{
  "id": "mortgage",
  "version": "5b53603d993f",
  "status": "published",
  "name": "Mortgage Calculator",
  "question": "What will my mortgage payment be?",
  "summary": "Computes the monthly mortgage payment with property tax, insurance, HOA dues, and mortgage insurance for conventional, FHA, and VA loans, with the full amortization schedule.",
  "category": "finance",
  "subcategory": "loans",
  "url": "https://www.acalculator.org/finance/mortgage-calculator",
  "markdown": "https://www.acalculator.org/finance/mortgage-calculator.md",
  "kind": "schedule",
  "method": "principal and interest = L × r ÷ (1 − (1 + r)^−n), with L the loan, r the rate ÷ 12, and n the months; tax, insurance, HOA dues, and mortgage insurance are added.",
  "assumptions": [
    "The rate is fixed, interest is charged monthly at the rate ÷ 12, and the first payment is one month after the start.",
    "PMI is a yearly percent of the loan, charged while the balance is above 78% of the price and never after mid-term.",
    "FHA premiums follow HUD Mortgagee Letter 2023-05; FHA and VA upfront fees are added to the loan.",
    "Tax, insurance, and HOA dues stay the same, and nothing is rounded between months."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "price": {
        "title": "Home price",
        "description": "The price of the home.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 1000,
        "maximum": 1000000000
      },
      "down": {
        "title": "Down payment",
        "description": "The cash you pay toward the price. The loan is the price minus this.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 1000000000
      },
      "rate": {
        "title": "Interest rate",
        "description": "The fixed yearly 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
      },
      "type": {
        "title": "Loan type",
        "description": "Conventional, FHA, or VA.",
        "type": "string",
        "enum": [
          "conventional",
          "fha",
          "va"
        ]
      },
      "pmi": {
        "title": "PMI rate (per year)",
        "description": "Private mortgage insurance per year, as a percent of the loan, charged under 20% down.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 5
      },
      "use": {
        "title": "VA loan benefit",
        "description": "First or later use of the VA home loan benefit, or exempt from the funding fee.",
        "type": "string",
        "enum": [
          "first",
          "subsequent",
          "exempt"
        ]
      },
      "tax": {
        "title": "Property tax (per year)",
        "description": "The yearly property tax as a percent of the home price.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 10
      },
      "insurance": {
        "title": "Home insurance",
        "description": "The homeowners insurance premium.",
        "type": "number",
        "x-unit": "USD",
        "x-period": "year",
        "minimum": 0,
        "maximum": 1000000
      },
      "hoa": {
        "title": "HOA dues",
        "description": "Homeowners association or condo dues.",
        "type": "number",
        "x-unit": "USD",
        "x-period": "month",
        "minimum": 0,
        "maximum": 100000
      },
      "extra": {
        "title": "Extra each month",
        "description": "An extra amount paid toward principal with every payment.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 10000000
      },
      "start": {
        "title": "Loan start date",
        "description": "The day the loan starts. The first payment is one month later.",
        "type": "string",
        "format": "date"
      }
    }
  },
  "outputs": {
    "monthly": {
      "label": "Monthly payment",
      "description": "The first month’s total: principal, interest, tax, insurance, mortgage insurance, and HOA dues.",
      "format": "money"
    },
    "pi": {
      "label": "Principal and interest",
      "description": "The level monthly payment on the loan.",
      "format": "money"
    },
    "taxes": {
      "label": "Property tax",
      "description": "The property tax for one month.",
      "format": "money"
    },
    "insurance": {
      "label": "Home insurance",
      "description": "The home insurance for one month.",
      "format": "money"
    },
    "mi": {
      "label": "Mortgage insurance",
      "description": "PMI or the FHA annual premium in the first month.",
      "format": "money"
    },
    "hoa": {
      "label": "HOA dues",
      "description": "The HOA dues for one month.",
      "format": "money"
    },
    "loan": {
      "label": "Loan amount",
      "description": "The price minus the down payment, plus any financed FHA or VA fee.",
      "format": "money"
    },
    "upfront": {
      "label": "Upfront fee added to the loan",
      "description": "The FHA upfront premium or VA funding fee, added to the loan.",
      "format": "money"
    },
    "ltv": {
      "label": "Loan-to-value",
      "description": "The price minus the down payment, as a percent of the price.",
      "format": "percent"
    },
    "interest": {
      "label": "Total interest",
      "description": "All the interest over the life of the loan.",
      "format": "money"
    },
    "miTotal": {
      "label": "Total mortgage insurance",
      "description": "All the PMI or FHA annual premium paid.",
      "format": "money"
    },
    "miMonths": {
      "label": "Months of mortgage insurance",
      "description": "How many monthly payments include PMI or the FHA annual premium.",
      "format": "integer"
    },
    "payoff": {
      "label": "Paid off in",
      "description": "The month of the last payment, when a start date is given.",
      "format": "month-year"
    },
    "total": {
      "label": "Total cost",
      "description": "The down payment plus everything paid over the loan.",
      "format": "money"
    },
    "saved": {
      "label": "Interest saved by paying extra",
      "description": "The interest the extra monthly amount saves.",
      "format": "money"
    },
    "sooner": {
      "label": "Months saved by paying extra",
      "description": "How many fewer payments the extra monthly amount takes.",
      "format": "integer"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "price": 400000,
      "down": 80000,
      "rate": 6.5,
      "years": 30,
      "type": "conventional",
      "pmi": 0.5,
      "use": "first",
      "tax": 1.1,
      "insurance": 1800,
      "hoa": 0,
      "extra": 0,
      "start": "2026-09-29"
    },
    "outputs": {
      "monthly": 2539.2843418441507,
      "pi": 2022.6176751774838,
      "taxes": 366.66666666666674,
      "insurance": 150,
      "mi": 0,
      "hoa": 0,
      "loan": 320000,
      "ltv": 80,
      "interest": 408142.36306389567,
      "miTotal": 0,
      "miMonths": 0,
      "payoff": "2056-09-29",
      "total": 994142.3630638942
    },
    "text": "A $320,000.00 mortgage at 6.5% over 30 years costs $2,539.28 a month, of which $2,022.62 is principal and interest."
