What compounding means on a mortgage
Compounding is how often the lender converts your annual interest rate into actual interest charges. A 5% annual rate could be charged as 5% once a year, 2.5% twice a year, or 0.4167% every month. Each produces a slightly different total, because interest charged earlier in the year starts earning interest of its own sooner.
The more often interest compounds, the more you pay for the same headline rate. That's why the effective annual rate, the rate you actually pay over a full year, is always a little higher than the quoted rate unless interest compounds only once a year.
The Canadian rule
Section 6 of the federal Interest Act requires a mortgage with blended principal-and-interest payments to state its rate calculated "yearly or half-yearly, not in advance." If a mortgage doesn't include that statement, the Act says no interest can be charged on it. Not surprisingly, Canadian lenders comply, and the industry standard for fixed-rate mortgages is semi-annual compounding.
So when your mortgage contract says 5.00% compounded semi-annually, it means the lender charges 2.5% every six months. Over a year, that comes to:
(1 + 0.05 ÷ 2)2 − 1 = 5.0625% effective annual rate
In the United States, mortgages are quoted with monthly compounding. A 5.00% American mortgage charges 5 ÷ 12 = 0.4167% a month, which works out to an effective annual rate of 5.1162%.
| Quoted rate | Effective rate, Canadian | Effective rate, American |
|---|---|---|
| 4.00% | 4.0400% | 4.0742% |
| 5.00% | 5.0625% | 5.1162% |
| 6.00% | 6.0900% | 6.1678% |
What it does to your payment
Because a Canadian mortgage charges a little less interest at the same quoted rate, the payment is a little lower. Here's a $500,000 mortgage amortized over 25 years:
| Rate | Canadian payment | American-method payment | Overstated by (25 yrs) |
|---|---|---|---|
| 4.00% | $2,630.10 | $2,639.18 | $2,725 |
| 5.00% | $2,908.02 | $2,922.95 | $4,478 |
| 6.00% | $3,199.03 | $3,221.51 | $6,742 |
The gap widens as rates rise. It's not a fortune, but it's enough to make a lender's figures look "wrong" when you check them against a generic online calculator, and enough to skew an affordability budget.
How to convert a Canadian rate yourself
To find the interest rate per payment, take the semi-annual rate and spread it across the payments in each six-month period:
rate per payment = (1 + quoted rate ÷ 2)(2 ÷ payments per year) − 1
- Monthly payments: exponent 2/12 = 1/6. At 5.00%, that's 0.41239% per month.
- Bi-weekly payments: exponent 2/26. At 5.00%, that's 0.19012% per payment.
- Weekly payments: exponent 2/52.
Then plug the rate per payment into the standard payment formula, payment = P × i ÷ (1 − (1 + i)−n). In a spreadsheet, that's:
=PMT((1+B1/2)^(1/6)-1, B2*12, -B3)
with the quoted rate in B1 (as a decimal), the amortization in years in B2, and the mortgage amount in B3.
Decoder ring: "not in advance"
Interest "in advance" would mean charging a period's interest at the start of that period, before you've had the money for that time. The Interest Act rules it out. Your interest is always calculated on what you've owed over the period that has just passed.
Where semi-annual compounding doesn't apply
- Variable-rate mortgages often compound monthly. Your contract states the method. Because the rate floats with prime, the compounding difference is usually swamped by rate changes anyway.
- Lines of credit and HELOCs generally charge simple interest calculated daily and charged monthly.
- Reverse mortgages follow the lender's contract. The compounding matters a great deal here, because no payments are made and interest keeps compounding on interest. See the reverse mortgage calculator.
Why it's worth knowing
You can't change how your mortgage compounds. What you can do is check the numbers you're given. If a lender's payment doesn't match your own math, you now know the first thing to check. And if you're comparing a Canadian lender's quote with figures from an American website, you'll know why they don't line up.
Every calculator on this site uses semi-annual compounding. Start with the payment calculator.