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. Consider the following hypothetical scenario: 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% daily. The first set of scholarships is to be offered today. 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.

Answer 1

The size of the endowment fund RBC needs to establish today to cover $150,000 of scholarships in perpetuity, starting in five years, assuming a 5.25% annual growth rate, is $2,219,636.70.

Step-by-step explanation:

The student's question is concerned with establishing the necessary size of an endowment fund that RBC needs to set up today to ensure it can offer $150,000 worth of scholarships every year in perpetuity, assuming a 5.25% annual interest rate and that the first set of scholarships is to be funded in five years, not immediately.

To solve this, we need to use the formula for perpetuity: PV = PMT / r, where PV is the present value of the perpetuity, PMT is the annual payment (scholarship amount), and r is the annual interest rate (as a decimal). However, since the scholarships begin in five years, we must first calculate the present value of the perpetuity five years from now and then discount that back to today's value.

Using the perpetuity formula, reflecting the first scholarship beginning in five years, we get: PV (in 5 years) = $150,000 / 0.0525 = $2,857,142.86. To find today's present value, we then discount this amount back five years using the formula PV = FV / (1 + r)^n, where FV is the future value we just calculated, r is the annual interest rate, and n is the number of periods (years). This gives us PV (today) = $2,857,142.86 / (1 + 0.0525)^5.

Performing this calculation, the size of the endowment fund RBC would need to set up today is $2,219,636.70 (rounded to the nearest cent).