How a Canadian mortgage payment is calculated
Canadian fixed and variable mortgages compound semi-annually, not in advance. A rate of 4.43% is not 4.43 divided by 12. The monthly rate used to build the payment is a shade higher than that simple split, because of the compounding.
The formula
Let r be the annual rate as a decimal. The equivalent monthly rate is (1 + r / 2) raised to the power of 1/6, minus 1. On a principal P and n monthly payments, the payment is P times i times (1 + i) to the n, divided by (1 + i) to the n minus 1.
At 4.43%, r is 0.0443. Half of that is 0.02215. One plus that, raised to 1/6, minus 1, is the monthly i. Over 300 payments on $500,000, the payment is $2,747.94. At 4.54% the same mortgage is $2,778.49. The gap is $30.55 a month, about $367 a year, for as long as both rates stayed in force. A three-year term is 36 payments, not 300. The comparison is the payment while the rate applies, not the interest over a full 25 years.
| Rate | Payment on $500,000 | Payment on $400,000 |
|---|---|---|
| 3.55% | $2,509.57 | $2,007.65 |
| 3.80% | $2,576.17 | $2,060.94 |
| 4.43% | $2,747.94 | $2,198.35 |
| 4.54% | $2,778.49 | $2,222.79 |
| 6.43% (4.43 plus 2, a qualifying rate) | $3,327.92 | $2,662.34 |
The $400,000 column is balance times 0.8, because the payment scales in a straight line with the balance when the rate and the amortization stay the same. The 6.43% row is the stress-test rate for a 4.43% contract, not a rate you pay. The stress test guide explains why that higher payment is the one in the qualification math.
What people mix up
Amortization is how long the math takes to bring the balance to zero. The term is how long the rate contract lasts. A 25-year amortization with a 3-year term reprices in three years on whatever balance is left. A 30-year amortization, which showed up on one uninsured refinance in the thread, cuts the payment and leaves a larger balance at the end of the term.
Payment frequency changes the schedule. Monthly, semi-monthly, biweekly, and accelerated biweekly are different numbers of payments. Accelerated biweekly is the monthly payment divided by two, paid 26 times, so you pay the equivalent of one extra month a year. A lender's "biweekly" quote is not automatically the accelerated one. Ask which.
Use the calculator on the rate board for a balance that is actually yours. Then request cheaper rates if you want those rates on your file rather than on a $500,000 example.