Create a retirement plan for Betty and Hans Hardy. They have just celebrated their 30th birthdays and have decided to get serious about saving for retirement. Betty and Hans hope to retire 35 years from now (on their 65th birthdays), and they expect to live until age 90. Their hope is to be able to withdraw $125,000 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. They expect to leave their children a total inheritance of $1,000,000 to split amongst themselves. So, on their 90th birthdays, the account is expected to have a $1,000,000 value (i.e., they expect to leave their children a total inheritance of $1,000,000).

Betty and Hans currently have $10,000 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 31st birthdays) and continue to make those deposits through age 65. (Again, the account has an expected annual return of 8%). Thus, they will make 35 annual end-of-year deposits to this account.

a. How much do Betty and Hans need to deposit into the account at the end of each of the next 35 years to accomplish their goals?

b. Betty and Hans recognize that the value of their $125,000 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 for the first 12 years after retirement and then increase the withdrawals by 5% a year for the last 13 years of retirement to account for expected inflation. In other words, they want to withdraw $125,000 at age 65 and $130,000 at age 66 ($125,000 1.04). The last withdrawal at the 4% inflation rate will be $192,431.76 at age 76. After then, the retirement withdrawals will grow at 5% a year -- so the retirement withdrawal at age 77 will be $202,053.34 ($192,431.76 1.05). From that point forward, the withdrawals will increase 5% a year up until age 90.

-How much would they need to deposit into the account at the end of each of the next 35 years to meet this revised goal, which protects them against rising inflation? Assume they still plan to leave their children a total inheritance of $1,000,000.

Please provide explanation and how to set up this problem using Excel.