Mortgage Payoff Calculator

What is a Mortgage Payoff Calculator?

A Mortgage Payoff Calculator is a financial tool that helps homeowners estimate how quickly they can pay off their mortgage and how much they can save in interest by making extra payments. This calculator takes into account the loan amount, interest rate, loan term, and any additional monthly payments to provide a comprehensive payoff schedule.

Formula for Mortgage Payoff Calculation

The primary formulas used in mortgage payoff calculations are:

1. Monthly Payment Formula:

\[P = L[\frac{r(1+r)^n}{(1+r)^n-1}]\]

Where:

• P = Monthly Payment
• L = Loan Amount
• r = Monthly Interest Rate (Annual Rate / 12)
• n = Total Number of Payments (Years × 12)

2. Remaining Balance Formula:

\[B_k = L[(1+r)^n - (1+r)^k] / [(1+r)^n - 1]\]

Where:

• B_k = Remaining Balance after k payments
• k = Number of payments made

Calculation Steps

1. Calculate the monthly payment using the Monthly Payment Formula.
2. For each month:
   • Calculate the interest portion of the payment: Balance × Monthly Rate
   • Calculate the principal portion: Monthly Payment - Interest Portion + Extra Payment
   • Subtract the principal portion from the balance
   • Add the interest portion to the total interest paid
3. Repeat step 2 until the balance reaches zero.
4. Calculate the total amount paid, time saved, and interest saved.

Example

Let's consider a scenario with the following details:

• Loan Amount: $200,000
• Interest Rate: 4%
• Loan Term: 30 years
• Extra Monthly Payment: $100

Calculation:

1. Monthly Payment: $954.83
2. Payoff Time: 25 years and 1 month
3. Total Interest Paid: $143,739.47
4. Interest Saved: $43,604.63
5. Time Saved: 4 years and 11 months