Problem 6 (13 marks) The Warren Buffett NCAA March Madness Bracket Challenge is an annual contest that awards any Berkshire Hathaway employee who can pick every first and second round game correctly $1 million a year for life. You just celebrated your 45th birthday and you expect to live until the age of 85. a) If you won, and can invest each year's winnings at 5% compounded quarterly, what is the value of the prize today? (5 marks) b) If you wanted to establish a scholarship when you die that would provide annual scholarships totaling $100,000 paid at the end of each year and growing at 4% per year, how much would you have to invest each month if you could still earn 5% compounded quarterly? (8 marks)