Problem $10(6$ marks$)$

You had such a good time at SMU while you were here studying that you decide to set up a scholarship for future students. You would like a student studying finance to receive $$9,000$ in the first year $($end of year$)$ of offering the scholarship. Due to increasing tuition, you would like to increase the scholarship by $2\mathrm{.}5$ percent annually.

a$)$ If the current rate of interest is $6$ percent, how much will you need to donate to SMU to create the scholarship? $(3$ marks$)$

b$)$ How much would you have to donate today if you only want the scholarship to last for $10$ years? $(3$ marks$)$