{
  "id": "canadian-mortgage",
  "version": "6b943de3456f",
  "status": "published",
  "name": "Canadian Mortgage Calculator",
  "question": "Semi-annual compounding mortgage",
  "summary": "Computes a Canadian mortgage payment with interest compounded twice a year, for monthly, biweekly, weekly and accelerated payments, with the minimum down payment, the time to pay off and the total interest.",
  "category": "finance",
  "subcategory": "loans",
  "url": "https://www.acalculator.org/finance/canadian-mortgage-calculator",
  "markdown": "https://www.acalculator.org/finance/canadian-mortgage-calculator.md",
  "kind": "function",
  "method": "monthly payment = L × i ÷ (1 − (1 + i)^−n), i = (1 + j ÷ 2)^(1/6) − 1, n = years × 12; other payments from the monthly one as FCAC defines them; each payment pays interest at (1 + j ÷ 2)^(2/p) − 1 for p payments a year, and the rest lowers the balance until it is paid off.",
  "assumptions": [
    "The rate is fixed and compounds twice a year, not in advance, as most fixed-rate Canadian mortgages state; variable-rate mortgages may compound monthly.",
    "Payments are at the end of each period; the last payment is whatever is left. Nothing is rounded between payments.",
    "The term (often 5 years) is not modelled: the rate stays the same for the whole amortization.",
    "Property tax, home insurance and provincial sales tax on the premium are not included."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "price": {
        "title": "Home price (CAD)",
        "description": "The purchase price of the home, in Canadian dollars.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 10000,
        "maximum": 100000000
      },
      "down": {
        "title": "Down payment (CAD)",
        "description": "The cash you put down. FCAC sets a minimum: 5% of the first $500,000 and 10% of the rest.",
        "type": "number",
        "x-unit": "USD",
        "minimum": 0,
        "maximum": 100000000
      },
      "rate": {
        "title": "Interest rate",
        "description": "The yearly rate, compounded twice a year (semi-annually, not in advance) as on a fixed-rate mortgage.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 25
      },
      "years": {
        "title": "Amortization (years)",
        "description": "The years to pay off the mortgage at the monthly payment, often 25 (30 at most).",
        "type": "integer",
        "minimum": 1,
        "maximum": 30
      },
      "freq": {
        "title": "Payment frequency",
        "description": "How often you pay. Accelerated payments pay off the mortgage sooner.",
        "type": "string",
        "enum": [
          "monthly",
          "semimonthly",
          "biweekly",
          "weekly",
          "acc-biweekly",
          "acc-weekly"
        ]
      },
      "premium": {
        "title": "Mortgage loan insurance premium",
        "description": "Usually needed when the down payment is under 20%. Type the premium your lender quotes as a percent of the loan; it is added to the mortgage.",
        "type": "number",
        "x-unit": "percent",
        "minimum": 0,
        "maximum": 10
      }
    }
  },
  "outputs": {
    "payment": {
      "label": "Your payment",
      "description": "The payment at the frequency you chose.",
      "format": "money"
    },
    "monthly": {
      "label": "Monthly payment",
      "description": "The payment that repays the mortgage over the amortization, paid monthly.",
      "format": "money"
    },
    "loan": {
      "label": "Mortgage amount",
      "description": "Price − down payment + insurance premium.",
      "format": "money"
    },
    "insurance": {
      "label": "Insurance premium",
      "description": "Premium percent × (price − down payment).",
      "format": "money"
    },
    "minDown": {
      "label": "Minimum down payment",
      "description": "5% of the first $500,000 and 10% of the rest, or 20% from $1.5 million.",
      "format": "money"
    },
    "count": {
      "label": "Number of payments",
      "description": "Payments until the mortgage is paid off.",
      "format": "integer"
    },
    "paidOff": {
      "label": "Years to pay off",
      "description": "Number of payments ÷ payments a year.",
      "format": "number"
    },
    "interest": {
      "label": "Total interest",
      "description": "All the interest over the life of the mortgage.",
      "format": "money"
    },
    "total": {
      "label": "Total of payments",
      "description": "Mortgage amount + total interest.",
      "format": "money"
    },
    "effective": {
      "label": "Effective yearly rate",
      "description": "(1 + rate ÷ 2)² − 1: the rate with the twice-a-year compounding counted.",
      "format": "percent"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "price": 600000,
      "down": 120000,
      "rate": 4.5,
      "years": 25,
      "freq": "monthly",
      "premium": 0
    },
    "outputs": {
      "payment": 2656.6701805703674,
      "monthly": 2656.6701805703674,
      "loan": 480000,
      "insurance": 0,
      "minDown": 35000,
      "count": 300,
      "paidOff": 25,
      "interest": 317001.05417111027,
      "total": 797001.0541711103,
      "effective": 4.550625
    },
    "text": "You pay $2,656.67 each payment, 300 payments in 25 years, with $317,001.05 of interest in total."
