Monthly Payment
Total Interest
Payoff Date
Table of Contents
Student loans, in one sentence
Student loans are amortizing installment debt — you owe a fixed monthly payment that combines interest (on the remaining balance) and principal until the loan is cleared. The two big levers for paying less total interest are a shorter term and any extra payments above the minimum.
How student loan payments are calculated
Standard student loans use the same amortization formula as mortgages and personal loans — equal monthly payments split between interest and principal:
M = P × [ r(1+r)n ] ÷ [ (1+r)n − 1 ]
- M — monthly payment
- P — loan principal (current balance)
- r — monthly interest rate (annual rate ÷ 12)
- n — total number of monthly payments (months in loan term)
Worked example using the calculator's defaults ($35,000 balance, 6.5% APR, 10-year term):
- P = 35,000; r = 0.065 ÷ 12 ≈ 0.005417; n = 120 months
- (1.005417)120 ≈ 1.9097
- M = 35,000 × (0.005417 × 1.9097) ÷ (1.9097 − 1)
- M = 35,000 × 0.010345 ÷ 0.9097 ≈ $397 per month
Total paid over 120 months: about $47,700. Total interest: about $12,700, or roughly 36% of the original principal.
Federal student loans use daily simple interest: interest accrues daily on the current balance at rate APR ÷ 365, then capitalizes (adds to principal) at specific events — the end of a grace period, end of deferment or forbearance, or when you change repayment plans. This formula approximates the monthly result closely; the exact result depends on payment timing and capitalization events.
The power of extra payments
Because student loans accrue interest daily on the current balance, every extra dollar of principal stops accruing interest for the rest of the loan. The savings compound over the loan life. On the calculator's $35,000 / 6.5% / 10-year default:
| Extra monthly payment | New payoff time | Total interest | Interest saved |
|---|---|---|---|
| $0 (standard) | 120 months (10.0 years) | $12,700 | — |
| $50 | 104 months (8.7 years) | $10,800 | $1,900 |
| $100 | 89 months (7.4 years) | $9,200 | $3,500 |
| $200 | 71 months (5.9 years) | $7,000 | $5,700 |
| $400 | 52 months (4.3 years) | $4,800 | $7,900 |
Important: when sending an extra payment, instruct your servicer in writing to apply it to principal on the current loan — not as an advance payment for next month, and not spread across multiple loans. Federal servicers default to behaviors that can blunt the savings if you don't specify.
Federal vs private student loans
| Feature | Federal loans | Private loans |
|---|---|---|
| Rate (2024–25) | 6.53% undergrad / 8.08% grad / 9.08% PLUS | ~4–15% (credit-dependent) |
| Rate type | Fixed, set annually by Congress | Fixed or variable |
| Credit check | None for Direct loans (PLUS excepted) | Required; cosigner often needed |
| Income-driven repayment | Yes (SAVE, PAYE, IBR, ICR) | No |
| Forbearance / deferment | Yes, multiple options | Limited, lender-dependent |
| Forgiveness programs | PSLF, Teacher Loan Forgiveness, IDR forgiveness | None |
| Bankruptcy protection | Very limited (undue hardship test) | Very limited (same test) |
For most undergraduates, federal loans should be exhausted before any private borrowing. Private loans only make sense after the federal annual and aggregate limits are reached, or to refinance high-rate debt when federal protections aren't needed.
Federal repayment plan options
| Plan | Monthly payment | Term | Best for |
|---|---|---|---|
| Standard | Fixed; calculated to pay off in 10 years | 10 years | Minimizing total interest paid |
| Graduated | Starts low, increases every 2 years | 10 years | Expecting income growth |
| Extended | Fixed or graduated; lower payment | Up to 25 years | High balances, need lower payment |
| SAVE (formerly REPAYE) | 5–10% of discretionary income | 20–25 years, then forgiveness | High debt-to-income ratio |
| PAYE | 10% of discretionary income (capped at standard) | 20 years, then forgiveness | High debt-to-income ratio |
| IBR | 10–15% of discretionary income | 20–25 years, then forgiveness | Older loans, partial financial hardship |
| ICR | 20% of discretionary or 12-year fixed (lower) | 25 years, then forgiveness | Parent PLUS borrowers (after consolidation) |
Public Service Loan Forgiveness (PSLF) forgives the remaining balance after 120 qualifying monthly payments while working full-time for a government or qualifying nonprofit employer. If you're targeting PSLF, do not refinance federal loans into private — doing so permanently forfeits eligibility. Note that income-driven plan rules, particularly for SAVE, have been subject to litigation and may change — always confirm current details at studentaid.gov.
