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.)