Question

Four years ago, you set up a fund to finance your plans to undertake a two-year Master’s programme in Canada. The cost of this programme including living expenses was estimated at that time to be $66,000. The average inflation rate for Canada is 3% per annum. Your plan was to invest for five years to achieve this goal. You have decided to borrow the remaining funds after five years if you do not have sufficient funds in your account. Every month, you contributed $400 to meet this objective. The funds were invested in a mutual fund with an asset allocation of 70:30 in stocks and bonds respectively. The return on the mutual was 54% per annum for each year. At the end of the fourth year, you decided to invest the funds in treasury bills for another year. You, therefore, called your investment manager to transfer all the funds into treasury bills. You instruction to the broker was to purchase 91-day treasury bills to be rolled over for a year. The discount rate for the 91-day Treasury Bill is given as 23.7280%.

a. How much would it cost you to pay for your education at the end of year 4?
b. How much would you have in your Education Fund account at the end of year 4?
c. What may have informed the decision to invest in the mutual fund and subsequently treasury bills?
d. How much will the investor be debited with to fulfill his request to purchase Treasury Bills? Assume that the amount in the mutual fund is the face value of the Treasury bill.
e. How much will you earn, in terms of the interest rate (p.a)

Answer 1

a. To calculate how much it would cost to pay for your education at the end of year 4, we need to account for inflation over the four-year period. Using the average inflation rate of 3% per annum for Canada, the cost of the program including living expenses would have increased to:

$66,000 x (1 + 0.03)^4 = $77,696.88

Therefore, it would cost approximately $77,696.88 to pay for the program at the end of year 4.

b. To calculate how much you would have in your Education Fund account at the end of year 4, we need to calculate the value of the mutual fund after four years of investing:

Year 1: $4,800 = ($400 x 12 months)

Value of mutual fund = ($4,800 x 1.54) x 0.7 + ($4,800 x 1.54) x 0.3 = $11,167.20

Year 2: $9,600 = ($400 x 12 months x 2 years)

Value of mutual fund = ($9,600 x 1.54) x 0.7 + ($9,600 x 1.54) x 0.3 = $22,334.40

Year 3: $14,400 = ($400 x 12 months x 3 years)

Value of mutual fund = ($14,400 x 1.54) x 0.7 + ($14,400 x 1.54) x 0.3 = $33,501.60

Year 4: $19,200 = ($400 x 12 months x 4 years)

Value of mutual fund = ($19,200 x 1.54) x 0.7 + ($19,200 x 1.54) x 0.3 = $44,668.80

At the end of year 4, the value of the mutual fund would be approximately $44,668.80.

c. The decision to invest in the mutual fund was likely informed by the desire to achieve higher returns than other low-risk investments, such as savings accounts or CDs. The asset allocation of 70:30 in stocks and bonds allowed for potential growth while minimizing risk. The decision to invest in treasury bills for the fifth year was likely motivated by a desire to preserve the capital and ensure that the funds were available when needed for the education program.

d. To purchase Treasury Bills, the investor would need to sell their mutual fund and use the proceeds to buy the Treasury Bills. Assuming the face value of the Treasury Bills is the same as the amount in the mutual fund, the investor would be debited with $44,668.80 to fulfill their request.

e. The interest rate on the 91-day Treasury Bill is given as 23.7280%. This represents the annualized yield on the Treasury Bill. Therefore, the investor would earn 23.7280% per annum on their investment in the Treasury Bills.