Use this calculator to determine the exact number of years and months required to pay off your mortgage, based on your current principal balance, interest rate, and monthly payment amount.
How Long to Pay Off a Mortgage Calculator
How Long to Pay Off a Mortgage Formula
The time (in number of months, $N$) required to pay off a loan is derived from the standard annuity formula, solved using logarithms. This formula assumes a fixed monthly interest rate ($i$) and regular payments ($M$).
N = ln(M / (M - P * i)) / ln(1 + i)
where:
P = Principal Loan Amount
M = Monthly Payment
i = Monthly Interest Rate (Annual Rate / 1200)
ln = Natural Logarithm
Variables Explained
- Current Principal Loan Amount ($P$): The remaining balance on your mortgage today.
- Annual Interest Rate ($r$): The yearly nominal rate (e.g., 6.5%). The calculator converts this to a monthly rate.
- Regular Monthly Payment ($M$): The fixed amount you pay each month towards the principal and interest.
- Total Time to Pay Off Mortgage ($N$): The resulting time, expressed in years and months.
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What is “How Long to Pay Off a Mortgage”?
The mortgage payoff term is the remaining duration, expressed in time (months/years), until the outstanding principal balance of a loan is completely zero. Understanding this term is crucial for financial planning, as it directly impacts the total amount of interest you will pay over the life of the loan.
Factors like the interest rate and the size of your monthly payment are the primary determinants. Making extra principal payments, even small ones, can drastically reduce the payoff term due to the power of compound interest working in reverse (i.e., compound interest savings). This calculator provides the exact date you will be debt-free.
How to Calculate the Mortgage Payoff Term (Example)
Let’s find the payoff term for a $200,000 balance at 4.0% interest with a $1,100 monthly payment:
- Determine Monthly Interest Rate ($i$): $4.0\% / 1200 = 0.003333$.
- Calculate Required Minimum Payment: Principal $\times$ Monthly Rate = $200,000 \times 0.003333 \approx \$666.67$. Since the payment of $1,100$ is greater than the interest, the loan is solvable.
- Apply the Formula: $$N = \frac{\ln(1100 / (1100 – 200000 \times 0.003333))}{\ln(1 + 0.003333)}$$ $$N \approx \frac{\ln(1100 / 433.33)}{\ln(1.003333)} \approx \frac{0.9298}{0.003327} \approx 279.4 \text{ months}$$
- Convert to Years and Months: $279.4$ months is 23 years and 3.4 months.
Frequently Asked Questions (FAQ)
Is the payoff term the same as the original loan term?
No. The payoff term calculated here is the *remaining* time, which changes if you make extra payments or your loan balance changes. The original term is fixed (e.g., 30 years) when the loan starts.
What happens if my monthly payment is too low?
If your monthly payment ($M$) is less than or equal to the interest accrued for that month ($P \times i$), the loan will never be paid off, and the balance may even increase. Our calculator will return an error message in this scenario.
Does this calculator account for taxes and insurance?
No. This calculation focuses only on the principal and interest portion of your monthly payment. Taxes and insurance (Escrow) do not affect the duration of the loan term.
How much time can I save by paying extra?
The easiest way to find out is to use this calculator. Input your current data, note the result, and then increase the ‘Regular Monthly Payment’ value to see the dramatic reduction in the payoff term.