Federal Loan Interest Rate Calculator
Calculate your monthly payment, total interest paid, and effective cost for federal student loans based on official U.S. Department of Education interest rates and your loan details.
Formulas Used
Monthly Interest Rate:
r = Annual Rate / 100 / 12
Grace Period Interest Accrual (Unsubsidized Loans Only — Simple Interest):
Grace Interest = P × (Annual Rate / 100) × (Grace Days / 365)
where Grace Days ≈ Grace Months × 30.4375
Capitalized Balance (Unsubsidized):
P_cap = Principal + Grace Interest
For subsidized loans: P_cap = Principal (government covers grace interest)
Monthly Payment (Standard Amortization Formula):
M = P_cap × [r × (1 + r)ⁿ] / [(1 + r)ⁿ − 1]
where n = total number of monthly payments (years × 12)
Total Amount Paid:
Total = M × n
Total Interest Paid:
Total Interest = Total − P_cap
Amortization (each month i):
Interest Portion = Balance × r
Principal Portion = M − Interest Portion
New Balance = Balance − Principal Portion
Assumptions & References
- Interest rates shown reflect U.S. Department of Education federal student loan rates for loans first disbursed on or after July 1, 2023: Undergraduate Direct Subsidized/Unsubsidized: 5.50%; Graduate Unsubsidized: 7.05%; PLUS Loans: 8.05%. The preset values in this calculator use illustrative prior-year rates; always verify current rates at studentaid.gov.
- The standard repayment plan for most federal loans is 10 years (120 payments).
- Grace period interest is calculated using simple (non-compounding) daily interest as per federal loan servicing practice.
- For unsubsidized loans, unpaid interest accrued during the grace period is capitalized (added to principal) at repayment start, increasing the balance on which monthly payments are calculated.
- For subsidized loans, the U.S. government pays accrued interest during in-school periods, the grace period, and authorized deferment periods — so no interest capitalizes at repayment start.
- This calculator uses the standard fixed-rate amortization formula. Income-driven repayment (IDR) plans (IBR, PAYE, SAVE, ICR) use different payment calculations based on discretionary income and are not modeled here.
- Origination fees (1.057% for Direct Loans, 4.228% for PLUS Loans as of 2023) are not included in this calculation. These fees reduce the actual disbursed amount.
- This calculator does not account for loan forgiveness programs (PSLF, Teacher Loan Forgiveness, etc.).
- Reference: 20 U.S.C. § 1077a (Higher Education Act, interest rate provisions); U.S. Department of Education, Federal Student Aid — Interest Rates and Fees.