Answer the following questions. Explain your answers:

a. A contest advertises that the winner wins $1,000,000. The $1,000,000 prize is paid in equal instalments over 25 years, with the first payment being made one year from the date the contest winner is announced. What is the "real" (present) value of the prize? Assume a discount rate of 8 percent.

b. You have the option of receiving $2,000,000 today or $250,000 a year for 15 years, beginning one year from now. If your discount rate is 12 percent, which would you choose?

c. A store allows you to purchase a new computer for $200 down and $50 a month for 36 months. If the appropriate discount rate is 1 percent per month, what would be the equivalent cash price today for the computer?

d. You can purchase an investment that pays interest of $200 per year for ten years plus $2,500 in the tenth year. If your discount rate is 10 percent, what is the maximum amount you should pay for the investment? (When answering, remember that calculating an annuity only applies to equal payments. In this question, the present value of the additional $2,500 received in the tenth year must be determined separately.)