Problem 1. (15 points] I have $5,000 and am weighing various options to save more for my sons' college tuition. There are 4 different account options: direct portfolio, guaranteed interest, high risk stock, or do nothing. The guaranteed interest account has a return of $9,000. The direct portfolio has a 5% chance of returning $20,000 a 60% chance of returning $15,000, a 30% chance of returning $10,000, and a 5% chance of returning $4,000. The high risk stock has a 1% chance of returning $100,000 and a 99% chance of losing everything. A) Use decision tree method to choose the best option. B) Assume the same situation except that the maximum return on the high risk investment ($100k) is now unknown. What payoff would the high risk investment have to have to make it the best alternative? Assume the same situation except that in the high risk stock case, the initial payoff is $1,000,000 and that if you get that payoff you have the opportunity to play roulette and put your money on red or black (each has a 0.5 probability). Which one is the best option now