An RBC mortgage ad in a newspaper drew my attention. It offered a 3-year mortgage at 2.99% and a 7-year mortgage at 3.59%. However, what really caught my eye were some percentages in large font in the fine print. It turns out the advertised rates assume a $250 processing fee, and the actual rates when this fee is accounted for are higher than the advertised rates.
The fine print says that the advertised rates are “based on a $200,000 mortgage and a mortgage processing fee of $250.” The fine print goes on to say that the 3-year 2.99% offer is really 3.04%, and the 7-year 3.59% offer is really 3.61%. To RBC’s credit, the real rates were in a huge font compared to the rest of the fine print. However, it would be better if they just advertise the real rates in the first place.
Being a math guy I wondered how RBC came up with the real rates. I used a spreadsheet to try one method that matches RBC’s numbers, so it may be how they did it. For starters, I assumed a 25-year mortgage.
A $200,250 mortgage amortized over 25 years at 2.99% gives a payment of $946.65 per month. The mortgage balance after 3 years is $183,298.88. The next step was to find the interest rate that makes a $200,000 mortgage with the same payments end up with the same mortgage balance after 3 years. The result was 3.036%, which rounds to the 3.04% in RBC’s fine print. Repeating this process for the 7-year mortgage gave an interest rate of 3.613%, which rounds to the rate in the fine print.
But why stop here? Why not bake in a $10,000 fee? Then the advertised rates can be 1.25% for 3 years and 2.74% for 7 years. I suspect RBC’s response to this is that the $250 fee represents a real cost they have for processing a mortgage. However, baking in a processing fee just makes it harder for Canadians to properly compare mortgage rates.