{
  "id": "mortgage-preapproval",
  "version": "5868444c3865",
  "status": "published",
  "name": "Mortgage Approval Calculator",
  "question": "What mortgage approval can I get?",
  "summary": "Computes the largest mortgage a lender’s housing and total debt-to-income limits allow for your income and debts, and checks whether a loan amount you want fits them.",
  "category": "finance",
  "subcategory": "loans",
  "url": "https://www.acalculator.org/finance/mortgage-preapproval-calculator",
  "markdown": "https://www.acalculator.org/finance/mortgage-preapproval-calculator.md",
  "kind": "function",
  "method": "housing budget = min(front × income ÷ 12, back × income ÷ 12 − debts); largest loan = (budget − other housing costs) ÷ a, with a = r ÷ (1 − (1 + r)^−n), r the rate ÷ 12, and n the months.",
  "assumptions": [
    "Lenders compare payments with gross (before-tax) monthly income; the limits are yours to set.",
    "The rate is fixed; tax, insurance, HOA dues, and mortgage insurance are one monthly amount.",
    "Credit score, cash reserves, residual income, employment, and down payment rules are not checked, so this is an estimate, not a preapproval.",
    "The default rate is an example, not a current market rate."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "income": {
        "title": "Gross income",
        "description": "Your household income before tax and deductions.",
        "type": "number",
        "x-unit": "USD",
        "x-period": "year",
        "exclusiveMinimum": 0,
        "maximum": 100000000
      },
      "debts": {
        "title": "Other debt payments a month",
        "description": "Monthly payments on other debts: car loans, student loans, minimum credit card payments, child support.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 10000000
      },
      "rate": {
        "title": "Interest rate",
        "description": "The fixed yearly mortgage rate. The monthly rate is this ÷ 12.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 30
      },
      "years": {
        "title": "Loan term (years)",
        "description": "The length of the mortgage, for example 30 or 15 years.",
        "type": "integer",
        "minimum": 1,
        "maximum": 40
      },
      "costs": {
        "title": "Tax, insurance, and HOA a month",
        "description": "Property tax, home insurance, HOA dues, and any mortgage insurance, for one month.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000
      },
      "amount": {
        "title": "Loan you want (optional)",
        "description": "A loan amount to check against the limits. Leave it empty to see only the largest loan.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 1000,
        "maximum": 100000000
      },
      "front": {
        "title": "Housing limit (front-end ratio)",
        "description": "The most the housing payment may be, as a percent of gross monthly income.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 1,
        "maximum": 100
      },
      "back": {
        "title": "Total debt limit (back-end ratio)",
        "description": "The most all debt payments, housing included, may be, as a percent of gross monthly income.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 1,
        "maximum": 100
      }
    }
  },
  "outputs": {
    "maxLoan": {
      "label": "Largest loan you may qualify for",
      "description": "The loan whose payment, with the other housing costs, fits both debt-to-income limits.",
      "format": "money"
    },
    "maxPayment": {
      "label": "Principal and interest at that loan",
      "description": "The monthly loan payment on the largest loan.",
      "format": "money"
    },
    "housing": {
      "label": "Housing budget a month",
      "description": "The most the whole housing payment may be under both limits.",
      "format": "money"
    },
    "limit": {
      "label": "Limit",
      "description": "Which debt-to-income limit sets the budget.",
      "format": "text"
    },
    "payment": {
      "label": "Principal and interest on your loan",
      "description": "The monthly payment on the loan you want.",
      "format": "money"
    },
    "frontRatio": {
      "label": "Housing ratio (front-end)",
      "description": "The housing payment on the loan you want (or the largest loan) as a percent of gross monthly income.",
      "format": "percent"
    },
    "backRatio": {
      "label": "Total debt ratio (back-end)",
      "description": "That housing payment plus other debts, as a percent of gross monthly income.",
      "format": "percent"
    },
    "verdict": {
      "label": "Your loan",
      "description": "Whether the loan you want fits both limits.",
      "format": "text"
    },
    "room": {
      "label": "Room below the largest loan",
      "description": "The largest loan minus the loan you want.",
      "format": "money"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "income": 100000,
      "debts": 500,
      "rate": 6.5,
      "years": 30,
      "costs": 500,
      "front": 30,
      "back": 36
    },
    "outputs": {
      "maxLoan": 316421.6390741469,
      "maxPayment": 2000,
      "housing": 2500,
      "limit": "The housing limit (front-end ratio) sets the budget.",
      "frontRatio": 30,
      "backRatio": 36
    },
    "text": "With $100,000.00 of yearly income and $500.00 of other monthly debts, you may qualify for a loan of up to $316,421.64."
  },
  "examples": [
    {
      "given": {
        "income": 100000,
        "debts": 500,
        "rate": 6.5,
        "years": 30,
        "costs": 500,
        "front": 30,
        "back": 36
      },
      "expect": {
        "housing": 2500,
        "maxPayment": 2000,
        "maxLoan": 316421.63907414617,
        "frontRatio": 30,
        "backRatio": 36
      },
      "source": "hand calculation in content.mdx, checked in Python 3 (docs/progress/WP-48/python/preapproval.py)"
    },
    {
      "given": {
        "income": 90000,
        "debts": 900,
        "rate": 7,
        "years": 30,
        "costs": 450,
        "front": 31,
        "back": 43,
        "amount": 350000
      },
      "expect": {
        "housing": 2325,
        "maxLoan": 281826.6899021649,
        "payment": 2328.558733127138,
        "frontRatio": 37.047449775028504,
        "backRatio": 49.047449775028504,
        "verdict": "Over both limits.",
        "room": -68173.31009783508
      },
      "source": "FHA limits of 31% and 43% (HUD Mortgagee Letter 2014-02); hand calculation in content.mdx; Python 3 in docs/progress/WP-48/python/preapproval.py"
    },
    {
      "given": {
        "income": 120000,
        "debts": 2500,
        "rate": 0,
        "years": 30,
        "costs": 400,
        "front": 30,
        "back": 41,
        "amount": 300000
      },
      "expect": {
        "housing": 1600,
        "maxLoan": 432000,
        "payment": 833.3333333333334,
        "backRatio": 37.333333333333336,
        "verdict": "Within both limits.",
        "room": 132000
      },
      "source": "VA limit of 41% (38 CFR 36.4340); hand calculation in content.mdx: at 0%, (1,600 − 400) × 360 = 432,000"
    }
  ],
  "sources": [
    "Fannie Mae Selling Guide B3-6-02, Debt-to-Income Ratios (36% manual, up to 45% with credit score and reserves, 50% for Desktop Underwriter). https://selling-guide.fanniemae.com/sel/b3-6-02/debt-income-ratios",
    "U.S. Department of Housing and Urban Development, Mortgagee Letter 2014-02 (FHA manual underwriting: 31% housing and 43% total without compensating factors). https://www.hud.gov/sites/documents/14-02ml.pdf",
    "38 CFR 36.4340, Underwriting standards (VA: debt-to-income ratio of 41% and residual income). https://www.ecfr.gov/current/title-38/chapter-I/part-36/subpart-B/section-36.4340",
    "Freddie Mac, How much home can I afford? (housing expense ratio ideally less than 30%). https://myhome.freddiemac.com/blog/homebuying/how-much-can-you-afford",
    "Consumer Financial Protection Bureau, What is a debt-to-income ratio? https://www.consumerfinance.gov/ask-cfpb/what-is-a-debt-to-income-ratio-en-1791/"
  ],
  "related": [
    "home-affordability",
    "debt-to-income-ratio",
    "mortgage",
    "fha-loan"
  ],
  "changelog": []
}