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Student Loan Calculator

Computes the monthly payment and total interest of a student loan under a standard (level) plan or an approximation of the US federal graduated plan, including interest that accrues during a grace period and is capitalized when repayment starts.

When to use

You want the monthly payment, total cost or effect of a grace period for a fixed-rate student loan under standard or graduated repayment.

Do not use when: The loan is income-driven (IBR, PAYE, SAVE), variable-rate, or you know the payment and want the payoff time (use debt-payoff).

Formula

capitalized_interest = balance × annual_rate_percent/1200 × grace_months (if accruing); B = balance + capitalized_interest; i = annual_rate_percent/1200; n = 12·term_years. Standard: payment = B × i / (1 − (1 + i)^−n). Graduated: k = ceil(n/24) steps, step ratio g = 3^(1/(k−1)), first payment P solves Σ_s P·g^s × (1 − (1+i)^−m_s)/i × (1+i)^(−24s) = B, with P raised to at least B × i (interest-only) and g reduced accordingly.

Federal Standard plan arithmetic is exact. The Graduated plan is an approximation of the federal rule (payments rise every two years, first payment at least the monthly interest, last payment at most three times the first); servicers set the actual steps. Capitalization follows federal Direct Loan practice for unsubsidized loans.

Inputs

Parameter	Type	Unit	Required	Description
`balance`	number		yes	Principal owed when the grace period starts (or today if repayment has begun). Range: > 0, ≤ 100000000
`annual_rate_percent`	number	%	yes	Fixed annual rate in percent. Range: ≥ 0, ≤ 100
`term_years`	number	years	default 10	Length of repayment in years (10 for federal Standard and Graduated plans; up to 25–30 for extended plans). Range: > 0, ≤ 30
`grace_months`	integer	months	default 0	Months before the first payment (6 for federal Direct loans). Range: ≥ 0, ≤ 36
`interest_accrues_during_grace`	boolean		default true	True for unsubsidized loans (interest accrues and is capitalized); false for subsidized loans, where the government pays grace-period interest.
`repayment_plan`	enum: standard \| graduated		default standard	Standard: equal monthly payments. Graduated: payments step up every 24 months, the last step no more than 3× the first.

Outputs

Output	Type	Description
`balance_at_repayment_start`	number	balance + capitalized_interest.
`capitalized_interest`	number	balance × rate/12 × grace_months (simple interest), added to principal when repayment starts.
`number_of_payments`	integer	12 × term_years.
`monthly_payment`	number	Level payment (standard) or the first-step payment (graduated).
`final_monthly_payment`	number	Payment in the final step (same as monthly_payment for standard).
`total_paid`	number	Sum of all payments.
`total_interest`	number	total_paid − balance (includes capitalized grace interest).
`payment_steps`	list	Rows of from_month, to_month and payment for each step (one row for standard).

Example

30,000 at 6 % over 10 years, standard: {"balance":30000,"annual_rate_percent":6,"term_years":10} → {"balance_at_repayment_start":30000,"capitalized_interest":0,"number_of_payments":120,"monthly_payment":333.06,"final_monthly_payment":333.06,"total_paid":39967.38,"total_interest":9967.38}

30,000 at 6 %, 6-month grace, graduated over 10 years: {"balance":30000,"annual_rate_percent":6,"term_years":10,"grace_months":6,"repayment_plan":"graduated"} → {"balance_at_repayment_start":30900,"capitalized_interest":900,"monthly_payment":196.17,"final_monthly_payment":588.51,"total_paid":43915.06,"total_interest":13915.06}

GET https://tttkmbb.com/api/v1/calculate/student-loan?balance=30000&annual_rate_percent=6&term_years=10

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/student-loan (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/student-loan · Markdown: https://tttkmbb.com/finance/student-loan.md · JSON definition: https://tttkmbb.com/finance/student-loan.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="student-loan"
OpenAPI operationId: calculate_student_loan_payment
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Federal Student Aid – Repayment plans (Standard and Graduated) (government)
Federal Student Aid – Interest rates and how interest is calculated and capitalized (government)
Wikipedia – Amortization calculator (annuity payment formula) (reference)

FAQ

Why does the graduated plan cost more?

Lower early payments leave more principal outstanding for longer, so more interest accrues; on 30,900 at 6 % the graduated plan costs about 3,900 more than the standard plan over 10 years.

How much does a grace period cost?

For an unsubsidized loan, interest accrues at the simple rate and is capitalized: 30,000 at 6 % accrues 900 in six months, and interest is then charged on 30,900.

Related calculators

Loan Payment Calculator — Level payment on any amortizing loan.
Amortization Schedule Calculator — Year-by-year balance of the standard plan.
Debt Payoff Calculator — Payoff time for a chosen payment.