Loan Payoff Calculator

How to Calculate Loan Payoff

The Loan Payoff Calculator is a valuable tool for anyone looking to understand how long it will take to pay off their loan and how much interest they'll pay over the life of the loan. This calculator takes into account extra payments, which can significantly reduce the loan term and total interest paid.

Loan Payoff Formula

The loan payoff calculation uses an iterative process, applying the following formulas for each payment period:

$$\text{Interest} = \text{Balance} \times \frac{\text{Annual Interest Rate}}{12 \times 100}$$

$$\text{Principal} = \text{Total Payment} - \text{Interest}$$

$$\text{New Balance} = \text{Previous Balance} - \text{Principal}$$

Where:

• Balance: The remaining loan balance
• Annual Interest Rate: The loan's interest rate expressed as a percentage
• Total Payment: The sum of the regular monthly payment and any extra payment

Calculation Steps

1. Calculate the monthly interest rate by dividing the annual rate by 12 and 100.
2. Determine the total monthly payment by adding the regular payment and any extra payment.
3. For each month:
   • Calculate the interest portion of the payment.
   • Calculate the principal portion of the payment.
   • Subtract the principal from the current balance to get the new balance.
   • Add the interest to the total interest paid.
4. Repeat step 3 until the balance reaches zero.
5. Count the number of iterations to determine the number of months to payoff.
6. Calculate the total amount paid by adding the original loan balance and the total interest paid.

Example Calculation

Let's calculate the payoff for a loan with the following parameters:

• Loan Balance: $200,000
• Annual Interest Rate: 4.5%
• Monthly Payment: $1,013.37
• Extra Monthly Payment: $100

Step 1: Calculate the monthly interest rate

$$\text{Monthly Rate} = \frac{4.5\%}{12 \times 100} = 0.00375$$

Step 2: Calculate total monthly payment

$$\text{Total Payment} = 1,013.37 + 100 = 1,113.37$$

Step 3: Iterate through months (showing first month)

$$\text{Interest} = 200,000 \times 0.00375 = 750$$

$$\text{Principal} = 1,113.37 - 750 = 363.37$$

$$\text{New Balance} = 200,000 - 363.37 = 199,636.63$$

This process continues until the balance reaches zero.

Final Result (after all iterations):

• Payoff Time: 20 years and 6 months
• Total Interest Paid: $95,983.62
• Total Amount Paid: $295,983.62

Visual Representation

This diagram illustrates the loan payoff progress for a $200,000 loan over 20 years and 6 months with a 4.5% annual interest rate, $1,013.37 monthly payment, and $100 extra monthly payment. The blue area represents the remaining loan balance, which decreases over time as payments are made. The purple area shows the cumulative interest paid, which increases over the life of the loan but at a decreasing rate due to the extra payments. This visual representation helps to understand how the loan balance decreases and the total interest paid increases over the loan term, and how extra payments can significantly reduce both the payoff time and total interest paid.