Mortgage math

Canadian fixed-rate mortgages don’t compound the way most calculators assume. The rate a lender quotes you is compounded semi-annually, not in advance — twice a year, not monthly — even though you make monthly (or biweekly, or weekly) payments. The calculator follows the same convention, so its numbers line up with the rate on your actual mortgage documents.

Where this comes from

The registry entry the engine cites for this rule (Interest Act, R.S.C. 1985, c. I-15, s. 6) points at the statute behind the convention. It’s not that the law explicitly mandates semi-annual compounding for every blended-payment mortgage. Section 6 of the federal Interest Act is a disclosure rule with teeth: if a mortgage blends principal and interest into one payment (which almost all residential mortgages do), the lender forfeits the right to collect any interest at all unless the mortgage states the rate “calculated yearly or half-yearly, not in advance.” Rather than risk that penalty, Canadian lenders settled on pricing and disclosing fixed-rate mortgages on a half-yearly-not-in-advance basis — which is how “semi-annual compounding” became the universal market convention rather than a line-item legal requirement.

The monthly-rate conversion

Because the quoted annual rate compounds twice a year but payments are usually monthly, the engine converts between the two with the standard formula:

monthlyRate = (1 + annualRate / 2) ^ (1/6) − 1

This is algebraically the same as computing the semi-annual effective rate and then finding the monthly rate that compounds to it twelve times a year. It’s the formula every Canadian amortization calculator (and every lender’s payment quote) uses under the hood, and it’s why plugging a Canadian mortgage rate into a generic (US-style, monthly-compounding) loan calculator gives you a slightly wrong payment.

A deliberate simplification

Real lender amortization schedules round every payment and every period’s interest to the nearest cent, then true up the very last payment so the balance lands exactly at zero. HouseDeltas keeps the unrounded, exact figures throughout the projection instead — it’s simpler to reason about and the difference from a live lender schedule is at most a few cents per period, immaterial at the multi-year horizon this calculator is built for. Variable-rate mortgages (not modeled by the calculator yet) conventionally compound monthly rather than semi-annually, which is a further reason not to assume this formula applies outside the fixed-rate case.