Question $2$: Application of Time Value of Money $(20$ marks$)$

a$)$ In $30$ years, you plan to set up a fellowship fund for Carleton University that would pay out $$100,000$ a year in perpetuity with an annually compounded discount rate of $5\%.$ In order to set up the fund in $30$ years, how much do you need to save each year $($starting this year$)$ assuming you can get a return of $10\%$ per annum on your savings semi$-$annually compounded for the next $30$ years? $(4$ marks$)$