Student Loan Payoff Calculator
Estimate how many months it takes to pay off a student loan and the total interest paid, from the balance, interest rate, and monthly payment.
How to use this tool
- Enter your current loan balance.
- Enter the annual interest rate (APR).
- Enter a fixed monthly payment.
- Read the months to payoff, total paid, and total interest. A bigger payment shortens both.
See how fast you can clear a student loan and what the interest costs. Enter the balance, interest rate, and a fixed monthly payment to get the payoff time and total interest — and try a higher payment to see the savings.
Formula
With monthly rate r = annual rate ÷ 12, balance P, and payment A:
Months = −ln(1 − rP ÷ A) ÷ ln(1 + r), rounded up.
Total paid ≈ Payment × Months; Total interest = Total paid − Principal.
If A ≤ rP the payment never covers the interest and the loan never amortizes.
How it works
This calculator treats a student loan as a fixed-payment amortizing loan. Each month interest accrues on the outstanding balance at the monthly rate, your payment covers that interest first, and the remainder reduces principal. Solving the amortization equation for the number of payments gives a closed-form count, which we round up to the next whole month because the final payment is usually partial.
Total paid is reported as payment times months (a slight overstatement, since the last payment is smaller), and total interest follows as total paid minus the original balance — a conservative, easy-to-verify view of borrowing cost. If your monthly payment is less than or equal to the monthly interest, the balance never shrinks; the tool flags that case rather than returning a misleading number. The model assumes a constant rate and payment and excludes fees, capitalization of unpaid interest, and income-driven or forgiveness programs, which can change real outcomes significantly.
Reviewed by the AbraCalc Education Desk. This is an educational estimate, not financial advice; confirm your exact terms with your loan servicer and check federal repayment options at studentaid.gov.
Worked example
$20,000 balance, 5% APR, $250/month
- Monthly rate r = 5% ÷ 12 ≈ 0.004167.
- Monthly interest at the start: 20,000 × 0.004167 ≈ 83.33, well under the $250 payment, so the loan amortizes.
- Months = −ln(1 − 0.004167 × 20,000 ÷ 250) ÷ ln(1.004167) ≈ 97.3, rounded up to 98.
- Total paid ≈ 250 × 98 = 24,500; total interest = 24,500 − 20,000 = 4,500.
Months to pay off = 98 (total interest $4,500.00)
Payoff for a $20,000 loan at 5% APR by monthly payment
| Monthly payment | Months to pay off | Total interest |
|---|---|---|
| $200 | 128 | $5,600.00 |
| $250 | 98 | $4,500.00 |
| $300 | 78 | $3,400.00 |
| $400 | 56 | $2,400.00 |
| $500 | 44 | $2,000.00 |
Key terms
- Principal
- The outstanding loan balance on which interest is charged.
- APR
- Annual percentage rate — the nominal yearly interest rate; divided by 12 for the monthly rate here.
- Amortization
- Paying off a loan through regular payments that cover interest first, then reduce principal.
- Total interest
- The extra you pay above the original balance over the life of the loan.
Frequently asked questions
- Why is total paid slightly higher than my real payoff?
- We report payment × months, but the final month's payment is usually partial. The true total is a few dollars lower; this convention keeps the interest figure conservative and easy to check.
- What if my payment doesn't cover the interest?
- If your monthly payment is at or below the monthly interest, the balance never falls and the loan never amortizes. The calculator flags this instead of returning a payoff time.
- Does this include loan forgiveness or income-driven plans?
- No. It models a fixed payment on a standard amortizing loan. Income-driven repayment, forgiveness, and interest capitalization can change the real outcome — check studentaid.gov.