{
  "id": "mortgage-interest",
  "version": "3506cbb49d23",
  "status": "published",
  "name": "Mortgage Interest Calculator",
  "question": "What is my total mortgage interest?",
  "summary": "Computes the total interest on a fixed-rate mortgage, the interest in the first payment and the first year, the interest paid each year, and the interest an extra monthly payment saves.",
  "category": "finance",
  "subcategory": "loans",
  "url": "https://www.acalculator.org/finance/mortgage-interest-calculator",
  "markdown": "https://www.acalculator.org/finance/mortgage-interest-calculator.md",
  "kind": "schedule",
  "method": "payment = L × r ÷ (1 − (1 + r)^−n), with L the loan, r the rate ÷ 12, and n the months; each month, interest = balance × r and the rest of the payment lowers the balance; total interest is the sum.",
  "assumptions": [
    "The rate is fixed and interest is charged monthly at the yearly rate ÷ 12.",
    "The first payment is one month after the start date; the last payment clears the balance.",
    "Nothing is rounded to the cent between months; only the display is rounded.",
    "Property tax, insurance, mortgage insurance, and fees are not included."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "amount": {
        "title": "Loan amount",
        "description": "The amount borrowed: the home price minus the down payment.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 1000,
        "maximum": 100000000
      },
      "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
      },
      "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": {
    "interest": {
      "label": "Total interest",
      "description": "All the interest paid over the life of the loan.",
      "format": "money"
    },
    "payment": {
      "label": "Monthly payment",
      "description": "The level principal and interest payment, before any extra.",
      "format": "money"
    },
    "firstMonth": {
      "label": "Interest in the first payment",
      "description": "The loan amount × the rate ÷ 12.",
      "format": "money"
    },
    "firstYear": {
      "label": "Interest in the first year",
      "description": "The interest in the first 12 payments.",
      "format": "money"
    },
    "share": {
      "label": "Interest share of all payments",
      "description": "Total interest as a percent of everything paid.",
      "format": "percent"
    },
    "principal": {
      "label": "Principal repaid",
      "description": "The loan amount, repaid in full.",
      "format": "money"
    },
    "total": {
      "label": "Total paid",
      "description": "The loan amount plus all the interest.",
      "format": "money"
    },
    "payoff": {
      "label": "Paid off in",
      "description": "The month of the last payment, when a start date is given.",
      "format": "month-year"
    },
    "saved": {
      "label": "Interest saved by paying extra",
      "description": "The interest without the extra payment minus the interest with it.",
      "format": "money"
    },
    "sooner": {
      "label": "Months saved by paying extra",
      "description": "How many fewer payments the extra monthly amount takes.",
      "format": "integer"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "amount": 320000,
      "rate": 6.5,
      "years": 30,
      "extra": 0,
      "start": "2026-09-30"
    },
    "outputs": {
      "interest": 408142.36306389567,
      "payment": 2022.6176751774838,
      "firstMonth": 1733.3333333333335,
      "firstYear": 20694.690601457856,
      "share": 56.052550128590795,
      "principal": 320000,
      "total": 728142.3630638956,
      "payoff": "2056-09-30"
    },
    "text": "A $320,000.00 mortgage at 6.5% over 30 years charges $408,142.36 of interest in total."
  },
  "examples": [
    {
      "given": {
        "amount": 320000,
        "rate": 6.5,
        "years": 30
      },
      "expect": {
        "payment": 2022.6176751774892,
        "interest": 408142.3630638906,
        "firstMonth": 1733.3333333333335,
        "firstYear": 20694.690601457853,
        "total": 728142.3630638906
      },
      "source": "CFPB, How does paying down a mortgage work? (interest on the balance each month); hand calculation in content.mdx, checked in Python 3 (docs/progress/WP-48/python/mortgage_interest.py)"
    },
    {
      "given": {
        "amount": 320000,
        "rate": 6.5,
        "years": 15
      },
      "expect": {
        "payment": 2787.54356895157,
        "interest": 181757.84241127857
      },
      "source": "hand calculation in content.mdx, checked in Python 3 (docs/progress/WP-48/python/mortgage_interest.py)"
    },
    {
      "given": {
        "amount": 120000,
        "rate": 0,
        "years": 10
      },
      "expect": {
        "payment": 1000,
        "interest": 0,
        "share": 0,
        "firstYear": 0
      },
      "source": "hand calculation in content.mdx: at 0% the payment is 120,000 ÷ 120 and no interest is charged"
    },
    {
      "given": {
        "amount": 320000,
        "rate": 6.5,
        "years": 30,
        "extra": 300
      },
      "expect": {
        "interest": 269696.46043795766,
        "saved": 138445.90262593294,
        "sooner": 106
      },
      "source": "hand calculation in content.mdx, checked in Python 3 (docs/progress/WP-48/python/mortgage_interest.py)"
    }
  ],
  "sources": [
    "Consumer Financial Protection Bureau, How does paying down a mortgage work? https://www.consumerfinance.gov/ask-cfpb/how-does-paying-down-a-mortgage-work-en-1943/",
    "Consumer Financial Protection Bureau, What is a prepayment penalty? https://www.consumerfinance.gov/ask-cfpb/what-is-a-prepayment-penalty-en-1957/",
    "IRS Publication 936, Home Mortgage Interest Deduction ($750,000 limit). https://www.irs.gov/publications/p936",
    "Amortized loan payment (annuity) formula: S. A. Broverman, Mathematics of Investment and Credit, chapter 3."
  ],
  "related": [
    "mortgage",
    "amortization",
    "mortgage-payoff",
    "interest-only-mortgage"
  ],
  "changelog": []
}