About this student loan calculator
This professional-grade student loan calculator uses standard amortization mathematics and optional capitalization to model how your balance evolves from disbursement through repayment. It helps you compare scenarios, plan extra payments, and understand trade-offs before you borrow—or while you’re repaying.
Data Source and Methodology
Authoritative sources:
- U.S. Department of Education – Federal Student Aid, “Loan Simulator” Methodology and Repayment Concepts, 2024. URL: studentaid.gov/loan-simulator.
- 34 CFR § 685.202(b) – Interest capitalization rules for Direct Loans, 2024. URL: ecfr.gov.
All calculations strictly follow the formulas and regulatory sources cited above.
The Formula Explained
Glossary of Variables
| Symbol / Field | Definition |
|---|---|
| P | Loan amount (principal/face value). |
| APR (%) | Nominal annual interest rate. |
| m | Months in in-school/grace period. |
| AccruedInterestDuringGrace | Interest accrued before repayment begins. |
| P0 | Principal at repayment start (after optional capitalization). |
| r | Monthly interest rate = APR / 12. |
| n | Number of scheduled payments (months) = years × 12. |
| Payment | Monthly scheduled payment from amortization formula. |
| Extra | Optional extra payment applied each month. |
| Total Interest | Sum of interest paid over the life of the loan. |
| Total Paid | Principal + total interest. |
Worked Example
How It Works: A Step-by-Step Example
- Inputs: P = $30,000; APR = 5.50%; Term = 10 years; m = 6 months; Capitalize = Yes; Extra = $50.
- Accrued interest during grace: 30,000 × 0.055/12 × 6 = $825; P0 = 30,825.
- Monthly rate: r = 0.055/12 ≈ 0.0045833; n = 120.
- Payment: P0 × r / (1 − (1 + r)^−120) ≈ $333.31.
- With Extra = $50, pay $383.31 monthly. Amortize month-by-month to get a shorter payoff time and less total interest.
Frequently Asked Questions (FAQ)
Do student loans accrue interest during school or grace periods?
Unsubsidized federal and most private loans accrue interest during in-school/grace periods. If you do not pay it, the interest may capitalize at repayment start, increasing principal.
What is interest capitalization and why does it matter?
Capitalization adds unpaid interest to your principal. Future interest is then calculated on the higher balance, increasing total cost and monthly payment.
Does this calculator handle zero-interest promos?
Yes. If APR is 0, the monthly payment becomes principal divided by the number of months.
Can I compare scenarios quickly?
Yes. Adjust inputs and the results update instantly. You can also add an extra monthly payment to see time and interest savings.
Are origination fees financed?
Federal origination fees are generally deducted from disbursement. Your payment is calculated on the principal (face value). The calculator shows your estimated net disbursement for transparency.
Does this support income-driven repayment (IDR)?
This tool focuses on fixed-payment amortization. For IDR, consult your servicer or the official Federal Student Aid Loan Simulator.
Amortization schedule (with extra payments if any)
| Month | Payment | Interest | Principal | Balance |
|---|---|---|---|---|
| Enter your details to see the schedule. | ||||
Formula (LaTeX) + variables + units
','
r = \frac{\text{APR}}{12} \quad,\quad n = \text{years} \times 12
\text{AccruedInterestDuringGrace} = P \cdot \frac{\text{APR}}{12} \cdot m
P_0 = \begin{cases} P + \text{AccruedInterestDuringGrace}, & \text{if capitalized} \\ P, & \text{otherwise} \end{cases}
\text{Payment} = \begin{cases} \dfrac{P_0}{n}, & r = 0 \\ \dfrac{P_0 \cdot r}{1 - (1 + r)^{-n}}, & r \neq 0 \end{cases}
\text{Extra Payment Scenario: amortize month-by-month with } \text{Payment}_\text{total} = \text{Payment} + \text{Extra}
$ r = \frac{\text{APR}}{12} \quad,\quad n = \text{years} \times 12 $ $ \text{AccruedInterestDuringGrace} = P \cdot \frac{\text{APR}}{12} \cdot m $ $ P_0 = \begin{cases} P + \text{AccruedInterestDuringGrace}, & \text{if capitalized} \\ P, & \text{otherwise} \end{cases} $ $ \text{Payment} = \begin{cases} \dfrac{P_0}{n}, & r = 0 \\ \dfrac{P_0 \cdot r}{1 - (1 + r)^{-n}}, & r \neq 0 \end{cases} $ $ \text{Extra Payment Scenario: amortize month-by-month with } \text{Payment}_\text{total} = \text{Payment} + \text{Extra} $
- P = principal (loan amount) (currency)
- r = periodic interest rate (annual rate ÷ payments per year) (1)
- n = total number of payments (years × payments per year) (count)
- M = periodic payment for principal + interest (currency)
- Finance — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/finance - Personal Loans — calcdomain.com · Accessed 2026-01-19
https://calcdomain.com/subcategories/finance-personal-loans - studentaid.gov/loan-simulator — studentaid.gov · Accessed 2026-01-19
https://studentaid.gov/loan-simulator - ecfr.gov — ecfr.gov · Accessed 2026-01-19
https://www.ecfr.gov/current/title-34/part-685
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.