Canadian Mortgage Math: Semi-Annual Compounding
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Canadian Mortgage Math: Semi-Annual Compounding
Canadian mortgage semi-annual compounding is the rule that fixed-rate mortgages are compounded semi-annually, not in advance — so a “6%” mortgage is not 6% ÷ 12 a month. You first convert the posted rate to an effective monthly rate, then compute the payment. US formulas (which compound monthly) get this wrong, and so do students who divide by 12.
How are Canadian mortgage rates compounded?
By law, a Canadian fixed mortgage rate is a nominal annual rate compounded semi-annually. To find the monthly payment you convert that to the equivalent monthly rate — the rate that compounds to the same amount over a year.
Step 1: convert the rate (6% example)
Semi-annual periodic rate = 6% ÷ 2 = 3% per half-year.
Effective annual rate (EAR) = (1.03)2 − 1 = 6.09%.
Equivalent monthly rate = (1.03)1/6 − 1 ≈ 0.4939% per month — not 0.5%.
That third step is the whole game: the true monthly rate is 0.4939%, slightly below the 0.5000% you’d get by naively dividing 6% by 12.
Step 2: the monthly payment
On a $500,000 mortgage amortized over 25 years (300 months):
| Method | Monthly rate | Payment |
|---|---|---|
| Correct (semi-annual) | 0.4939% | ≈ $3,199 |
| Wrong (6% ÷ 12) | 0.5000% | ≈ $3,222 |
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Frequently asked questions
How are Canadian mortgage rates compounded?
Fixed-rate mortgages are compounded semi-annually, not monthly — so you convert the posted rate to an effective monthly rate before computing payments.
Why isn’t a 6% mortgage 0.5% a month?
Because 6% compounds twice a year, the equivalent monthly rate is (1.03)^(1/6) − 1 ≈ 0.4939%, slightly less than 6% ÷ 12.
What’s the EAR on a 6% Canadian mortgage?
(1.03)² − 1 = 6.09%. That’s the true annual cost once semi-annual compounding is counted.
Do variable-rate mortgages work the same way?
Variable rates are often compounded monthly, so always check the compounding basis — it changes the conversion.
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