1. You are advising a client who is currently 50 years old. Your client is worried about her retirement in another 15 years. She currently has $20,000 in savings, invested in equal proportions in a benchmark portfolio of stocks and risk-free assets. Your client has the following question: \Suppose I save $25,000 annually and continue my current investment policy. Suppose further that my life expectancy is 80 years and that for the last 15 years of my life (at the start of years 66 to 80), I intend to withdraw $100,000 annually from my savings account. Will I nish my life with a non-negative account balance?" As an experienced investment advisor, you estimate that the annual return on the stock portfolio is normally distributed with mean = 10% and standard deviation = 15%. The risk-free interest rate (continuously compounded) is 5%. What is the probability your client will end up with a non-negative balance? 2. The client in the previous question has a favorite nephew and would like to leave $50,000 to him. What is the probability that she will achieve her goal?