5. Retirement Planning

Sally Rathbun recently accepted a job with an advertising company.  Although she likes her job, she is also looking forward to retiring one day.  To ensure that her retirement is comfortable, Sally intents to invest $3,000 of her salary into a tax-sheltered retirement fund at the end of each year. Sally is not certain what the rate of return on this investment will earn each year. But she expects each year’s rate of return could be modeled appropriately as a normally distributed random variable with a mean of 12.5% and standard deviation of 2%.

a. If Sally is 30 years old, how much money should she expect to have in her retirement fund at age 60?

b. Construct a 90% confidence interval for the average amount that Sally will have at age 60. 

c. What is the probability that Sally will have more than $1 million in her retirement fund when she reaches age 60?

d. How much should she invest each year if she wants there to be a 90% chance of having at least $1 million in her retirement fund at age 60?

e. Suppose that Sally contributes $3,000 annually to her retirement fund for eight years and then terminates these annual contributions.  How much of her salary would she have contributed to this retirement plan and how much money could she expect (the average amount) to have accumulated at age 60?

f. Now suppose that Sally contributes nothing to her retirement fund for eight years and then begins contributing $3,000 annually until age 60.  How much of her salary would she expect to have accumulated at age 60?

g. What should Sally (and you) learn from the answers to questions e and f?