Why Canadian mortgage calculators disagree with each other

Put the same numbers into three mortgage calculators and you will often get three answers. They are not rounding differently. Two of them are almost certainly using the American convention, and on a $500,000 mortgage that is about $15 a month you were not expecting.

The one line that differs

A mortgage payment is the same formula everywhere. What changes between countries is the monthly interest rate the formula is fed, and that comes from how often interest is compounded.

The penalty for getting the disclosure wrong is that the lender collects no interest at all, so lenders are careful about it. The Act allows yearly or half-yearly, and Canadian lenders settled on half-yearly for fixed rate mortgages. That is where semi-annual compounding comes from: not a formula somebody preferred, but the wording of a statute from a century ago.

American mortgages compound monthly. So an American calculator divides the annual rate by twelve, which is the obvious thing to do and the wrong thing here. The Canadian monthly rate is the rate that, compounded six times, equals half the annual rate.

American   monthly rate  =  0.05 / 12               =  0.00416667
Canadian   monthly rate  =  (1 + 0.05/2)^(1/6) - 1  =  0.00412392

Both then use the same payment formula:
payment  =  principal x rate / (1 - (1 + rate)^-periods)

What the difference is worth

Small rates compound into numbers that are not small. On $500,000 over 25 years at 5%:

How to tell which one you are using

• Put in $500,000, 5%, 25 years, monthly payments. If it says about $2,923 it is American. If it says about $2,908 it is Canadian.
• Look for the word semi-annual anywhere on the page. Canadian tools usually say so, because it is the thing that makes them Canadian.
• Check the domain. A .com calculator with no mention of provinces, CMHC or a 25 year amortisation is written for an American mortgage.

The exceptions

Semi-annual compounding is the rule for fixed rate mortgages. Variable rate mortgages and most home equity lines of credit compound monthly, which is the same convention American fixed mortgages use. So a calculator being American is not always wrong: it is wrong for the product most Canadians have.

While you are checking the arithmetic

Two other things separate a Canadian mortgage calculator from an American one, and both change the answer more than compounding does.

And accelerated payments, which are close to free money and almost never modelled by a foreign tool. An accelerated bi-weekly payment is simply your monthly payment halved and paid 26 times a year, so you make the equivalent of thirteen monthly payments instead of twelve. On the $500,000 example that takes three and a half years off the amortisation and saves more than $60,000 in interest, without changing anything about the mortgage itself.