How this calculator works
Enter the mortgage amount, the annual interest rate and the amortization in years, then choose how often you pay. Canadian mortgages must state interest calculated half-yearly, not in advance, under section 6 of the Interest Act, so the annual rate is compounded twice a year. A monthly payment uses the monthly rate that is equivalent to that semi-annual compounding, and the bi-weekly and weekly payments use the rate equivalent to 26 and 52 periods a year. A regular bi-weekly or weekly schedule keeps the same amortization, so its payment is smaller than half or a quarter of the monthly payment. An accelerated bi-weekly schedule instead pays half the monthly amount every two weeks, which produces 26 half-payments a year, the equivalent of 13 monthly payments, and pays the mortgage off sooner. The comparison line shows the monthly payment if the same annual rate were compounded monthly, as a US mortgage typically is. Out of scope: mortgage default insurance, property tax, heating and other costs, prepayment privileges and penalties, a variable or changing rate, and any fee added to the balance. The result assumes one rate for the whole amortization and payments at the end of each period.
Formula
Semi-annual rate = annual rate / 2. Periodic rate i = (1 + annual rate / 2)^(2 / payments per year) - 1. Payment = P x i / (1 - (1 + i)^(-N)), where N is the number of payments. Accelerated bi-weekly = monthly payment / 2, with each payment applied to the balance until it reaches zero. US monthly payment = P x (annual rate / 12) / (1 - (1 + annual rate / 12)^(-300)) over 25 years.
Worked example
A $500,000 mortgage at 5% over 25 years has a semi-annual rate of 2.5%. The monthly rate is (1.025)^(1/6) - 1, or 0.4124%, giving a payment of $2,908.02 and total interest of $372,407.48. Compounded monthly instead, the rate is 5% / 12, or 0.4167%, and the payment is $2,922.95, which is $14.93 more a month. Accelerated bi-weekly pays $1,454.01 every two weeks and clears the mortgage in about 21.5 years.
Frequently asked questions
Why is Canadian mortgage interest compounded semi-annually?
Section 6 of the federal Interest Act requires a mortgage rate to be stated calculated yearly or half-yearly, not in advance. Lenders therefore convert the stated annual rate to the payment frequency from a semi-annual base, which produces a lower effective annual rate than monthly compounding at the same nominal rate.
How is accelerated bi-weekly different from ordinary bi-weekly?
Ordinary bi-weekly spreads the same amortization over 26 payments a year, so each payment is slightly less than half a monthly payment. Accelerated bi-weekly pays exactly half the monthly payment every two weeks, adding one extra monthly payment a year and shortening the amortization.
Does the payment include mortgage insurance or property tax?
No. It covers principal and interest only. CMHC or other default insurance, property tax, heating and condo fees are separate, and a lender may collect property tax through the payment.
Why is the US payment higher?
A US mortgage usually compounds the nominal rate monthly, while a Canadian mortgage compounds it semi-annually. At the same stated rate, monthly compounding produces a slightly higher effective rate, so the payment is a little higher over the same amortization.