The analysis isn't quite as simple as comparing fixed vs variable rates and taking a SWAG at what the bank prime rate will do in the future. The principal paydown on a mortgage varies over time (increasing with time), so a more precise analysis of fixed vs variable will look at the total cost (P + I) paid in various scenarios over a period of time.

To help understand the problem, I created a spreadsheet to analyze the cost differences between a fixed rate loan and several variable rate scenarios over a 5-year term. Five years is the typical term for a fixed-rate, closed mortgage so it makes sense to use that as the baseline comparison. I then modeled 3 different scenarios of rising interest rates: a low rate of 0.5% annual increase in the prime rate, an average rate of about 0.75% and a high rate of 1.25% increase. Obviously, there's no need to model flat or declining interest rates, since in those cases, the variable rate will always be cheaper.

Some additional assumptions/parameters of the analysis:

- 25 year amortization
- Bank Prime rate of 2.25% (this is actually irrelevant as all other rates are relative to this)
- Fixed borrowing rate at P + 2% (more on this later)
- Variable rates at prime
- Variables rising at 0.5%, 0.75% and 1.25% annually
- Prime moves up quarterly each year
- Variable loan payments increase with each prime rate change
- Costs calculated per $1000 borrowed

This graph shows the total (P +I) expense over a five year period, comparing a fixed rate with the three rising rate scenarios above:

So we see that in this case, only the highest rising rate ever costs more over the 5 year period. Comparing the costs on a percentage basis, that's even more obvious:

I also modeled a couple other scenarios:

1) What if prime moved up even faster? Here's the analysis for annual increases of 0.75%, 1.0%, 1.5%:

Very similar to the first one. In this case, the highest increasing rate starts to cost more in the 3rd year of the loan, and the middle increase only costs more in the last year. Again, the percentage difference in total cumulative cost:

2) What annual rate of increase is required to exactly equal the cost of a fixed rate loan? Solving backward for this, we find that it's at about 0.825% annual increase for the 5 year term.

Percentage difference is (by definition of the solution) zero.

So the big takeaway here is this: Given a typical spread of 2% between fixed and variable rates, interest rates

*, before a fixed rate mortgage starts to cost less than a variable rate loan. Even in a climate of rising interest rates, if the annual interest rate increase is less than 0.83%,*

**must increase at greater than 0.83% per year, every year for five years***. That works out to a total increase of 4.25% in 5 years. So the question you want to ask is how likely is it that prime will increase by that much?*

**the variable rate loan is the better deal**Another point to keep in mind is that in all scenarios, we're assuming the same prime +2% spread for the fixed rate, which is about the BEST available right in Canada now. This chart shows that some banks are currently quoting as high as prime + 4%! At that cost, prime would have to move steadily to over 10% in the next 5 years (+2% annual increase in prime) before a variable loan would cost more.

The spreadsheet I used to make this calculation is available in Google Docs for you to view or copy as you wish. If you choose to publish the spreadsheet elsewhere, I would appreciate an attribution. Thanks.

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