1.Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.)2. Jia has just won a $20 million lottery, which will pay her $1 million at the end of each year for 20 years. An investor has offered her $10 million for this annuity. She estimates that she can earn 10 percent interest, compounded annually, on any amounts she invests. She asks your advice on whether to accept or reject the offer. What will you tell her? (Ignore Taxes)

3. You have provided your friend with a service worth $8,500. Your friend offers you the following cash flow instead of paying $8,500 today. Should you accept his offer if your opportunity cost is 8 percent?