You invest $1 in Alphabet Inc. stock in year 1. In each subsequent year, you expect the value of your portfolio to double with probability p = 0.45 or to decrease by half with p = 0.55. For example, if you have $100 in your portfolio at the end of year 9, then in year 10, you expected to have $200 with p = 0.45 and $50 with p = 0.55.
a) How much would you expect to have at the end of year 50, when you wish to retire?
b) Use a standard normal variable to approximate the likelihood that your portfolio will be greater than the starting value of $1 at the end of year 50.