# Mortgage Affordability Calculator

> Applies the front-end (housing) and back-end (total debt) debt-to-income limits to gross income, subtracts taxes and insurance to get the affordable principal-and-interest payment, and converts it into a maximum loan amount and home price for the given rate and term.

- Calculator id: `mortgage-affordability` · Category: Investing & Real Estate (`investing`) · Tool name: `calculate_mortgage_affordability`
- Canonical page: https://tttkmbb.com/investing/mortgage-affordability · This document: https://tttkmbb.com/investing/mortgage-affordability.md · JSON definition: https://tttkmbb.com/investing/mortgage-affordability.json

## Purpose

Applies the front-end (housing) and back-end (total debt) debt-to-income limits to gross income, subtracts taxes and insurance to get the affordable principal-and-interest payment, and converts it into a maximum loan amount and home price for the given rate and term.

**Use when:** You want to know how much house or mortgage an income supports under standard lender ratios, before applying for a loan.

**Do not use when:** You already have a loan amount and want its payment (use mortgage-payment) or want to check ratios for an existing payment (use debt-to-income). Lender rules vary; informational only, not financial advice.

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `annual_gross_income` | number |  | required | Household income before taxes, per year. (> 0, max 1000000000) |
| `monthly_debt_payments` | number |  | optional, default 0 | Minimum payments on car loans, student loans, credit cards and other debts (excluding the new housing payment). (min 0, max 10000000) |
| `down_payment` | number |  | optional, default 0 | Cash available for the down payment; added to the loan to get the home price. (min 0, max 10000000000) |
| `interest_rate_percent` | number | % per year | required | Annual mortgage rate; the monthly rate is rate/12. (min 0, max 30) |
| `term_years` | number | years | optional, default 30 | Amortization period in years. (min 1, max 40) |
| `front_end_ratio_percent` | number | % | optional, default 28 | Maximum housing payment (principal, interest, taxes, insurance) as a percent of gross monthly income. (min 1, max 100) |
| `back_end_ratio_percent` | number | % | optional, default 36 | Maximum total debt payments including housing as a percent of gross monthly income. (min 1, max 100) |
| `monthly_taxes_insurance` | number |  | optional, default 0 | Property tax, homeowner's insurance, HOA and mortgage insurance per month, which count toward the housing payment. (min 0, max 1000000) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `front_end_limit` | number |  | monthly income × front_end_ratio. |
| `back_end_limit` | number |  | monthly income × back_end_ratio − monthly_debt_payments. |
| `max_monthly_housing_payment` | number |  | The lower of the two limits (PITI). |
| `limiting_ratio` | string |  | Which ratio sets the limit. |
| `max_principal_and_interest` | number |  | max_monthly_housing_payment − monthly_taxes_insurance. |
| `max_loan_amount` | number |  | P&I × (1 − (1 + i)^−n) / i with i = rate/12 and n = term × 12. |
| `max_home_price` | number |  | max_loan_amount + down_payment. |
| `income_multiple` | number |  | max_loan_amount / annual_gross_income. |

## Formula

`monthly_income = annual_gross_income / 12; housing = min(monthly_income × front_end/100, monthly_income × back_end/100 − monthly_debt_payments); P&I = housing − monthly_taxes_insurance; max_loan = P&I × (1 − (1 + r/12)^−(12·term)) / (r/12); max_price = max_loan + down_payment`

Classic 28/36 qualifying ratios (front-end housing, back-end total debt) as used in conventional US underwriting; actual approvals also depend on credit score, reserves, loan program and the appraisal. Informational mathematics only; not financial advice.

## Data Sources

- CFPB – What is a debt-to-income ratio? — https://www.consumerfinance.gov/ask-cfpb/what-is-a-debt-to-income-ratio-en-1791/ (government, retrieved 2026-09-24)
- Fannie Mae Selling Guide B3-6-02 – Debt-to-Income Ratios (36 % maximum for manual underwriting) — https://selling-guide.fanniemae.com/sel/b3-6-02/debt-income-ratios (standard, 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/mortgage-affordability?annual_gross_income=…&interest_rate_percent=…`
- `POST https://tttkmbb.com/api/v1/calculate/mortgage-affordability` 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/mortgage-affordability · OpenAPI operationId `calculate_mortgage_affordability` 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": "mortgage-affordability", "inputs": {…}}`

## Example

- 90,000 income, 500 debts, 50,000 down, 6 %, 30 years, 300 taxes/insurance: inputs `{"annual_gross_income":90000,"monthly_debt_payments":500,"down_payment":50000,"interest_rate_percent":6,"term_years":30,"monthly_taxes_insurance":300}` → `{"front_end_limit":2100,"back_end_limit":2200,"max_monthly_housing_payment":2100,"limiting_ratio":"Front-end ratio (28 % of gross income)","max_principal_and_interest":1800,"max_loan_amount":300224.91,"max_home_price":350224.91,"income_multiple":3.34}`
- 120,000 income, 1,200 debts, 80,000 down, 5.5 %, 25 years, 450 taxes/insurance: inputs `{"annual_gross_income":120000,"monthly_debt_payments":1200,"down_payment":80000,"interest_rate_percent":5.5,"term_years":25,"monthly_taxes_insurance":450}` → `{"front_end_limit":2800,"back_end_limit":2400,"max_monthly_housing_payment":2400,"limiting_ratio":"Back-end ratio (36 % of gross income minus other debts)","max_principal_and_interest":1950,"max_loan_amount":317544.33,"max_home_price":397544.33}`

```
GET https://tttkmbb.com/api/v1/calculate/mortgage-affordability?annual_gross_income=90000&monthly_debt_payments=500&down_payment=50000&interest_rate_percent=6&term_years=30&monthly_taxes_insurance=300
```

## Limitations

You already have a loan amount and want its payment (use mortgage-payment) or want to check ratios for an existing payment (use debt-to-income). Lender rules vary; informational only, not financial advice. Classic 28/36 qualifying ratios (front-end housing, back-end total debt) as used in conventional US underwriting; actual approvals also depend on credit score, reserves, loan program and the appraisal. Informational mathematics only; not financial advice. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Where do 28 and 36 come from?**

They are the traditional conventional-mortgage guidelines: housing costs up to 28 % of gross income and all debt up to 36 %. Fannie Mae allows up to 36 % (45 % with compensating factors) for manually underwritten loans and up to 50 % through automated underwriting.

**Is the result what a lender will approve?**

No. It is the payment the ratios allow; lenders also weigh credit history, employment, cash reserves and the property, and some use different ratios.

## Related

- [Mortgage Payment Calculator](https://tttkmbb.com/finance/mortgage-payment.md) — Full payment for a chosen loan amount.
- [Debt-to-Income Ratio Calculator](https://tttkmbb.com/finance/debt-to-income.md) — Check the ratios for an existing payment.
- [Loan Payment Calculator](https://tttkmbb.com/finance/loan-payment.md) — Level payment on any amortizing loan.