$6.$ A benefactor proposes to set up an endowment for student scholarship at the Business

School. The proposal is to provide scholarship of $$15,000($at the end of$)$ each year.

Suppose the interest rate earned by endowments is $4\%.$

$($a$)$ How much should the benefactor donate? $[$Hint: This is a perpetuity problem.$]$

$($b$)$ What if the proposal is to provide $$15,000$ plus a raise of $3\%$ each year? $[$Hint: This is a

growth perpetuity problem.$]$