Rory McIlroy, professional golfer from Northern Ireland, just won the 2016 FedEx Cup which paid him $10 million. Suppose Rory wanted to establish a scholarship fund 10 years from now, which would pay annual scholarships totalling $1,000,000 per year forever (10 annual scholarships of $100,000 each). Scholarships would be paid at the beginning of each year. The funds invested in 2016 would earn 5.5% compounded quarterly over the next 10 years. After that, the funds would be moved to a more conservative investment earning 4% compounded annually.
a) How much would Rory have to invest today to fund this scholarship fund?
b) If Rory only wanted to spend his Fed Ex Cup earnings, how much would the scholarship fund have available each year to pay out forever?