Angelica is already trying to decide what to do with future lottery winnings, but she hasn't won yet! The drawing this Saturday has a projected lump-sum payout of $4,560,000. Alternatively, the winner could accept an annual payout of $400,000 for the next 20 years. Angelica, who is 25 years old, estimates that a comparable investment could earn a 12% return in the current market.

(Ignore Taxes)

a. Which payout option should Angelica choose when she wins the lottery? Explain.

b. If Angelica chooses the lump-sum payment, she will invest it and try not to touch any of the earnings until her retirement. She will then use the entire value of the investment to purchase an island in the Mediterranean. If she plans to retire in 20 years and her investment consistently earns 12% annually, how much will her budget be for the island? What if the investment earns only 5% annually?

c. If Angelica instead plans to purchase a nice home on the coast with her lump-sum lottery winnings right now, but also wants to purchase an island in the Mediterranean when she retires in 20 years, how much would she need to invest each year in order to reach the same total investment value as in part (b) (consider both the 12% and 5% options)?