Second Mortgage Loan Calculator Payoff

Loan Payoff Formula:

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

Number of Payments (n):

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1. What is a Second Mortgage Loan Payoff Calculator?

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

Purpose: It helps homeowners understand how long it will take to pay off their second mortgage under current payment terms.

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 amount (USD)
\( P \) — Principal loan amount (USD)
\( r \) — Monthly interest rate (decimal)

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

3. Importance of Loan Payoff Calculation

Details: Understanding payoff time helps with financial planning, budgeting, and evaluating refinancing options.

4. Using the Calculator

Tips: Enter your monthly payment, original loan amount, and monthly interest rate (divide APR by 1200). All values must be > 0 and payment must exceed interest.

5. Frequently Asked Questions (FAQ)

Q1: What if my payment doesn't cover the interest?
A: The calculation won't work if M ≤ P×r because the loan would never be paid off (negative amortization).

Q2: How do I convert APR to monthly rate?
A: Divide your annual percentage rate by 1200 (e.g., 6% APR = 0.06/12 = 0.005 monthly rate).

Q3: Does this include taxes and insurance?
A: No, this calculates based on principal and interest only (P&I payment).

Q4: Can I use this for other loans?
A: Yes, it works for any fixed-rate, fixed-payment amortizing loan.

Q5: Why does my result have decimal payments?
A: The calculation is precise - you'd make a smaller final payment in the last month.