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 young couple, Charles and Marie Smythe. They have just celebrated their 40th birthdays and have decided to get serious about saving for retirement. Charles and Marie hope to retire 25 years from now (on their 65th birthdays), and they expect to live until age 85. Their hope is to be able to withdraw $175,000 a year from their retirement account – the first withdrawal will occur on their 65th birthdays, and the 20th and final withdrawal will occur on their 84th birthdays. They expect to leave their children a total inheritance of $750,000 to split amongst themselves. So, on their 85th birthdays, the account is expected to have a $750,000 value (i.e., they expect to leave their children a total inheritance of $750,000). Charles and Marie currently have $75,000 saved in a retirement account, which consists of a portfolio of mutual funds that is expected to produce an annual return of 8%. To accomplish their goals, they would like to deposit an equal annual amount into their account starting one year from today (on their 41st birthdays) and continue to make those deposits through age 65. (Again, the account has an expected annual return of 8%.) Thus, they will make 25 annual end-of-year deposits to this account.

a. How much do Charles and Marie need to deposit into the account at the end of each of the next 25 years to accomplish their goals?

b. Charles and Marie recognize that the value of their $175,000 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 $175,000 at age 65, $182,000 at age 66, and $182,000 × 1.04 at age 67, etc.  

How much would they need to deposit into the account at the end of each of the next 25 years to meet this revised goal, which protects them against rising inflation?  Assume they still plan to leave their children a total inheritance of $750,000.