A recent MBA would like your assistance in determining how much to save for retirement. He is planning to invest $3,000 in a tax-sheltered retirement fund at the end of each year (i.e., appreciation of the fund is not taxed). The rate of return each year can be modeled as a normally distributed random variable with a mean of 12 percent and a standard deviation of 2 percent.

a. If he is 30 years old now, how much money should he expect to have in his retirement fund at age 60?
b. What is the probability that he will have more than $1 million in his retirement fund when he reaches age 60?
c. How much should he invest each year if he wants the mean value of his portfolio to be at least $1 million at age 60?
d. How much should he invest each year if he wants there to be a 90 percent chance of having at least $1 million in his retirement fund at age 60?