Question

The RBC Students Leading Change Scholarship is awarded to eight students graduating high

school and seven students currently enrolled in a post-secondary program each year. Each of the
fifteen scholarships is worth $10,000, totaling $150,000 worth of scholarships.
In order to continue to offer these scholarships every year in perpetuity, RBC was looking into
setting up an endowment fund, growing at 5.25% per annum, compounded daily. The first set of
scholarships is to be offered today.
a) What should be the size of the endowment fund set up by RBC today in order to fully
cover the costs of offering the scholarships every year in perpetuity?
b) RBC currently has $3,900,000 that they are able to invest in the endowment fund. If RBC
invested this amount in the fund today, what is the maximum amount that may be
withdrawn every year to put towards the scholarships?
c) What should be the size of the endowment fund set up by RBC today in order to fully
cover the costs of offering the scholarships every year in perpetuity, if the first set of
scholarships is offered in five years instead of today?
d) Instead of investing in an endowment fund today, RBC contemplated setting up a
high-growth fund using their monthly profits to save up for the cost of the endowment
fund. If they make payments at the end of every month, what would be the size of RBC’s
first monthly payment in order to accumulate to the value calculated in (a) in five years?
The fund has an interest rate of 10.5% per annum, compounded monthly.
e) Does RBC earn more interest if it follows the payment plan laid out in (c) or (d)? By how
much?

Answer 1

The size of the endowment fund set up by RBC today to fully cover the costs of offering the scholarships every year in perpetuity is $2,857,142.86. The maximum amount that may be withdrawn every year from an endowment fund with an initial investment of $3,900,000 is $204,750.

Step-by-step explanation:

To calculate the size of the endowment fund set up by RBC today, we need to determine the present value of the perpetuity. The perpetuity is the total annual cost of the scholarships divided by the interest rate. In this case, the perpetuity is $150,000 and the interest rate is 5.25%. So, the size of the endowment fund is:

Endowment Fund Size = Perpetuity / Interest Rate

$150,000 / 0.0525 = $2,857,142.86

To calculate the maximum amount that may be withdrawn every year from an endowment fund, we need to determine the future value of the investment. The future value is the initial investment multiplied by the interest rate. In this case, the initial investment is $3,900,000 and the interest rate is 5.25%. So, the maximum withdrawal amount is:

Maximum Withdrawal Amount = Initial Investment * Interest Rate

$3,900,000 * 0.0525 = $204,750