You have recently been hired as a consultant for a personal financial planning firm. One of your first projects is creating a retirement plan for a couple, Tom and Diane Matthews. They have just celebrated their 50th birthdays and after paying for their childrens education, they have decided to get serious about saving for retirement. Tom and Diane hope to retire 15 years from now (on their 65th birthdays), and they expect to live until age 90. Their hope is to be able to withdraw $120,000 a year from their retirement account the first withdrawal will occur on their 65th birthdays, and the 25th and final withdrawal will occur on their 89th birthdays. On their 90th birthdays, the account is expected to have a zero value (i.e., they dont expect to have any remaining funds left for their childrens inheritance). Tom and Diane currently have $250,000 saved in a retirement account, which consists of a portfolio of mutual funds that is expected to produce an annual return of 9%. To accomplish their goals, they would like to deposit an equal annual amount into their account starting one year from today (on their 51st birthdays) and continue to make those deposits through age 65. (Again, the account has an expected annual return of 9%.) Thus, they will make 15 annual end-of-year deposits to this account.

a. How much do Tom and Diane need to contribute to the account at the end of each of the next 15 years to accomplish their goals?

b. If they wanted to have $500,000 available for inheritance at age 90, how much would they need to contribute to the account at the end of each of the next 15 years? (Assume everything else stays the same.)

c. If they instead expected to earn only 6% a year from their mutual funds, how much would they need to contribute to the account at the end of each of the next 15 years? (Continue to assume that they want to have $500,000 available for inheritance at age 90.)

d. Tom and Diane realize that there are a lot of variables in their retirement plan. The two variables that they are particularly interested in are the expected return of their mutual funds and the amount they have available for inheritance at age 90. Create in Excel a two-input Data Table that tests the sensitivity of their annual deposit amount by varying the expected returns from 2% to 10% in 1% increments and varying the inheritance level from 0 to $4 million in $0.5 million increments. The data table should be constructed with the expected returns shown on the side of the table and the amount available for inheritance shown across the table.

e. Tom and Diane have one last concern. They recognize that the value of their $120,000 annual withdrawals during retirement will steadily decline because of expected inflation. Assume that they want to have the value of these withdrawals increase by 4% a year during retirement to account for expected inflation. In other words, they want to withdraw $120,000 at age 65, $124,800 at age 66, and $124,800 1.04 at age 67, etc. Going back to the other original assumptions (9% return and no expected inheritance), how much would they need to contribute to the account at the end of each of the next 15 years to meet this revised goal which protects them against rising inflation? Set up this problem using Excel.