# Semi-annual compounding mortgage

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.

- Page: https://www.acalculator.org/finance/canadian-mortgage-calculator
- JSON spec: https://www.acalculator.org/finance/canadian-mortgage-calculator.json
- Version: 6b943de3456f

## Default answer

Example with the default inputs (Home price (CAD) $600,000.00, Down payment (CAD) $120,000.00, Interest rate 4.5%, Amortization (years) 25, Payment frequency Monthly, Mortgage loan insurance premium 0%): You pay $2,656.67 each payment, 300 payments in 25 years, with $317,001.05 of interest in total.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| price | Home price (CAD) | The purchase price of the home, in Canadian dollars. |
| down | Down payment (CAD) | The cash you put down. FCAC sets a minimum: 5% of the first $500,000 and 10% of the rest. |
| rate | Interest rate | The yearly rate, compounded twice a year (semi-annually, not in advance) as on a fixed-rate mortgage. |
| years | Amortization (years) | The years to pay off the mortgage at the monthly payment, often 25 (30 at most). |
| freq | Payment frequency | How often you pay. Accelerated payments pay off the mortgage sooner. |
| premium | Mortgage loan insurance premium | 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. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| payment | Your payment | The payment at the frequency you chose. |
| monthly | Monthly payment | The payment that repays the mortgage over the amortization, paid monthly. |
| loan | Mortgage amount | Price − down payment + insurance premium. |
| insurance | Insurance premium | Premium percent × (price − down payment). |
| minDown | Minimum down payment | 5% of the first $500,000 and 10% of the rest, or 20% from $1.5 million. |
| count | Number of payments | Payments until the mortgage is paid off. |
| paidOff | Years to pay off | Number of payments ÷ payments a year. |
| interest | Total interest | All the interest over the life of the mortgage. |
| total | Total of payments | Mortgage amount + total interest. |
| effective | Effective yearly rate | (1 + rate ÷ 2)² − 1: the rate with the twice-a-year compounding counted. |

## 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.

## Worked examples

1. price = $600,000.00, down = $120,000.00, rate = 4.5%, years = 25, freq = monthly, premium = 0% gives monthly = $2,656.67, count = 300, interest = $317,001.05, effective = 4.550625%. Source: 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).
2. price = $600,000.00, down = $120,000.00, rate = 4.5%, years = 25, freq = acc-biweekly, premium = 0% gives payment = $1,328.34, count = 564, paidOff = 21.692308, interest = $268,926.00. Source: 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).
3. price = $700,000.00, down = $45,000.00, rate = 5%, years = 30, freq = biweekly, premium = 4% gives minDown = $45,000.00, insurance = $26,200.00, loan = $681,200.00, monthly = $3,635.50, payment = $1,677.92, count = 779, interest = $624,259.11. Source: 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).
4. price = $400,000.00, down = $100,000.00, rate = 0%, years = 25, freq = monthly, premium = 0% gives monthly = $1,000.00, interest = $0.00, count = 300.

## FAQ

### Why are Canadian mortgage payments different from US ones?

The Interest Act requires a blended-payment mortgage to state its rate calculated yearly or half-yearly, not in advance, and fixed-rate mortgages compound twice a year. A 4.5% rate is then 4.5506% a year, and the monthly rate is (1.0225)^(1/6) − 1, a little less than 4.5% ÷ 12.

### How are biweekly and accelerated payments worked out?

As FCAC defines them, from the monthly payment: semi-monthly = monthly ÷ 2; biweekly = monthly × 12 ÷ 26; weekly = monthly × 12 ÷ 52; accelerated biweekly = monthly ÷ 2; accelerated weekly = monthly ÷ 4.

### How much faster do accelerated payments pay off a mortgage?

They add about one monthly payment a year. On $480,000 at 4.5% over 25 years, accelerated biweekly payments of $1,328.34 pay off the mortgage in about 21.7 years and save about $48,000 of interest.

### What is the minimum down payment in Canada?

5% of the first $500,000 of the price and 10% of the part above it; from $1.5 million, 20% of the price. On $700,000 it is $25,000 + $20,000 = $45,000.

### When do I need mortgage loan insurance?

Usually when your down payment is less than 20% of the price. The premium is a percent of the loan, set by the insurer, and is usually added to the mortgage. Type the premium your lender quotes.

### How long can the amortization be?

With less than 20% down, at most 30 years for a first-time buyer or a new build and 25 years otherwise. With 20% or more, your lender sets the maximum.

## 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)