53. An investment of $5,000 is expected to generate the probabilistic returns shown in the table below over its three year life. Assume the annual cash fl ows are independent and that the distribution of present worth is normal.

EOY Annual Return 1 $2,500 with probability 0.4 or $1,800 with probability 0.6 2 $3,000 with probability 0.5 or $2,000 with probability 0.5 3 $3,500 with probability 0.7 or $2,500 with probability 0.3 For the following questions, determine an analytical solution:

a. Determine the probability that the present worth is negative.

b. Using a Monte Carlo simulation with 10,000 iterations, estimate the probability that the present worth is negative.