Time value and discount rates Personal Finance Problem You just won a lottery that promises to pay you $500,000 exactly 20 years from today. Because the $500,000 payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate single cash payment. a. What is the least you will sell your claim for if you can earn the following rates of return on similar-risk investments during the 20-year period? (1) 6% (2) 9% (3) 12% b. Rework part a under the assumption that the $500,000 payment will be received in 30 rather than 20 years. c. On the basis of 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 present value of a future sum. a. (1) The least you will sell your claim for if you can earn a rate of return of 6% during the 20-year period is $. (Round to the nearest cent.) (2) The least you will sell your claim for if you can earn a rate of return of 9% during the 20-year period is $ (Round to the nearest cent.) (3) The least you will sell your claim for if you can earn a rate of return of 12% during the 20-year period is $ (Round to the nearest cent.) b. (1) The least you will sell your claim for if you can earn a rate of return of 6% during the 30-year period is $ (Round to the nearest cent.) (2) The least you will sell your claim for if you can earn a rate of return of 9% during the 30-year period is $ (Round to the nearest cent.) (3) The least you will sell your claim for if you can earn a rate of return of 12% during the 30-year period is $. (Round to the nearest cent.) c. On the basis of 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 present value of a future sum. (Select the best answer below.) A. As the discount rate increases, the present value becomes larger. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies. B. As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies. C. As the discount rate increases, the present value becomes smaller. Also, the longer the time until the lottery payment is collected, the greater the present value due to the greater time over which the opportunity cost applies. D. As the discount rate increases, the present value becomes smaller. Also, the shorter the time until the lottery payment is collected, the smaller the present value due to the greater time over which the opportunity cost applies