Retirement Planning In the next two questions we will examine a realistic retirement planning situation.

• Assume you are 30 years old (t=0) and you will retire when you are 65 (t=35).

• You will save the maximum amount allowed into your 401-k plan every year, starting next year, when you are 31 (t=1).

• Assume the maximum amount you can save next year is $17,500 and that this amount will grow by 1% per year until you retire. Hint: This is a growing annuity.

• Assume that in retirement, you will spend the same amount each year.

• Assume you will live until you are 90 years old.

• Assume the market interest rate for this question is 2%.

Problem 2, Question 1. Based on the above, if you follow this retirement savings plan, saving the maximum allowed, how much cash would you have in the bank when you retire; i.e., what is the future value at t=35 (age 65) of the cash flows?

Problem 2, Question 2. Given your answer to the last question, assume you take all of the money from your 401-k account and use it to buy an annuity when you are 65. The annuity will pay you a constant cash amount each year from the age 66 to 90 (t=36 to 60); i.e., this is a simple (non-growing) annuity.

How much will the annuity pay you each year through your retirement?