Question

The Dean of the School of Business and Applied Arts at Red River College in Winnipeg wants to establish a scholarship program for the newly created finance major in its Business Administration stream. He wants to distribute five $2,000 scholarships annually starting immediately. How much money must he raise from college supporters if the perpetuity can earn 3.6% compounded monthly?

A) $400,000
B) $500,000
C) $600,000
D) $700,000

Answer 1

The dean needs to raise approximately $3,333,333.33 to fund a perpetuity that awards five $2,000 scholarships annually at a 3.6% rate of return compounded monthly. This figure is calculated using the formula for the present value of a perpetuity.

Step-by-step explanation:

The student is asking about the amount of money needed to establish a scholarship program funded by a perpetuity that will distribute five $2,000 scholarships yearly, with a 3.6% rate of return compounded monthly. To find the sum of money needed to fund the perpetuity, we use the formula for the present value of a perpetuity:

PV = PMT / i

where PMT is the annual payment and i is the monthly interest rate. In this case, PMT is 5 scholarships times $2,000 each, which equals $10,000 annually, and the monthly interest rate is 3.6% per year, or 0.036/12 per month. Before proceeding with the calculation, we convert the annual interest rate to a monthly rate by dividing it by 12. Thus:

PV = $10,000 / (0.036/12)

Calculating this gives us the present value (PV) needed. To find the answer, divide $10,000 by the monthly interest rate:

PV = $10,000 / (0.003)

PV = $3,333,333.33

Thus, the dean needs to raise approximately $3,333,333.33 to fund the perpetuity. However, since this figure is not among the options provided, the student might need to check the problem statement or the options given. However, based on standard mathematical principles, this is the amount to be raised to create the intended perpetuity.