  },
  "examples": [
    {
      "given": {
        "price": 400000,
        "down": 80000,
        "rate": 6.5,
        "years": 30,
        "type": "conventional",
        "pmi": 0.5,
        "tax": 1.1,
        "insurance": 1800
      },
      "expect": {
        "pi": 2022.6176751774892,
        "monthly": 2539.284341844156,
        "mi": 0,
        "interest": 408142.3630638906,
        "total": 994142.3630638908
      },
      "source": "hand calculation in content.mdx"
    },
    {
      "given": {
        "price": 300000,
        "down": 30000,
        "rate": 7,
        "years": 30,
        "type": "conventional",
        "pmi": 0.5
      },
      "expect": {
        "pi": 1796.3167369837922,
        "mi": 112.5,
        "miMonths": 115,
        "miTotal": 12937.5
      },
      "source": "hand calculation in content.mdx"
    },
    {
      "given": {
        "price": 300000,
        "down": 10500,
        "rate": 6.25,
        "years": 30,
        "type": "fha"
      },
      "expect": {
        "upfront": 5066.25,
        "loan": 294566.25,
        "mi": 131.98289166042298,
        "pi": 1813.6950679010142,
        "miMonths": 360
      },
      "source": "hand calculation in content.mdx"
    },
    {
      "given": {
        "price": 350000,
        "down": 0,
        "rate": 6,
        "years": 30,
        "type": "va",
        "use": "first"
      },
      "expect": {
        "upfront": 7525,
        "loan": 357525,
        "mi": 0,
        "pi": 2143.5430150523944
      },
      "source": "hand calculation in content.mdx"
    },
    {
      "given": {
        "price": 400000,
        "down": 80000,
        "rate": 6.5,
        "years": 30,
        "type": "conventional",
        "pmi": 0.5,
        "extra": 300
      },
      "expect": {
        "interest": 269696.46043795766,
        "saved": 138445.9026259384,
        "sooner": 106
      },
      "source": "hand calculation in content.mdx"
    }
  ],
  "sources": [
    "Consumer Financial Protection Bureau, When can I remove private mortgage insurance (PMI) from my loan? https://www.consumerfinance.gov/ask-cfpb/when-can-i-remove-private-mortgage-insurance-pmi-from-my-loan-en-202/",
    "Freddie Mac, Breaking down PMI. https://myhome.freddiemac.com/buying/breaking-down-pmi",
    "U.S. Department of Housing and Urban Development, Mortgagee Letter 2023-05, Reduction of FHA Annual Mortgage Insurance Premium Rates (February 22, 2023). https://www.hud.gov/sites/dfiles/OCHCO/documents/2023-05hsgml.pdf",
    "U.S. Department of Housing and Urban Development, Monthly (Periodic) Mortgage Insurance Premium Calculation. https://www.hud.gov/hud-partners/housing-premium-calculation",
    "U.S. Department of Housing and Urban Development, What is the minimum down payment requirement for FHA? https://answers.hud.gov/FHA/s/article/What-is-the-minimum-down-payment-requirement-for-FHA",
    "U.S. Department of Veterans Affairs, VA funding fee and loan closing costs. https://www.va.gov/housing-assistance/home-loans/funding-fee-and-closing-costs/",
    "Amortized loan payment (annuity) formula: S. A. Broverman, Mathematics of Investment and Credit, chapter 3."
  ],
  "related": [
    "amortization",
    "mortgage-payoff",
    "mortgage-recast",
    "home-equity-loan"
  ],
  "changelog": []
}