Student Loan Payoff Calculator

Calculate Your Student Loan Payoff

Use this calculator to estimate when you'll pay off your student loans and see how increasing your monthly payment can help you become debt-free faster.

How to Calculate Student Loan Payoff

Understanding how to calculate your student loan payoff is crucial for managing your educational debt effectively. This guide will walk you through the process of determining your payoff date and how extra payments can impact your loan term and total interest paid.

Student Loan Payoff Formula

The formula used to calculate the number of months needed to pay off a student loan is:

$$n = \frac{\log(1 - \frac{Br}{P})}{\log(1 + r)}$$

Where:

  • n = Number of months to payoff
  • B = Loan balance
  • r = Monthly interest rate (annual rate divided by 12)
  • P = Monthly payment

Calculation Steps

  1. Determine the current loan balance (B), annual interest rate, and monthly payment (P).
  2. Calculate the monthly interest rate (r) by dividing the annual rate by 12.
  3. Apply the formula to calculate the number of months to payoff (n).
  4. Convert the result to years and months.
  5. Calculate the total interest paid by multiplying the monthly payment by the number of months and subtracting the original loan balance.
  6. Repeat the process with any extra monthly payments to compare the results.

Example Calculation

Let's calculate the payoff time and total interest for a student loan with the following terms:

  • Loan Balance (B) = $30,000
  • Annual Interest Rate = 5%
  • Monthly Payment (P) = $318.20
  • Extra Monthly Payment = $100

Step 1: Calculate the monthly interest rate

$$r = \frac{5\%}{12} = 0.4167\% = 0.004167$$

Step 2: Calculate the number of months to payoff without extra payments

$$n = \frac{\log(1 - \frac{30000 \times 0.004167}{318.20})}{\log(1 + 0.004167)} = 120 \text{ months}$$

Step 3: Convert to years and months

120 months = 10 years

Step 4: Calculate the number of months to payoff with extra payments

$$n = \frac{\log(1 - \frac{30000 \times 0.004167}{418.20})}{\log(1 + 0.004167)} = 86 \text{ months}$$

Step 5: Convert to years and months

86 months = 7 years and 2 months

Step 6: Calculate total interest paid without extra payments

Total Interest = (318.20 × 120) - 30,000 = $8,184

Step 7: Calculate total interest paid with extra payments

Total Interest = (418.20 × 86) - 30,000 = $5,965.20

Result: By making an extra $100 monthly payment, you can pay off the loan 2 years and 10 months earlier and save $2,218.80 in interest.

Visual Representation

This diagram illustrates how a $30,000 student loan is paid off over time with and without extra payments. The blue line represents the loan balance with regular payments of $318.20 per month, while the red line shows the accelerated payoff with an additional $100 monthly payment. Notice how the extra payments significantly reduce the loan term and result in substantial interest savings.