You have recently won the super jackpot in the Illinois State lottery, with a payoff of $4,960,000. On reading the fine print, you discover that you have the following two options: 1. You receive $160,000 at the end of each year for 31 years. 2. You receive $960,000 now and $100,000 at the end of each year for 40 years. Assume the market interest rate is 10% per year for all maturities. a. Which option would you prefer, 1 or 2? Why? Support your answer with the proper calculations. b. Suppose the lottery administrator offers you a third option where you will receive an equal annual payment at the beginning of each year for 31 years. If you are indifferent between this option and option 1, what should be the annual payment