You plan to invest $5,000 of your annual salary into a tax-sheltered IRA retirement fund (Vanguard VBIAX 60/40% stocks/bonds) every year. Looking at the past eighteen years of the VBIAX’s existence, you find its average annual rate of return is 6.84% with a standard deviation of 12.58%. Assume that returns are normally distributed.

Using Analytic Solver for Excel:

a. If you start saving for retirement at 25 years old, how much money should you expect to have in her retirement fund at age 59?

b. Construct a 95% confidence interval for the average amount you will have at age 59

c. What is the probability that you will have more than $1 million in your retirement fund when you reach age 59?

d. How much should you invest each year if you want there to be a 90% chance of having at least $1 million in your retirement fund at age 59? How much should you invest each year if you want there to be a 75% chance of having at least $1 million in your retirement fund at age 59?

e. Suppose that you contribute $5,000 annually to your retirement fund for nine years and then stop these contributions. How much of your salary would you have contributed to this retirement plan and how much money could you expect to have at age 59?

f. Now suppose that you contribute nothing to your retirement fund for nine years and then begin to contribute $5,000 annually until age 59. How much of your salary would you have contributed to this retirement plan and how much money could you expect to have at age 59?