Mortgage Payoff Calculator

Each monthly payment first covers the interest that built up on the balance that month. The rest pays down the loan. Any extra you pay goes straight to the balance, so next month there is less for interest to build on, and a little more of your regular payment goes to the loan. That snowballs: the loan ends sooner and you pay less interest overall. Your required payment stays the same.

The formula

monthly rate = yearly rate ÷ 12 ÷ 100
payment = balance × monthly rate ÷ (1 − (1 + monthly rate)^−months left)
each month: interest = balance × monthly rate
new balance = balance − (payment − interest) − extra
months left from a payment = −ln(1 − balance × monthly rate ÷ payment) ÷ ln(1 + monthly rate)
interest saved = interest without extras − interest with extras
every 2 weeks = payment ÷ 2 × 26 a year = one extra payment a year (payment ÷ 12 extra each month)

Worked example

You owe $250,000 at 6.5% a year with 25 years (300 payments) left. The monthly rate is 6.5 ÷ 12 ÷ 100 = 0.0054167, and (1.0054167)³⁰⁰ = 5.0562, so the payment is $250,000 × 0.0054167 × 5.0562 ÷ 4.0562 = $1,688.02.

In month 1 the interest is $250,000 × 0.0054167 = $1,354.17, so $1,688.02 − $1,354.17 = $333.85 pays down the loan. With $200 extra the balance falls to $250,000 − $333.85 − $200 = $249,466.15, instead of $249,666.15.

Keep adding $200 a month and the loan is gone after 234 payments instead of 300, 5 years 6 months sooner. Interest falls from $256,405.37 to $191,477.49, a saving of $64,927.88 for $46,600 of extra payments.

Every 2 weeks

Half the payment ($844.01) every 2 weeks is 26 half payments, or 13 full payments, a year. On the same loan that clears it in 250 months and saves $49,727.73 in interest. We count it as one-twelfth of a payment ($140.67) extra each month. Some lenders hold your half payments and apply them monthly, which gives this result; others apply each one as it arrives, which saves a little more. Check that a biweekly plan has no set-up fee.

Mortgage-free by a date

To clear the same loan in 15 years (180 payments) you'd need a payment of $2,177.78. That is $289.76 a month on top of the $1,688.02 payment and the $200 you already add. The calculator finds this by trying amounts until the loan ends on time, so it also works with yearly and lump-sum extras.

Pay off early or invest the extra?

We compare two people who spend exactly the same each month until the date the loan would have ended anyway (300 months). One pays the extra $200 into the loan, then invests the whole payment once the loan is gone. The other pays the loan as normal and invests the $200 every month. At a 7% return (compounded monthly) the first ends with $151,932 and the second with $162,014, so investing comes out $10,083 ahead. At about 6.5%, the same as the loan rate, they come out even; below it, paying off wins. Investing returns aren't guaranteed and may be taxed; paying off the loan is a sure, tax-free saving.

Before you pay extra

• Ask your lender to put the extra towards the principal, not next month's payment.
• Check for early repayment fees or yearly limits on overpayments.
• Keep an emergency fund and clear dearer debts (like credit cards) first.

Assumes a fixed interest rate, interest worked out monthly on the balance, and a payment of principal and interest only. Your lender's figures may differ slightly because of rounding and day counts. For your full payment with tax and insurance see the mortgage calculator; for any loan's full schedule see the amortization calculator; to swap to a cheaper loan see the refinance calculator.