HesapHanem

Student Loan Payoff Calculator

See how fast your payment clears the loan.

How it is calculated

Enter the current balance, the annual interest rate in percent, and the fixed amount you pay each month. The monthly rate is i = rate ÷ 100 ÷ 12. The number of months to clear the loan is n = −ln(1 − B·i ÷ P) ÷ ln(1 + i), where B is the balance and P the monthly payment. Total paid is P × n and total interest is P × n − B. At a 0% rate it is just B ÷ P. If the payment does not exceed the first month's interest (P ≤ B × i), the balance never falls and the tool shows no result. The months figure is not rounded up, so the last payment is treated as a fraction of a full one.

Worked example

A $30,000 balance at 6% with a $350 monthly payment. The monthly rate is 6 ÷ 100 ÷ 12 = 0.005. First-month interest is 30,000 × 0.005 = $150, less than $350, so the balance falls. Then 1 − 150 ÷ 350 = 0.5714, and ln(0.5714) = −0.5596, while ln(1.005) = 0.004988. So n = 0.5596 ÷ 0.004988 = 112.2 mo, which is about 9 years and 4 months. Total paid is 350 × 112.2027 = $39,270.96 and total interest is $39,270.96 − $30,000 = $9,270.96.

Try this example →

Common mistakes

  • Choosing a payment at or below the monthly interest. With $30,000 at 6% the interest is $150 a month, so a $150 payment (or less) never reduces the balance and the tool returns nothing, while $151 takes over 1,000 months.
  • Entering the rate as a decimal (0.06) instead of a percent (6). A rate of 0.06 means 0.06% a year here and would badly understate the interest.
  • Entering an annual payment, or the total of several loans' payments, as the monthly payment. The formula assumes one rate and one fixed monthly amount.
  • Ignoring capitalised interest or fees. The tool starts from the balance you type; unpaid interest added to it or origination fees must be included in that figure.
  • Reading the total as exact to the cent. The last payment is usually smaller than the others, so the real total is slightly lower than this fractional-month estimate.

Sources

About this calculator

This calculator works in reverse from a standard loan amortization schedule: instead of computing the payment from a fixed term, it takes your loan balance, interest rate, and a fixed payment amount you plan to make, then calculates how many months it will take to pay the balance down to zero as interest accrues on the shrinking balance each period.

This is especially useful for student loan borrowers considering paying more than the minimum required payment, since even a modest increase can cut years off the payoff timeline and substantially reduce total interest paid, thanks to how amortization front-loads interest on the earliest balance.

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Comments (1)

  • Editorial team

    Try the same loan with a payment that is only a little higher. In the 30,000 at 6% example, raising 350 to 400 a month cuts the payoff from 112.2 to 94.2 months, almost a year and a half sooner, and lowers total interest from 9,270.96 to 7,694.21. The tool covers one balance at one rate, so run each loan separately. What extra amount per month could you realistically add, and how did you decide it?

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