# Loan Payment Calculator

> Computes the level monthly payment of a fully amortizing fixed-rate loan from principal, annual rate and term, plus the total paid and total interest over the life of the loan.

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

## Purpose

Computes the level monthly payment of a fully amortizing fixed-rate loan from principal, annual rate and term, plus the total paid and total interest over the life of the loan.

**Use when:** You need the monthly payment or total interest cost of an auto, personal, student or other fixed-rate installment loan given its amount, APR and term.

**Do not use when:** You need property tax, insurance and HOA in the payment (use mortgage-payment), or you know the payment and want the payoff time (use debt-payoff).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `principal` | number |  | required | Amount borrowed. (> 0, max 1000000000000) |
| `annual_rate_percent` | number | % | required | Nominal annual rate in percent; the monthly rate is this / 12. 0 is allowed for interest-free loans. (min 0, max 100) |
| `term_years` | number | years | optional | Loan term in years; fractional values allowed. Added to term_months when both are given. (min 0, max 100) |
| `term_months` | integer | months | optional, default 0 | Additional months of term (e.g. term_months=60 alone for a 5-year auto loan). (min 0, max 1200) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `monthly_payment` | number |  | Level payment due each month (principal + interest). |
| `number_of_payments` | integer |  | Total months = 12 × term_years + term_months. |
| `total_payment` | number |  | monthly_payment × number_of_payments (unrounded payment). |
| `total_interest` | number |  | total_payment − principal. |
| `payoff_summary` | string |  | Plain-language summary of the schedule. |

## Formula

`i = annual_rate_percent / 1200; n = 12·term_years + term_months; monthly_payment = principal × i / (1 − (1 + i)^−n); if i = 0, monthly_payment = principal / n. total_payment = monthly_payment × n; total_interest = total_payment − principal.`

Standard annuity (amortization) formula with monthly compounding and payments at the end of each month, as used for US fixed-rate consumer loans. Lenders round the payment to cents and adjust the final payment, so real totals can differ by a few cents.

## Data Sources

- Wikipedia – Amortization calculator (annuity payment formula) — https://en.wikipedia.org/wiki/Amortization_calculator (reference, retrieved 2026-09-23)
- Investopedia – Amortization: Definition, Formula and Example — https://www.investopedia.com/terms/a/amortization.asp (reference, retrieved 2026-09-23)

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/loan-payment?principal=…&annual_rate_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/loan-payment` 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/loan-payment · OpenAPI operationId `calculate_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: `calculate_loan_payment` (dedicated) or `run_calculator` with `{"calculator_id": "loan-payment", "inputs": {…}}`

## Example

- 200,000 at 6 % for 30 years: inputs `{"principal":200000,"annual_rate_percent":6,"term_years":30}` → `{"monthly_payment":1199.1,"number_of_payments":360,"total_payment":431676.38,"total_interest":231676.38}`
- 25,000 auto loan at 7 % for 60 months: inputs `{"principal":25000,"annual_rate_percent":7,"term_months":60}` → `{"monthly_payment":495.03,"number_of_payments":60,"total_payment":29701.8,"total_interest":4701.8}`

```
GET https://tttkmbb.com/api/v1/calculate/loan-payment?principal=200000&annual_rate_percent=6&term_years=30
```

## Limitations

You need property tax, insurance and HOA in the payment (use mortgage-payment), or you know the payment and want the payoff time (use debt-payoff). Standard annuity (amortization) formula with monthly compounding and payments at the end of each month, as used for US fixed-rate consumer loans. Lenders round the payment to cents and adjust the final payment, so real totals can differ by a few cents. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Is the APR the same as the interest rate used here?**

The formula uses the note rate divided by 12. A lender's disclosed APR also folds in fees, so if you enter the APR the payment will be slightly overstated when fees are large.

**What if the rate is 0 %?**

The annuity formula divides by zero, so the calculator returns principal / number_of_payments instead (e.g. 12,000 over 12 months = 1,000 per month).

**How do I model extra payments?**

This calculator assumes the fixed schedule only. Use debt-payoff with the higher payment to see the shortened payoff time and interest saved.

## Related

- [Mortgage Payment Calculator](https://tttkmbb.com/finance/mortgage-payment.md) — Same amortization plus taxes, insurance and HOA for a home purchase.
- [Debt Payoff Calculator](https://tttkmbb.com/finance/debt-payoff.md) — Given a payment, find how long a balance takes to clear.
- [APY Calculator](https://tttkmbb.com/finance/apy.md) — Effective annual cost of a nominal rate with monthly compounding.