6%, a 1,500 payment ends in 221 months, 1,600 ends in 197 and 1,700 in 178. That is 24 months saved for 100 more a month. The tool does not model fees or penalties, so check your loan contract for early-repayment charges before changing the payment. By how much would you raise your payment, and why?

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