Loans & Mortgages
How To Calculate Mortgage Payoff
Every extra dollar paid against a mortgage removes principal that would otherwise be charged interest for the rest of the term. A modest extra payment can cut years off the loan and save tens of thousands.
Quick Answer
Months with extra = -ln(1 - rate x balance / (payment + extra)) / ln(1 + rate)
- balance
- Amount still owed today
- rate
- Annual rate divided by twelve
- payment
- Required monthly payment
- extra
- Additional principal paid each month
Adding to the monthly payment shortens the term, and the interest saved is the difference between total interest with and without the extra. On a 250,000 balance at 6.5% with 300 months left, adding 200 a month clears the loan about 66 months early and saves roughly 64,929 of interest.
What Is Mortgage Payoff?
Paying off a mortgage early means directing extra money at the principal balance. Because mortgage interest is charged on whatever remains outstanding, every dollar of principal removed stops generating interest for the entire remaining term, which is why small extra payments have an outsized effect.
The mechanism is simple but the maths is not linear. A 200 monthly extra payment on a 250,000 balance does not simply remove 200 times the number of months; it removes the interest that those dollars would have accrued, which compounds the benefit over the life of the loan.
The payoff time with extra payments is found by rearranging the amortisation formula. Instead of solving for the payment, you solve for the number of months given a larger payment, using a logarithm. The result is the month the balance reaches zero.
The interest saved is the difference between two totals: the interest you would pay over the remaining term on the scheduled payment, and the interest you pay when the loan closes early. Both totals are the sum of payments minus the original balance.
The effect is largest when the loan is young, because early payments are mostly interest. An extra dollar paid in year two removes interest that would have been charged for twenty-eight more years on a thirty-year loan, while the same dollar paid in year twenty-five removes only five years of interest.
The rate matters as much as the balance. A mortgage at 6.5% guarantees a 6.5% return on every extra dollar prepaid, tax-free and risk-free. That is a competitive return compared with many investments, and it is certain, which is why prepaying appeals to cautious households.
The comparison is not purely financial. Money paid into a mortgage is illiquid, while money in savings or investments stays accessible. Prepaying reduces flexibility, so an emergency fund should come first, and only money that would otherwise sit idle is a good candidate.
Biweekly payments are a common structured approach. Paying half the monthly amount every two weeks produces twenty-six half-payments a year, which is one extra full payment annually. The effect is identical to adding one twelfth of the payment each month.
Lump sums from bonuses or windfalls accelerate the process further. A single large extra payment early in the loan can remove years from the term, because it eliminates interest over the whole remaining period rather than just the current month.
Some mortgages carry prepayment penalties, which claw back part of the benefit. They are more common on fixed-rate loans in some markets, and checking the terms before making extra payments avoids an unexpected charge that erases the saving.
The decision to prepay should be weighed against other uses of the money. Paying down higher-interest debt such as credit cards first is almost always better, because the guaranteed return is higher. After that, the choice between prepaying and investing depends on risk tolerance and the expected return.
The calculator shows both the time cut and the interest saved, which are the two numbers that make the decision concrete. Seeing that a 200 monthly extra payment removes five and a half years and about 65,000 of interest turns an abstract intention into a clear trade-off.
Finally, remember that the saving is realised only when the loan actually ends. If the home is sold or refinanced before then, the benefit is reduced to the interest avoided up to that point. Prepayment still helps, but the full figure applies only if the loan runs to its new, shorter end.
Formula
n = -ln(1 - r x balance / (payment + extra)) / ln(1 + r)
Solves the amortisation formula for the number of months at the higher payment.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| B | Balance | currency | Amount still owed. |
| P | Payment | currency | Required monthly payment. |
| E | Extra | currency | Additional principal each month. |
| r | Monthly rate | rate | Annual rate divided by twelve. |
Saved = (payment x remaining months) - ((payment + extra) x new months)
The difference in total payments between the two schedules, both net of the balance.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| n0 | Original months | count | Months left on the current schedule. |
| n1 | New months | count | Months with the extra payment. |
How To Calculate Mortgage Payoff
- 1
Find the current payment
Use the scheduled monthly payment on the outstanding balance at the current rate. This is the baseline before any extra.
- 2
Compute interest without extra
Multiply the payment by the remaining months and subtract the balance. That is the interest you would pay if you changed nothing.
- 3
Solve for the new payoff time
Plug the larger payment into the payoff formula using a logarithm. The result is the month the loan reaches zero with the extra.
- 4
Compute interest with extra
Multiply the larger payment by the shorter term and subtract the balance. That is the interest you pay with the extra.
