Charles is graduating from high school and contemplating whether or not to go to college. If he chooses to work with a high school diploma, he will have an annual income of $80000 for the next 45 years and will not have to pay any further cost. If he goes to college, he will have to pay an annual cost of $C for four years, after which he will have an annual income of $120000 for the next 40 years. (a) If the annual interest rate is 5%, what is the net present value of Charles' earnings if he starts working after high school? (5 points) (b) How about if he goes to college? (Including costs.) (5 points) (c) For what value of C is Charles indifferent between the two alternatives? (5 points) (d) What would Charles' optimal decision be for a value of C higher than the one derived in part (c)? (5 points)