# Canada Student Loan vs. BMO Line of Credit

We have a BMO line of credit and a Canada Student Loan. The interest rate is prime (5.0%) on the former and prime + 2.5% on the latter (7.5%). You would think that it would make sense to put everything in the much cheaper line of credit, but this is the first year that we have started to pay down either, and I knew that we received a federal and provincial tax credit on interest payments for the more expensive prime + 2.5% student loan so I figured it probably worked out to be about even, and besides, our student loan is a lot smaller than the line of credit (although not significantly close to \$0 yet to not worry about it). Without looking at the actual numbers, I had no idea. It’s one of things that no one can tell you the answer to (except maybe your accountant if you have one) and there is usually no universally true answer either. Anyways, I finally crunched the numbers and here’s what I got:

The annual interest owed in one year on the line of credit is Q(1+p), where Q is the amount drawn from the line of credit and p is the prime rate. The interest owned on the loan is Q(1+p+0.025), where Q is the amount owed of the student loan. But with the interest payment tax credit, the effective annual interest payment is reduced to Q(1+p+0.025) – Q(p+0.025)0.2105 = Q(1.0197+0.79p), where 21.05% is the tax credit rate, including the federal rate and provincial rate for BC.

So the loan is worse when Q(1.0197+0.79p) > Q(1+p). Re-arranging yields, p < 0.09 or "the loan is worse than the line of credit when p < 9%” Since the prime rate is currently at 5% at BMO, it looks like we are better off paying down the Canada Student Loan using funds from the line of credit. This will not only save us some money every year but will give us one less monthly payment to worry about and simplify our debt into one amortization plan. Simple is always better.

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