[SOLVED] Answering this question occupies dozens of

Answering this question occupies dozens of financial commentaries as the March 1 RRSP contribution deadline approaches each year. Many financial institutions and mutual fund companies promote the idea of arranging an “RRSP loan” to obtain money for an RRSP contribution. They sometimes present a scenario giving the impression that borrowing to contribute to an RRSP is so advantageous it is virtually a “no-brainer.” The conventional wisdom among financial planners seems to be that it is a good idea with two qualifications—the tax refund from the RRSP contribution should be applied to paying down the loan, and the loan should be paid off within a year. However, as often happens in financial analyses of even moderate complexity, the thinking is usually muddled and flawed.
In this case study, we will identify the key variable(s) for answering the question in the heading. We will discover that the decision (based strictly on financial considerations) turns on a single criterion. Here is the scenario. Suppose your marginal tax rate is 40%. Consequently, if you contribute $1000 to an RRSP, your taxable income will be reduced by $1000 and your income tax will be reduced by $400 (40% of $1000). To obtain the money for a $1000 RRSP contribution, you borrow $1000 at 6% compounded monthly and immediately use the $400 tax saving to reduce the loan balance to $600.
Questions
1. What is the monthly loan payment required to pay off the $600 balance in one year?
2. To what amount will the single $1000 contribution grow over the next 20 years if your RRSP earns 6% compounded monthly?
Virtually all analyses of the issue fail to mention a logical alternative to borrowing money for an RRSP contribution. If your budget permits monthly payments on an RRSP loan over the next year, then an alternative to borrowing for an immediate lump RRSP contribution is to use the same budget “room” to start monthly contributions to an RRSP. A subtle but key point will now be developed. In the loan scenario, you immediately applied the tax saving to reduce the loan balance. In effect, you needed to borrow only $600 to make a $1000 RRSP contribution. The $1000 contribution cost you only $600. Similarly, if you make a monthly RRSP contribution of $100, it will really cost you only $60 because of the $40 tax saving. In other words, your after-tax cost is only 60% of your monthly contribution.
Let’s turn the last point around and answer this question: How much can you contribute to an RRSP if the after-tax cost to you is to be, say, $50? In this case, the $50 cost represents 60% of your contribution. Therefore, the contribution is $ 50 0.6 = $ 83.33.
3. What monthly RRSP contribution will have the same after-tax cost to you as the monthly loan payment calculated in Question 1?
4. Suppose you make these monthly RRSP contributions. What amount will you have in the RRSP just after the 12th contribution?
5. To what future value will the Question 4 amount grow over the subsequent 19 years?
6. The future values calculated in Questions 2 and 5 are the amounts in your RRSP 20 years from now under two alternatives that have the same cost to you. Comment on the outcome. What is your response to the question in the case’s title when the interest rate on an RRSP loan is the same as the rate of return earned by your RRSP investments?
7. Suppose the RRSP earns 9% compounded monthly instead of 6% compounded monthly. Answer Questions 2, 4, and 5 again. Should you borrow for the RRSP contribution in this case?
8. What will be the nature of the outcome if the rate of return earned by the RRSP is less than the interest rate on the loan?
9. Summarize your findings as a general decision criterion. (Under what circumstance should you borrow to make an RRSP contribution?)

Question: Answering this question occupies dozens of