Semi-annual compounding, explained

Section 6 of the Interest Act requires a mortgage repayable by blended payments to state the rate calculated yearly or half-yearly, not in advance. Canadian lenders settled on half-yearly, and the effect is that a rate quoted as 4.5% is compounded twice a year rather than once per payment.

That makes the nominal rate and the effective rate different numbers. Interest is converted to a per-payment rate by taking the semi-annual growth and spreading it across the payments in the period — so the monthly rate on a 4.5% mortgage is not 4.5% divided by twelve. It is slightly less, and it is less every single month for twenty-five years.

Variable-rate mortgages follow the same convention, which surprises people who assume it applies only to fixed terms.

United States mortgages compound monthly, matching the payment. Every calculator built to that assumption divides the annual rate by twelve, and produces a payment that is too high for a Canadian mortgage on the same inputs. The error is small per payment and it never stops.

It also runs in one direction. A tool that assumes monthly compounding always overstates the Canadian payment, never understates it — so a shopper checking affordability against an American calculator concludes they can borrow less than they can. Which is the safer error of the two, and still the wrong number.

The first is the effective annual rate. Because the rate compounds twice, the amount actually earned over a year is slightly more than the quoted figure — a nominal 4.5% grows to about 4.55% effective. That is the opposite direction from the payment effect and it confuses people badly: the semi-annual basis makes your monthly rate lower and your annual rate higher than dividing and multiplying would suggest. Both are consequences of the same conversion, and the quoted rate is the nominal one in every Canadian disclosure.

The second is accelerated payments. An accelerated bi-weekly payment is not a compounding effect at all — it is half of a monthly payment made twenty-six times instead of twenty-four, so you make roughly one extra monthly payment a year and the principal falls faster. The two get conflated constantly because both are described as "paying less interest", but one is a rule about how interest is converted and the other is a decision to pay more money.

A useful test: the compounding basis changes what a given payment costs you, and accelerating changes how much you pay. If a claim about saving interest would still be true when you pay exactly the contractual amount, it is about compounding. If it needs you to pay more, it is not.