{
  "id": "land-loan",
  "version": "19aa66a09812",
  "status": "published",
  "name": "Land Loan Calculator",
  "question": "What will my land loan cost?",
  "summary": "Computes the payment, total interest, and yearly schedule of a fixed-rate land loan paid monthly, quarterly, twice a year, or yearly, with property tax, insurance, and extra payments.",
  "category": "finance",
  "subcategory": "mortgage-and-real-estate",
  "url": "https://www.acalculator.org/finance/land-loan-calculator",
  "markdown": "https://www.acalculator.org/finance/land-loan-calculator.md",
  "kind": "schedule",
  "method": "payment = L × r ÷ (1 − (1 + r)^−n), with L the price minus the down payment, r the APR ÷ payments per year, and n the years × payments per year; each payment, interest = balance × r and the rest lowers the balance.",
  "assumptions": [
    "The rate is fixed for the whole loan and interest is charged each payment period at APR ÷ payments per year.",
    "Payments are made at the end of each period.",
    "Property tax and insurance are yearly amounts split evenly over the year’s payments. They do not change the loan.",
    "A monthly extra amount is spread evenly over the year’s payments (three months’ worth with each quarterly payment).",
    "Extra payments go straight to the balance; the last payment is whatever is left.",
    "Values are not rounded to the cent between payments; only the display is rounded."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "price": {
        "title": "Purchase price",
        "description": "The price of the land.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 100000000
      },
      "down": {
        "title": "Down payment (%)",
        "description": "The share of the price you pay up front, as a percent. It lowers the amount you borrow.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 100
      },
      "rate": {
        "title": "Interest rate (APR)",
        "description": "The yearly interest rate. The rate per payment is this divided by the payments per year.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 50
      },
      "years": {
        "title": "Length of loan (years)",
        "description": "The number of years over which the loan is repaid, from 1 to 40.",
        "type": "integer",
        "minimum": 1,
        "maximum": 40
      },
      "freq": {
        "title": "Payments",
        "description": "How often you pay: 12, 4, 2, or 1 times a year.",
        "type": "string",
        "enum": [
          "monthly",
          "quarterly",
          "semi-annually",
          "annually"
        ]
      },
      "taxes": {
        "title": "Property tax per year",
        "description": "The yearly property tax, split evenly over the year’s payments.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 10000000
      },
      "insurance": {
        "title": "Insurance per year",
        "description": "The yearly property insurance, split evenly over the year’s payments.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 10000000
      },
      "extra": {
        "title": "Extra payment",
        "description": "An extra amount that goes straight to the balance, paid monthly, yearly, or once.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 10000000
      },
      "extraWhen": {
        "title": "Extra paid",
        "description": "Every month (spread evenly over the payments), once a year, or once, starting at the payment below.",
        "type": "string",
        "enum": [
          "monthly",
          "yearly",
          "one-time"
        ]
      },
      "extraFrom": {
        "title": "Starting with payment number",
        "description": "The payment the extra starts with (or is paid with, when paid once), counting from 1.",
        "type": "integer",
        "minimum": 1,
        "maximum": 480
      }
    }
  },
  "outputs": {
    "payment": {
      "label": "Your payment (principal and interest)",
      "description": "The level payment each period that repays the loan over its length, without extra payments.",
      "format": "money"
    },
    "total": {
      "label": "Payment with tax and insurance",
      "description": "The principal and interest payment plus the property tax and insurance split over the year’s payments.",
      "format": "money"
    },
    "payments": {
      "label": "Number of payments",
      "description": "How many payments it takes to repay the loan, with any extra payments.",
      "format": "integer"
    },
    "time": {
      "label": "Time to pay off",
      "description": "How long the payments last, in years and months, with any extra payments.",
      "format": "duration"
    },
    "amount": {
      "label": "Loan",
      "description": "The amount borrowed: the price minus the down payment.",
      "format": "money"
    },
    "downAmount": {
      "label": "Down payment",
      "description": "The down payment in dollars.",
      "format": "money"
    },
    "interest": {
      "label": "Interest",
      "description": "All the interest paid over the life of the loan.",
      "format": "money"
    },
    "paid": {
      "label": "Total you’ll repay",
      "description": "The amount borrowed plus all the interest.",
      "format": "money"
    },
    "saved": {
      "label": "Interest saved by paying extra",
      "description": "The interest the extra payments save, compared with no extra payments.",
      "format": "money"
    },
    "sooner": {
      "label": "Payments saved by paying extra",
      "description": "How many fewer payments it takes with the extra payments.",
      "format": "integer"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "price": 100000,
      "down": 20,
      "rate": 5.5,
      "years": 15,
      "freq": "monthly",
      "taxes": 1200,
      "insurance": 600,
      "extra": 0,
      "extraWhen": "monthly",
      "extraFrom": 1
    },
    "outputs": {
      "payment": 653.6667636969115,
      "total": 803.6667636969115,
      "payments": 180,
      "time": {
        "years": 15,
        "months": 0
      },
      "amount": 80000,
      "downAmount": 20000,
      "interest": 37660.017465444,
      "paid": 117660.01746544399
    },
    "text": "Borrowing $80,000.00 at 5.5% APR over 15 years costs $653.67 per payment (Monthly); it is paid off in 15 years, with $37,660.02 of interest in total."