  },
  "examples": [
    {
      "given": {
        "price": 600000,
        "down": 120000,
        "rate": 4.5,
        "years": 25,
        "freq": "monthly",
        "premium": 0
      },
      "expect": {
        "monthly": 2656.670180570345,
        "count": 300,
        "interest": 317001.05417110387,
        "effective": 4.550624999999986
      },
      "source": "hand calculation in content.mdx: monthly rate (1 + 0.045 ÷ 2)^(1/6) − 1; Justice Laws Website, Interest Act (R.S.C., 1985, c. I-15), section 6: a blended-payment mortgage states the rate calculated yearly or half-yearly, not in advance, https://laws-lois.justice.gc.ca/eng/acts/I-15/section-6.html (retrieved 2026-10-05)"
    },
    {
      "given": {
        "price": 600000,
        "down": 120000,
        "rate": 4.5,
        "years": 25,
        "freq": "acc-biweekly",
        "premium": 0
      },
      "expect": {
        "payment": 1328.3350902851726,
        "count": 564,
        "paidOff": 21.692307692307693,
        "interest": 268926.0022439411
      },
      "source": "hand calculation in content.mdx; Financial Consumer Agency of Canada, Choosing a mortgage that is right for you: payment frequency (semi-monthly = monthly ÷ 2, biweekly = monthly × 12 ÷ 26, weekly = monthly × 12 ÷ 52, accelerated biweekly = monthly ÷ 2, accelerated weekly = monthly ÷ 4), https://www.canada.ca/en/financial-consumer-agency/services/mortgages/choose-mortgage.html (retrieved 2026-10-05)"
    },
    {
      "given": {
        "price": 700000,
        "down": 45000,
        "rate": 5,
        "years": 30,
        "freq": "biweekly",
        "premium": 4
      },
      "expect": {
        "minDown": 45000,
        "insurance": 26200,
        "loan": 681200,
        "monthly": 3635.5009040452424,
        "payment": 1677.9234941747272,
        "count": 779,
        "interest": 624259.1098585214
      },
      "source": "hand calculation in content.mdx; Financial Consumer Agency of Canada, How much you need for a down payment (5% of the first $500,000, 10% of the part above, 20% from $1.5 million), https://www.canada.ca/en/financial-consumer-agency/services/mortgages/down-payment.html (retrieved 2026-10-05); Financial Consumer Agency of Canada, Choosing a mortgage that is right for you: payment frequency (semi-monthly = monthly ÷ 2, biweekly = monthly × 12 ÷ 26, weekly = monthly × 12 ÷ 52, accelerated biweekly = monthly ÷ 2, accelerated weekly = monthly ÷ 4), https://www.canada.ca/en/financial-consumer-agency/services/mortgages/choose-mortgage.html (retrieved 2026-10-05)"
    },
    {
      "given": {
        "price": 400000,
        "down": 100000,
        "rate": 0,
        "years": 25,
        "freq": "monthly",
        "premium": 0
      },
      "expect": {
        "monthly": 1000,
        "interest": 0,
        "count": 300
      },
      "source": "hand calculation in content.mdx: at 0%, 300,000 ÷ 300 months"
    }
  ],
  "sources": [
    "Justice Laws Website, Interest Act (R.S.C., 1985, c. I-15), section 6. https://laws-lois.justice.gc.ca/eng/acts/I-15/section-6.html (retrieved 2026-10-05)",
    "Financial Consumer Agency of Canada, Choosing a mortgage that is right for you. https://www.canada.ca/en/financial-consumer-agency/services/mortgages/choose-mortgage.html (retrieved 2026-10-05)",
    "Financial Consumer Agency of Canada, How much you need for a down payment. https://www.canada.ca/en/financial-consumer-agency/services/mortgages/down-payment.html (retrieved 2026-10-05)",
    "Financial Consumer Agency of Canada, Mortgage terms and amortization. https://www.canada.ca/en/financial-consumer-agency/services/mortgages/mortgage-terms-amortization.html (retrieved 2026-10-05)"
  ],
  "related": [
    "mortgage",
    "mortgage-comparison",
    "mortgage-payoff",
    "amortization"
  ],
  "changelog": []
}