You just won a lottery that promises to pay you $1 million exactly ten years from today. Because the $1 million payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate lump-sum cash payment. a. What is the least you will sell your claim for if you could earn the following rates of return on similar risk investments during the ten-year period? 1. 6 percent 2.9 percent 3. 12 percent b. Rework part (a) under the assumption that the $1 million payment will be received in fifteen rather than ten years. c. Based on your findings in parts (a) and (b), discuss the effect of both the size of the rate of return and the time until receipt of payment on the pres- ent value of a future sum.