How it works
Student loans differ from other installment debt in one critical way: federal programs offer income-driven repayment (IDR) plans that tie your monthly bill to earnings rather than the amortization schedule. This calculator handles the standard, fixed-schedule path—the most common starting point for both federal Direct Loans and private education loans—where you enter three values (balance, annual rate, term in years) and get back the exact monthly installment and total interest. If you later switch to an IDR plan, the math changes entirely because payments scale with discretionary income and any remaining balance may be forgiven after 20–25 years.
For the standard schedule, the calculator converts your annual rate to a monthly rate, converts years to months, and solves for the level payment that brings the balance to zero on the last month.
The formula
M = P × [r(1 + r)ⁿ] / [(1 + r)ⁿ − 1]
Where:
- M = monthly payment
- P = loan balance (principal)
- r = monthly interest rate (annual rate ÷ 12)
- n = total number of payments (years × 12)
Total interest paid = (M × n) − P.
Worked example
Consider a $35,000 federal student loan balance on the standard 10-year repayment plan at 5.5% interest.
- Convert the annual rate to a monthly rate: 5.5% ÷ 12 = 0.4583%, or r = 0.0045833.
- Convert the term to months: 10 years × 12 = 120 payments, so n = 120.
- Calculate the compounding factor: (1 + r)ⁿ = (1.0045833)¹²⁰ ≈ 1.7317.
- Solve the numerator: r × (1 + r)ⁿ = 0.0045833 × 1.7317 ≈ 0.007938.
- Solve the denominator: (1 + r)ⁿ − 1 = 1.7317 − 1 = 0.7317.
- Divide for the payment factor: 0.007938 ÷ 0.7317 ≈ 0.010848.
- Multiply by the balance: $35,000 × 0.010848 ≈ $379.69 per month.
- Total paid over 10 years: $379.69 × 120 = $45,562.80.
- Total interest: $45,562.80 − $35,000 = $10,562.80.
So a $35,000 balance at 5.5% on the standard 10-year plan costs roughly $380/month and generates about $10,560 in interest over the life of the loan.
| Input | Value |
|---|---|
| Balance | $35,000 |
| Annual rate | 5.5% |
| Term | 10 years (120 months) |
| Monthly payment | ~$379.69 |
| Total interest | ~$10,562.80 |
Tips
Federal loans offer IDR plans (SAVE, PAYE, IBR, ICLR) that private student loans do not. These plans cap payments at 5–20% of discretionary income and may forgive remaining balances after 20–25 years—but they can also rack up more interest if payments don't cover the monthly accrual. Use this calculator's standard-plan result as a baseline, then compare it against your IDR estimate before committing to a path.
This calculator provides an estimate, not professional financial advice. Actual payments may vary based on loan fees, capitalization rules, or servicer-specific terms.