Mortgage Payoff Calculator: Payoff Date and Balance
When will my mortgage be paid off? Enter your balance, rate and the payment you actually make to get the payoff date, the interest still to pay, and the balance after any number of payments.
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Formula
With monthly rate r = annual rate ÷ 100 ÷ 12, balance B and monthly payment P:
- Payments needed:
n = -ln(1 - r × B ÷ P) ÷ ln(1 + r), rounded up (the last payment is smaller). At 0% it isB ÷ P. - Balance after
kpayments:B × (1 + r)^k - P × ((1 + r)^k - 1) ÷ r - Interest to payoff: the sum of each month's
balance × runtil the balance reaches zero.
The payment must be larger than the first month's interest, r × B, or the loan never pays off.
Worked example
A balance of 200,000 at 6% a year with a payment of 1,500:
r = 0.005, son = -ln(1 - 0.005 × 200,000 ÷ 1,500) ÷ ln(1.005) = 220.27, which is 221 payments (18.4 years).- Total interest is 130,407.70.
- After 60 payments the balance is
200,000 × 1.005^60 - 1,500 × (1.005^60 - 1) ÷ 0.005 =165,114.98.
When to use it
Use this page when you know your current balance and payment and want the date the loan ends or the balance at a future date. To see what a bigger payment would save compared with your schedule, use the extra mortgage payment calculator. To see how each payment splits into interest and principal, use the amortization calculator.
Second example
A balance of 200,000 at 6% with a payment of 2,000 gives n = -ln(1 - 0.005 × 200,000 ÷ 2,000) ÷ ln(1.005) = 138.98, so 139 payments (11.6 years) and 77,951.56 of interest. After 60 payments the balance is 130,229.97.
Common mistakes
- Entering the original loan amount instead of today's balance.
- Using a payment that includes escrow for taxes and insurance; use principal and interest only.
- Expecting a payment equal to one month of interest to reduce the balance. It never does.
- Treating the result as the lender's payoff quote.
Frequently asked questions
How long will it take to pay off my mortgage?
The number of payments is n = -ln(1 - r × B ÷ P) ÷ ln(1 + r), where B is the balance, P the monthly payment and r the monthly rate. For 200,000 at 6% with 1,500 a month, r = 0.005 and n = 220.3, so 221 payments (18.4 years), the last one smaller.
How do I find the payoff amount after a number of payments?
Each month the balance grows by one month of interest and falls by your payment. After 60 payments of 1,500 on 200,000 at 6%, the balance is 165,114.98. Set the look-ahead to the number of payments you have made or plan to make.
Why do I get an error when my payment is small?
If the payment is no larger than one month of interest, the balance never falls. On 200,000 at 6% the monthly interest is 1,000, so a payment of 1,000 or less cannot pay the loan off. A payment that would need more than 1,200 months (100 years) is also reported as out of range.
Is this the exact figure my lender will quote?
No. A payoff quote from your lender adds interest accrued to the payoff date and any fees, and lenders round and day-count differently. Use this to compare plans and ask your lender for the official figure.
How long to pay off a mortgage paying 2,000 a month?
On a 200,000 balance at 6%, a payment of 2,000 pays the loan off in 139 payments, or 11.6 years, with 77,951.56 of interest. The same balance at 1,500 a month takes 221 payments, so the extra 500 saves 82 payments.
How do I calculate mortgage payoff time in Excel?
Use =NPER(rate/12, -payment, balance). For 200,000 at 6% with 1,500 a month, =NPER(0.06/12,-1500,200000) returns 220.27, which means 221 payments with a smaller last one. Round up to whole months.
What is the difference between payoff time and the payoff amount?
Payoff time is how many payments remain. The payoff amount is the balance you must send to close the loan on a given day, including interest accrued since your last payment. This page estimates the time and the balance after payments; your lender quotes the exact payoff amount.