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.

I'm confused, is the actual rate 3.036%, or is that the effective rate with the fixed fee?

ReplyDeleteIf you had a $500,000 mortgage, would the $250 fee make the effective rate something like 3.00%, or would they charge you 3.04% as the real rate?

If so, then adding big fees to tweak the advertised rate would work against them for larger mortgages...

@Potato: Depending on your point of view, it is either

ReplyDelete1) A $200,000 mortgage at 3.036% for 3 years, or

2) A $200,250 mortgage at 2.99% for 3 years, but they only give you $200,000 because of the fee.

You're right that the difference in rates would have been smaller if the mortgage size were bigger.

I had noticed something similar with some car manufacturers' websites: To get their advertised financing rate (e.g., 0.99%) you lose a cash incentive (often $1500). So the effective interest rate was higher. But the last time I put together a car quote, they also listed the effective rate ("Informational APR") underneath. It makes a huge difference, I put together a generic Toyota and the advertised rate was 0.9% but actual rate was 5.7%. Their note says including that rate is a government requirement.

ReplyDelete@Lewin: I wasn't aware of this governement requirement -- thanks for the information. You're right that the situation with car financing is similar. I think the next step should be to require that APRs be fully compounded yearly rates instead of the current nonsense with either semi-annual or monthly compounding.

DeleteWhen companies change to be more transparent, I always assume that new regulations forced them to ;)

DeleteSo if you're evaluating a loan from a car dealership and one from your bank, should you be using the dealers "informational APR" so that you're comparing apples to apples? A line of credit uses simple interest instead of front-loaded...assume that makes the LOC an even more attractive option?

ReplyDelete@Geoff: Every line of credit I've ever seen uses compound interest. They calculate the interest rate as though it were simple interest and then compound it anyway to make the true interest rate higher than advertised. As for loans from a car dealership, I'm no expert on any games they might play with interest rates. However, if they mention an APR in fine print that is higher than the advertised rate, you can bet that the true rate is at least as high as the APR.

Delete