  },
  "examples": [
    {
      "given": {
        "price": 250000,
        "down": 20,
        "rate": 7.25,
        "years": 20,
        "freq": "monthly",
        "taxes": 3000,
        "insurance": 1200
      },
      "expect": {
        "amount": 200000,
        "payment": 1580.7519698353462,
        "total": 1930.7519698353462,
        "interest": 179380.47276048682,
        "payments": 240
      },
      "source": "hand calculation in content.mdx, checked in Python (docs/progress/WP-21/python/land_loan.py); Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/"
    },
    {
      "given": {
        "price": 100000,
        "down": 20,
        "rate": 5.5,
        "years": 15,
        "freq": "monthly",
        "taxes": 1200,
        "insurance": 600
      },
      "expect": {
        "amount": 80000,
        "payment": 653.6667636969069,
        "total": 803.6667636969069,
        "interest": 37660.017465444565,
        "payments": 180
      },
      "source": "hand calculation in content.mdx, checked in Python (docs/progress/WP-21/python/land_loan.py); Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/"
    },
    {
      "given": {
        "price": 100000,
        "down": 20,
        "rate": 5.5,
        "years": 15,
        "freq": "quarterly",
        "taxes": 1200,
        "insurance": 600
      },
      "expect": {
        "payment": 1966.761687705791,
        "total": 2416.761687705791,
        "interest": 38005.70126234685,
        "payments": 60
      },
      "source": "hand calculation in content.mdx, checked in Python (docs/progress/WP-21/python/land_loan.py); Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/"
    },
    {
      "given": {
        "price": 100000,
        "down": 20,
        "rate": 5.5,
        "years": 15,
        "freq": "annually",
        "taxes": 0,
        "insurance": 0
      },
      "expect": {
        "payment": 7970.0478083849,
        "total": 7970.0478083849,
        "interest": 39550.717125773386,
        "payments": 15
      },
      "source": "hand calculation in content.mdx, checked in Python (docs/progress/WP-21/python/land_loan.py); Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/"
    },
    {
      "given": {
        "price": 100000,
        "down": 20,
        "rate": 5.5,
        "years": 15,
        "freq": "monthly",
        "extra": 10000,
        "extraWhen": "one-time",
        "extraFrom": 12
      },
      "expect": {
        "payments": 150,
        "interest": 27536.57763032143,
        "saved": 10123.439835121804,
        "sooner": 30
      },
      "source": "hand calculation in content.mdx, checked month by month in Python (docs/progress/WP-21/python/land_loan.py); Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/"
    },
    {
      "given": {
        "price": 100000,
        "down": 20,
        "rate": 5.5,
        "years": 15,
        "freq": "quarterly",
        "extra": 200,
        "extraWhen": "monthly"
      },
      "expect": {
        "payments": 41,
        "interest": 25177.22996952063,
        "saved": 12828.471292826827,
        "sooner": 19
      },
      "source": "hand calculation in content.mdx, checked payment by payment in Python (docs/progress/WP-21/python/land_loan.py); Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/"
    }
  ],
  "sources": [
    "Amortized loan payment (annuity) formula: S. A. Broverman, Mathematics of Investment and Credit, chapter 3 (loan payment and amortization schedule).",
    "Consumer Financial Protection Bureau, What are (discount) points and lender credits and how do they work? https://www.consumerfinance.gov/ask-cfpb/what-are-discount-points-and-lender-credits-and-how-do-they-work-en-136/",
    "Consumer Financial Protection Bureau, What is a balloon payment? When is one allowed? https://www.consumerfinance.gov/ask-cfpb/what-is-a-balloon-payment-when-is-one-allowed-en-104/",
    "Consumer Financial Protection Bureau, What is an escrow or impound account? https://www.consumerfinance.gov/ask-cfpb/what-is-an-escrow-or-impound-account-en-140/"
  ],
  "related": [
    "boat-loan",
    "rv-loan",
    "auto-loan"
  ],
  "changelog": [
    {
      "date": "2026-09-29",
      "note": "Worked examples name a published reference for their rule."
    },
    {
      "date": "2026-10-01",
      "note": "The answer says when the loan is paid off with any extra payments (“12 years, 2 months”)."
    }
  ]
}