An investor is considering investing $100,000 for four years in an investment. The annual return on the investment is normally distributed with mean 12% and standard deviation 15%. The returns are compounded, so you earn value not only on the principle $100,000 but also on any previous returns. Simulate the value of this investment over four years thousands of times.

a) What is the average net return after four years?

b) What is the standard deviation of the returns?

c) What is the probability you will lose money over the four-year period?

d) What net returns are in the top 10% of possibilities?