# 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.

- Calculator id: `student-loan` · Category: Finance (`finance`) · Tool name: `calculate_student_loan_payment`
- Canonical page: https://tttkmbb.com/finance/student-loan · This document: https://tttkmbb.com/finance/student-loan.md · JSON definition: https://tttkmbb.com/finance/student-loan.json

## Purpose

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.

**Use when:** 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).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `balance` | number |  | required | Principal owed when the grace period starts (or today if repayment has begun). (> 0, max 100000000) |
| `annual_rate_percent` | number | % | required | Fixed annual rate in percent. (min 0, max 100) |
| `term_years` | number | years | optional, default 10 | Length of repayment in years (10 for federal Standard and Graduated plans; up to 25–30 for extended plans). (> 0, max 30) |
| `grace_months` | integer | months | optional, default 0 | Months before the first payment (6 for federal Direct loans). (min 0, max 36) |
| `interest_accrues_during_grace` | boolean |  | optional, 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 |  | optional, default "standard" | Standard: equal monthly payments. Graduated: payments step up every 24 months, the last step no more than 3× the first. |

## Output

| Field | Type | Unit | 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). |

## 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.

## Data Sources

- Federal Student Aid – Repayment plans (Standard and Graduated) — https://studentaid.gov/manage-loans/repayment/plans (government, retrieved 2026-09-24)
- Federal Student Aid – Interest rates and how interest is calculated and capitalized — https://studentaid.gov/understand-aid/types/loans/interest-rates (government, retrieved 2026-09-24)
- Wikipedia – Amortization calculator (annuity payment formula) — https://en.wikipedia.org/wiki/Amortization_calculator (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/student-loan?balance=…&annual_rate_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/student-loan` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/student-loan · OpenAPI operationId `calculate_student_loan_payment` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "student-loan", "inputs": {…}}`

## Example

- 30,000 at 6 % over 10 years, standard: inputs `{"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: inputs `{"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
```

## Limitations

The loan is income-driven (IBR, PAYE, SAVE), variable-rate, or you know the payment and want the payoff time (use debt-payoff). 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. All values are computed from the formula above; no measurement or live data is involved.

## 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

- [Loan Payment Calculator](https://tttkmbb.com/finance/loan-payment.md) — Level payment on any amortizing loan.
- [Amortization Schedule Calculator](https://tttkmbb.com/finance/amortization-schedule.md) — Year-by-year balance of the standard plan.
- [Debt Payoff Calculator](https://tttkmbb.com/finance/debt-payoff.md) — Payoff time for a chosen payment.