- 5
Subtract for the saving
The difference between the two interest totals is your saving, and the difference in months is the time you take off the loan.
Examples
Example 1: 250,000 balance with 200 extra a month
- Remaining balance
- 250,000
- Interest rate
- 6.5%
- Remaining term
- 300 months
- Extra each month
- 200
| Step | Calculation | Result |
|---|---|---|
| Required monthly payment | loan payment formula | 1,688.02 |
| Interest without extra | 1,688.02 x 300 - 250,000 | 256,405.37 |
| Months with the extra | payoff formula at 1,888.02 | 233.83 |
| Interest with extra | 1,888.02 x 233.83 - 250,000 | 191,476.77 |
| Interest saved | 256,405.37 - 191,476.77 | 64,928.60 |
Result: Adding 200 a month pays the loan off in about 233.83 months instead of 300, saving roughly 64,928.60 of interest and cutting 66 months from the term.
Example 2: 200,000 balance with 300 extra a month
- Remaining balance
- 200,000
- Interest rate
- 5.5%
- Remaining term
- 240 months
- Extra each month
- 300
| Step | Calculation | Result |
|---|---|---|
| Required monthly payment | loan payment formula | 1,375.77 |
| Interest without extra | 1,375.77 x 240 - 200,000 | 130,185.91 |
| Months with the extra | payoff formula at 1,675.77 | 173.17 |
| Interest with extra | 1,675.77 x 173.17 - 200,000 | 90,195.47 |
| Interest saved | 130,185.91 - 90,195.47 | 39,990.44 |
Result: A 300 extra payment on a 200,000 balance clears it in about 173.17 months instead of 240, saving 39,990.44 of interest and cutting nearly 67 months off the term.
Calculator
Interest saved by paying extra
$64,928.60
- Required monthly payment
- $1,688.02
- Months with the extra
- 233.8308
- Months saved
- 66.1692
- Interest without extra
- $256,405.37
- Interest with extra
- $191,476.77
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
Prefer a full-width tool? Open the Mortgage Payoff calculator page.
Common Mistakes
Prepaying before building an emergency fund
Money in a mortgage is illiquid. An emergency fund should come first, or a job loss could force expensive borrowing against the very home you are trying to free up.
Paying down low-interest debt first
If credit cards or personal loans cost more than the mortgage, clearing them first gives a higher guaranteed return. Prepay the mortgage only after higher-rate debt is gone.
Ignoring prepayment penalties
Some loans charge a fee for early repayment that can erase the saving. Check the terms before committing extra money.
Forgetting to mark the payment as principal
Extra money sent without instruction may be treated as an early instalment rather than principal, which delays the benefit. Label it clearly.
Prepaying late in the loan
Late in the term most of the payment is already principal, so an extra dollar saves far less interest than it would in the early years.
Assuming the saving is realised early
The full interest saving only materialises if the loan runs to its new end. Selling or refinancing early reduces it to the interest avoided so far.
Overpaying to the point of strain
Directing every spare dollar at the mortgage can leave no room for other goals or emergencies. Balance prepayment against flexibility.
FAQ
How much interest does an extra payment save?
It depends on how early the extra is paid and the rate. On a 250,000 balance at 6.5% with 300 months left, adding 200 a month saves about 64,929 of interest and 66 months.
Is it better to pay extra monthly or in a lump sum?
A lump sum early in the loan saves the most, because it removes interest over the longest remaining period. Steady monthly extras are easier to sustain and nearly as effective if started early.
Do biweekly payments really help?
Yes. Paying half the monthly amount every two weeks produces one extra full payment a year, which shortens the term. It is equivalent to adding one twelfth of the payment each month.
Should I prepay my mortgage or invest?
Prepaying gives a guaranteed, tax-free return equal to the mortgage rate. Investing may earn more but carries risk. The choice depends on your risk tolerance and other goals.
Does prepaying hurt my credit?
No. Paying a loan off early does not hurt your credit score and may help by reducing your total debt and credit utilisation.
What if I have a prepayment penalty?
Then the benefit shrinks by the penalty amount. Some loans allow limited extra payments each year without a penalty, so check the terms before making large prepayments.
References
- [1]Consumer Financial Protection Bureau, How to pay off your mortgage faster — https://www.consumerfinance.gov/owning-a-home/
- [2]Investopedia, Mortgage prepayment — https://www.investopedia.com/terms/p/prepayment.asp
- [3]Consumer Financial Protection Bureau, Amortization explained — https://www.consumerfinance.gov/ask-cfpb/