Student loan repayment
Model the standard level-payment plan on a student loan balance, then test what an extra monthly payment does to the term and the total interest. The payment-to-income check keeps the result grounded in affordability.
| Year | Interest | Principal | Balance |
|---|---|---|---|
| Year 1 | $2,239 | $2,846 | $35,154 |
| Year 2 | $2,061 | $3,025 | $32,129 |
| Year 3 | $1,871 | $3,214 | $28,915 |
| Year 4 | $1,669 | $3,416 | $25,499 |
| Year 5 | $1,455 | $3,630 | $21,868 |
| Year 6 | $1,227 | $3,858 | $18,010 |
| Year 7 | $985.23 | $4,100 | $13,910 |
| Year 8 | $728.00 | $4,357 | $9,552 |
| Year 9 | $454.63 | $4,631 | $4,921 |
| Year 10 | $164.12 | $4,921 | $0.00 |
The standard plan is level-payment: the same amount every month for the whole term, with no income test.
PMT = B·i / (1 − (1+i)⁻ⁿ) · level payment over the term
I = n·PMT − B · total cost above the principal
Pₜ = PMT + e − Bₜ₋₁·i · the extra goes entirely to principal
DTI = 12·PMT / income · annual payment as a share of gross income
A clear path from inputs to results.
The standard student-loan plan is a level payment over a fixed term. This engine computes that payment, the total interest it implies, and what happens if you pay extra — federal loans normally carry no prepayment penalty, so extra principal is pure interest savings.
How to use
- Enter the total balance across your loans. If rates differ materially, model them separately.
- Set the interest rate — the weighted average if you have several loans.
- Choose the repayment term. Ten years is the federal standard; extended plans run to 25.
- Add an extra monthly payment to see the term reduction and the interest saved.
- Enter gross income to check the payment-to-income ratio.
- Review the yearly table to see how long the interest-heavy phase lasts.
The formula
Reference: Federal Direct Loan standard repayment mechanics (34 CFR 685.208).
Worked example
$38,000 at 6.1% over 10 years (default inputs)
- Balance $38,000.
- Interest rate 6.1%.
- Term 10 years (120 payments).
- Gross income $55,000.
- No extra payment.
- 1
Monthly rate: 6.1% / 12 = 0.508333%.
- 2
Payment: 38,000 × 0.00508333 / (1 − 1.00508333^−120) = $423.79.
- 3
Total paid: 120 × 423.79 = $50,855.
- 4
Total interest: 50,855 − 38,000 = $12,855.
- 5
Payment-to-income: (12 × 423.79) / 55,000 = 9.25%.
Monthly payment $423.79 · total interest $12,855 · payment-to-income 9.25%.
Interpreting the result
The 10-year standard plan costs about a third of the balance in interest. Stretching to 25 years cuts the payment by roughly 40% but more than doubles the interest. The payment-to-income ratio of 9.25% is comfortable; above about 10% student debt starts to constrain housing affordability, because mortgage underwriters count it in the debt-to-income calculation.
Assumptions & limitations
- A single fixed rate applies to the whole balance. A weighted average across loans approximates this but hides the per-loan amortisation.
- Interest is computed monthly. Federal loans accrue daily, which produces a slightly higher balance and a marginally different payment.
- No income-driven repayment, deferment, forbearance or forgiveness is modelled — those are policy features, not amortisation.
- Payments begin immediately; in-school deferment and the grace period are not represented.
- Extra payments are applied to principal with no prepayment penalty, which is the norm for federal loans.
Frequently asked questions
Is the standard plan always 10 years?
For federal Direct Loans, yes — the standard plan is a fixed 10-year term. Extended plans (up to 25 years) require a balance above a threshold, and graduated plans start lower and rise every two years.
What is a safe payment-to-income ratio?
Under about 8% is comfortable, 8–10% is manageable, and above 10% starts to compete with housing and savings. Lenders typically cap total debt at 36–43% of gross income.
How does interest capitalise?
Unpaid interest is added to principal at the end of deferment or forbearance, and then accrues interest itself. That capitalisation step is why the balance at repayment can exceed what you borrowed.
Do extra payments reduce interest?
Yes, because they reduce the balance on which interest accrues for every remaining month. On a 10-year loan, even a modest extra payment can remove a year or more from the term.
Should I refinance?
Refinancing lowers the rate but converts federal loans to private, which forfeits income-driven repayment, forgiveness eligibility and some deferment options. Price that optionality before chasing a lower rate.
What about income-driven repayment?
IDR sets the payment from income rather than balance, often below the standard payment, with forgiveness after 20–25 years. It is a policy calculation, not amortisation, so this engine does not model it.
Methodology last reviewed 2026-10-18. Results are informational and not financial or engineering advice — see our disclaimer.