The top prize in a state lottery is $100,000,000 and you decide to buy a ticket. Before you purchase a ticket you must decide to choose cash option or annual payment option. The cash option is $55,000,000. The annual payment option is 25 equal payments of 4,000,000 with first payment made immediately on days of lottery drawings. Your opportunity cost is 6%, which option should you choose? By how much more? (Please show all work)