When refinancing makes sense
Refinancing replaces existing loans with a new private loan, ideally at a lower rate. The math works when:
- Your credit has improved significantly since you originally borrowed (or you can add a creditworthy cosigner)
- Current market rates are meaningfully lower than your existing rate (typically 1.5%+ savings)
- You have stable, high income that won't need income-driven repayment
- You're not pursuing PSLF or any other federal forgiveness program
- You don't anticipate needing deferment or forbearance for grad school, unemployment, or hardship
Even when the rate is lower, run the numbers on total cost (rate × new term) and not just monthly payment — stretching a refinanced loan from 10 years to 20 can lower the monthly payment but increase total interest paid.
Limitations of this calculator
- Single loan, single rate. If you have multiple loans at different rates (common for federal borrowers), the math here only applies to one. Use the debt payoff calculator for a multi-loan strategy.
- No capitalization modeled. Federal loans capitalize accrued interest at specific events (end of grace period, end of deferment). This calculator assumes no capitalization — real federal loans can show higher total interest if capitalization occurred during deferment.
- Doesn't model income-driven plans. SAVE, PAYE, IBR, ICR all use formulas based on discretionary income, family size, and poverty guidelines. Use the official Federal Student Aid Loan Simulator for IDR scenarios.
- No forgiveness modeled. PSLF, IDR forgiveness, and Teacher Loan Forgiveness all change the effective cost of the loan dramatically. Not part of this calculation.
- No tax effects. The student loan interest deduction can reduce taxable income by up to $2,500/year (phased out at higher incomes). Not modeled here.
Sources & references
- U.S. Department of Education — Federal Student Aid — official source for federal loan rates, repayment plans, and forgiveness programs.
- Federal Student Aid Loan Simulator — official tool for modeling income-driven repayment scenarios.
- Federal Student Aid — Repayment Plans — detailed comparison of Standard, Graduated, Extended, SAVE, PAYE, IBR, and ICR.
- Federal Student Aid — Public Service Loan Forgiveness — PSLF eligibility, qualifying employment, and application process.
- Consumer Financial Protection Bureau — Student Loans — consumer-focused guidance on federal and private student loan choices.
FAQs
Standard student loan payments use the amortization formula M = P × [r(1+r)^n] ÷ [(1+r)^n − 1], where P is the balance, r is the monthly interest rate (APR ÷ 12), and n is the total number of monthly payments. For the calculator's defaults ($35,000 at 6.5% over 10 years), the monthly payment works out to about $397, with roughly $12,700 in total interest paid over the life of the loan.
For the 2024–25 academic year, federal Direct Subsidized and Unsubsidized loans for undergraduates carry a fixed rate of 6.53%. Graduate Direct Unsubsidized loans are at 8.08%, and Direct PLUS loans for parents and grad students are at 9.08%. Federal rates are set each May by Congress based on the 10-year Treasury yield plus a fixed add-on, and the rate you receive is locked for the life of that loan.
On the calculator's default scenario ($35,000 at 6.5% over 10 years), adding $100 extra per month reduces the payoff from 120 months to about 89 months — roughly 2.5 years saved — and cuts total interest from $12,700 to $9,200, a savings of about $3,500. The savings compound because every dollar paid early stops accruing interest for the remaining loan life.
It depends on your goals. Standard 10-year minimizes total interest but maximizes monthly payment. Income-driven plans (SAVE, PAYE, IBR) cap payments at 5–20% of discretionary income and forgive remaining balances after 20–25 years — best when your debt is high relative to income. Public Service Loan Forgiveness (PSLF) forgives the balance after 120 qualifying payments while working for government or nonprofit employers. Use the official Federal Student Aid Loan Simulator to compare plans on your actual numbers.
Only if you're certain you won't need federal protections. Refinancing federal loans into a private loan permanently forfeits income-driven repayment, deferment, forbearance, and forgiveness programs like PSLF. Refinancing makes sense for borrowers with stable, high incomes, excellent credit, and no public-service career plans. For everyone else, especially those who might pursue PSLF or use income-driven plans, keeping federal loans federal is the safer choice.