# Debt Payoff Calculator

> Computes how many months a fixed monthly payment takes to clear a balance charged a given APR with monthly compounding, plus the total interest paid and the size of the final payment.

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

## Purpose

Computes how many months a fixed monthly payment takes to clear a balance charged a given APR with monthly compounding, plus the total interest paid and the size of the final payment.

**Use when:** You know a credit-card, loan or other balance, its APR and what you can pay each month, and want the payoff date and interest cost.

**Do not use when:** You know the term and need the required payment (use loan-payment), or the payment is a percentage of the balance that shrinks over time (minimum-payment schedules).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `balance` | number |  | required | Amount owed today. (> 0, max 1000000000000) |
| `annual_rate_percent` | number | % | required | Annual percentage rate in percent; interest accrues monthly at APR / 12. (min 0, max 200) |
| `monthly_payment` | number |  | required | Fixed amount paid at the end of each month. Must exceed the first month's interest (balance × APR / 1200). (> 0, max 1000000000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `months_to_payoff` | integer | months | Number of monthly payments including the smaller final one. |
| `payoff_time` | string |  | months_to_payoff expressed in years and months. |
| `months_to_payoff_exact` | number | months | −ln(1 − i·balance/payment) / ln(1 + i), the unrounded annuity solution. |
| `total_paid` | number |  | balance + total_interest. |
| `total_interest` | number |  | Sum of the monthly interest charges until payoff. |
| `final_payment` | number |  | The last, usually smaller, payment that clears the balance. |
| `first_month_interest` | number |  | balance × APR / 1200, the minimum a payment must exceed. |

## Formula

`i = annual_rate_percent / 1200. Each month: interest = balance × i; balance = balance + interest − payment (last payment = remaining balance + interest). Closed form: months = −ln(1 − i × balance / monthly_payment) / ln(1 + i), rounded up.`

Month-by-month simulation with interest charged on the remaining balance and the payment applied at month end, matching the standard amortization formula; no fees, rate changes or new charges are assumed.

## Data Sources

- Federal Reserve – Credit Card Repayment Calculator — https://www.federalreserve.gov/creditcardcalculator/ (government, retrieved 2026-09-23)
- CFPB – Credit cards: paying down balances — https://www.consumerfinance.gov/consumer-tools/credit-cards/ (government, retrieved 2026-09-23)
- Wikipedia – Amortization calculator (annuity payment formula) — https://en.wikipedia.org/wiki/Amortization_calculator (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/debt-payoff?balance=…&annual_rate_percent=…&monthly_payment=…`
- `POST https://tttkmbb.com/api/v1/calculate/debt-payoff` 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/debt-payoff · OpenAPI operationId `calculate_debt_payoff` 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": "debt-payoff", "inputs": {…}}`

## Example

- 5,000 at 18 % APR, 200 per month: inputs `{"balance":5000,"annual_rate_percent":18,"monthly_payment":200}` → `{"months_to_payoff":32,"payoff_time":"2 years 8 months","months_to_payoff_exact":31.57,"total_paid":6313.96,"total_interest":1313.96,"final_payment":113.96,"first_month_interest":75}`
- 2,000 at 24 % APR, 50 per month: inputs `{"balance":2000,"annual_rate_percent":24,"monthly_payment":50}` → `{"months_to_payoff":82,"payoff_time":"6 years 10 months","total_interest":2063.8,"first_month_interest":40}`

```
GET https://tttkmbb.com/api/v1/calculate/debt-payoff?balance=5000&annual_rate_percent=18&monthly_payment=200
```

## Limitations

You know the term and need the required payment (use loan-payment), or the payment is a percentage of the balance that shrinks over time (minimum-payment schedules). Month-by-month simulation with interest charged on the remaining balance and the payment applied at month end, matching the standard amortization formula; no fees, rate changes or new charges are assumed. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What happens if my payment is too small?**

If the payment does not exceed the first month's interest the balance never falls; the calculator returns an error stating the minimum payment and a payment that clears the debt in 5 years.

**How much does paying extra help?**

Re-run with the higher payment: on 5,000 at 18 %, raising the payment from 200 to 300 cuts the time from 32 to 20 months and the interest from about 1,314 to about 800.

## Related

- [Loan Payment Calculator](https://tttkmbb.com/finance/loan-payment.md) — Find the payment for a chosen term instead.
- [Mortgage Payment Calculator](https://tttkmbb.com/finance/mortgage-payment.md) — Full housing payment for a home loan.
- [Rule of 72 Calculator](https://tttkmbb.com/finance/rule-of-72.md) — How fast an unpaid balance doubles at this APR.