After a wildly successful career in finance, you decide to thank the guy who showed you the true path to happiness, Dr$.$ H$.$ You thought about just buying him a Tesla Model S$,$ but inexplicably decided to endow a scholarship in his name instead. You want the annual scholarship payment to be $$12,000.$ Once started, this scholarship will then pay out $$12,000$ every year forever. The balance of the scholarship endowment fund will be invested at a $4\%$ annual return.

a$)$ How much will it cost you,to establish the $"$I$\text{'}$d rather just have the Model S$"$ scholarship if you want to start the first payment $1$ year from now?

b$)$ How much will it cost you today to establish the scholarship if you want to start the first payment $7$ years from now?