Creating an endowment

On completion of her LETU Principles of Finance course,

Marla Lee was so pleased with the amount of useful and

interesting knowledge she gained that she convinced her

parents, who were wealthy alumni of the university she was

attending, to create an endowment. The endowment will

provide for three students from low$-$income families to take

the introductory finance course each year in perpetuity. The

cost of taking the finance course this year is $$1500$ per student

$($or $$4500$ for $3$ students$),$ but that cost will grow by $2\%$ per

year forever. Marla's parents will create the endowment by

making a single payment to the university today. The

university expects to earn $8\%$ per year on these funds.

a$)$ How much will Marla's parents have to give the university

today to fund the endowment if it starts paying out cash

flow next year?

b$)$ What amount would be needed to fund the endowment if the

university could earn $12\%$ rather than $8\%$ per year on the

funds?