How the payoff date is worked out
Each payment first covers the interest charged since the last one, and the rest reduces the balance. With your current payment, the number of payments left is:
n = −ln(1 − r × B ÷ A) ÷ ln(1 + r)
- n
- the number of payments left
- B
- your current balance
- A
- your payment (principal and interest)
- r
- the interest rate per payment: the yearly rate divided by 12 for monthly payments, 26 for payments every two weeks, or 52 for weekly payments
The calculator doesn’t stop at the formula. It builds the full schedule one payment at a time, rounding each period’s interest to the cent as a lender does, and the last payment is whatever is left. The payoff date, the interest and every total come from that schedule.
The formula only works when the payment is larger than the interest. If a payment doesn’t cover the interest, the balance never goes down, and the calculator says so instead of showing a date.
Worked example
Take the calculator’s starting amounts, with the next payment due on November 1, 2026: a $150,000 balance at 6% a year and a $1,100 monthly payment.
- Monthly rate: r = 6% ÷ 12 = 0.5%
- First month’s interest: $150,000 × 0.005 = $750.00, so $350.00 of the first payment reduces the balance
- Payments left: n = −ln(1 − 0.005 × 150,000 ÷ 1,100) ÷ ln(1.005) = 229.6, so 230 payments, the last one smaller
As it is, the loan is paid off on December 1, 2045, with $102,559.07 of interest still to pay and a last payment of $659.07. Adding $200 to every payment ends it on March 1, 2041, 4 years 9 months sooner. Interest falls to $74,211.84, a saving of $28,347.23.
Paying off by a date
Choose “Pay off by a date” and enter the date. The calculator finds the smallest amount that, added to every payment, clears the loan on or before that date. It starts from the payment needed to repay the balance in the number of payments before your date, then checks the answer against the full schedule a cent at a time. The figure is therefore rounded up, and the date is met.
In the example, clearing the loan by October 1, 2036 takes $565.31 extra each month, $1,665.31 in total. That is 120 payments instead of 230, and $52,722.22 less interest.
Paying half every two weeks
Some borrowers pay half their monthly payment every two weeks. A year has 26 of those half-payments, which adds up to 13 monthly payments instead of 12. On the example loan, $550 every two weeks ends the loan on April 26, 2043, 2 years 8 months sooner, and saves $15,727.83 in interest.
That only works if each half-payment reaches your balance when you pay it. A lender may hold partial payments until a full payment has built up, and some paid biweekly programs pass the money on only once a month, for a fee. The Consumer Financial Protection Bureau explains how to pay down a loan faster on your own. Check how your lender applies the money before switching.
A lump sum or extra every month?
Money paid early saves the most, because it stops interest building on that amount for longer. On the example loan, a single $10,000 payment saves $19,313.49 in interest if it’s made with the next payment, $12,097.46 if it’s made five years later, and $6,591.14 after ten years.
Paying $100 extra every month instead adds up to $19,600 over the loan and saves $16,571.40. The lump sum made now saves more with less money, because all of it starts reducing interest straight away.
Before you pay extra
- Ask your lender to apply extra money to the principal. If it’s treated as an early payment of your next installment instead, it doesn’t reduce interest in the same way.
- Check whether the loan has a prepayment penalty.
- To pay a loan off completely, ask your lender for the payoff amount. It includes interest up to the day you pay and any unpaid fees, so it differs from the balance on your statement (Consumer Financial Protection Bureau).
- Some lenders will recast a loan after a large payment: the payment goes down and the end date stays the same. This calculator shows the other approach, where the payment stays the same and the loan ends sooner.
Assumptions and limitations
- The balance you enter is what you owe just after your most recent payment, and interest for the next payment is charged on all of it.
- The interest rate stays the same until the loan is paid off.
- Interest is charged once per payment period at the yearly rate divided by the number of payments per year. Loans that charge interest daily will differ slightly.
- The payment is principal and interest only. If your mortgage payment includes property tax or insurance, enter only the principal-and-interest part.
- Extra payments reduce the principal straight away, and the regular payment stays the same.
- Payments are made in full and on time, and there are no fees.
- Canadian fixed-rate mortgages are usually quoted with interest compounded twice a year rather than monthly, so a Canadian lender’s figures will differ slightly. The Mortgage Calculator can use that compounding.
- To clear the loan, ask your lender for a payoff quote: it includes interest to the day you pay.
Questions
Where do I find my current balance?
On your latest statement, or in your lender’s app or website. Use the principal balance after your most recent payment, not the payoff amount, which includes extra interest and fees.
My mortgage payment includes property tax and insurance. What do I enter?
Only the principal and interest. Your statement usually shows how each payment is split. The escrow part pays your tax and insurance bills and doesn’t reduce the loan.
What if I don’t know my payment?
Choose “Time left” and enter how long is left on the loan. The calculator works out the payment that repays the balance in that time. Your real payment may differ slightly, for example if the loan was refinanced or has fees built in, so use the payment from your statement when you have it.
Why is my lender’s payoff date different?
Usually because the lender charges interest daily, so the number of days between payments changes the interest a little each time. Late or early payments, fees and changes to the rate also move the date. The difference is usually small, but your lender’s figures are the ones that count.