Mortgage Payoff Calculator

Payoff Term Formula:

\[ n = \frac{\log\left(\frac{M}{M - P \times r}\right)}{\log(1 + r)} \]

Payoff Term (number of payments):

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1. What is a Mortgage Payoff Calculator?

Definition: This calculator determines how many payments are needed to fully pay off a mortgage based on the monthly payment amount, principal, and interest rate.

Purpose: It helps homeowners understand their mortgage timeline and plan for early payoff strategies.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ n = \frac{\log\left(\frac{M}{M - P \times r}\right)}{\log(1 + r)} \]

Where:

\( n \) — Number of payments (unitless)
\( M \) — Monthly payment (USD)
\( P \) — Principal amount (USD)
\( r \) — Monthly interest rate (decimal)

Explanation: The formula calculates how many periods are needed to amortize the loan completely given fixed payments.

3. Importance of Payoff Term Calculation

Details: Understanding your payoff term helps with financial planning, evaluating refinancing options, and assessing the impact of extra payments.

4. Using the Calculator

Tips: Enter your regular monthly payment, the remaining principal balance, and the monthly interest rate (annual rate ÷ 12). The monthly payment must exceed the interest accrued each month.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert annual rate to monthly?
A: Divide the annual percentage rate by 12 (e.g., 6% annual = 0.06/12 = 0.005 monthly).

Q2: What if my payment doesn't cover the interest?
A: The calculation won't work if M ≤ P×r because the principal would never decrease.

Q3: Does this include taxes and insurance?
A: No, use only the principal and interest portion of your payment.

Q4: How accurate is this for adjustable-rate mortgages?
A: It assumes a fixed rate. For ARMs, recalculate when rates change.

Q5: Can I see the impact of extra payments?
A: Yes, enter your regular payment plus any additional principal amount.