Mortgage Payoff Calculator
Find how long until a mortgage is paid off.
See how long a mortgage takes to clear at a given monthly payment.
How the Math Works
The Mortgage Payoff Calculator uses the formula n = -ln(1 - rB/PMT) / ln(1+r) to determine the number of months required to eliminate a mortgage. Here, B represents the remaining loan balance, PMT is the monthly payment amount, and r is the monthly interest rate (annual rate divided by 12). The natural logarithm (ln) accounts for the exponential decay of the loan balance over time, solving for n by rearranging the present value of an annuity equation. This formula precisely captures how interest accrues and payments reduce the principal, enabling accurate payoff time calculations.
Practical Applications
To use this calculator, input your current mortgage balance (B), fixed monthly payment (PMT), and annual interest rate (converted to monthly by dividing by 12). Adjust the payment amount to simulate scenarios like extra principal payments or refinancing. For example, increasing your monthly payment by $100 could dramatically shorten the payoff period, which the calculator quantifies instantly. This allows borrowers to test different strategies and choose the most financially efficient path.
Day-to-Day Use
This tool empowers daily financial decisions by revealing the true timeline of mortgage freedom. Knowing how extra payments shave years off your loan helps prioritize budgeting—whether allocating bonuses to reduce debt or planning for early retirement. It also clarifies the long-term cost of interest, motivating borrowers to secure lower rates or avoid lifestyle inflation. By visualizing the payoff horizon, users gain confidence in their financial planning and reduce stress about long-term debt obligations.
Worked example
$200k at 6%, $1,500/mo → ~166 months (13.8 yr).
FAQ
Payment too low?
If it's below the monthly interest, the loan never pays off.