Student Loan Interest Accrual Calculator
Calculate how interest accrues daily and monthly on your student loan, and see the total interest paid over the full repayment period.
Formulas Used
Daily Interest Accrual:
Daily Interest = Principal × (APR / 365)
Monthly Interest Accrual:
Monthly Interest = Principal × (APR / 12)
Standard Monthly Payment (Amortization):
M = P × [r(1+r)n] / [(1+r)n − 1]
where P = principal, r = monthly interest rate (APR/12), n = number of months
Total Interest Paid:
Total Interest = (M × n) − P (adjusted for actual payoff month)
Daily Rate:
rdaily = APR / 365 — the U.S. Department of Education uses a 365-day year for federal loans.
Assumptions & References
- Interest accrues daily using the actual/365 day-count convention, consistent with federal student loan servicer methodology.
- Monthly payment calculations use standard amortization (equal monthly installments).
- Extra payments are applied entirely to principal after interest is satisfied each month.
- Calculations assume a fixed interest rate for the entire loan term.
- No origination fees, grace periods, or income-driven repayment adjustments are modeled.
- Federal student loan interest rates are set annually by Congress; current rates range from ~5.5% (undergraduate) to ~8.05% (graduate PLUS) for 2024–2025.
- Reference: U.S. Department of Education — How Interest Is Calculated (studentaid.gov); Truth in Lending Act (Regulation Z), 12 CFR Part 1026.