$2.$ 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, Diane and James Davis. They have just celebrated their $40$th birthdays and after finishing saving for their children$$s education, they have decided to get serious about saving for their retirement. Diane and James hope to retire $25$ years from now $($on their $65$th birthdays$),$ and they expect to live until age $85.$ Their hope is to be able to withdraw $$110,000$ a year from their retirement account $$ the first withdrawal will occur on their $65$th birthdays, and the $20$th and final withdrawal will occur on their $84$th birthdays. After their final withdrawal, the account is expected to have a zero value $($i$.$e$.,$ they don$$t expect to have any remaining funds left for their children$$s inheritance$).$ Diane and James currently have $$140,000$ 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 $41$st 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 Diane and James need to contribute to the account at the end of each of the next $25$ years to accomplish their goals?

b$.$ If they wanted to leave their children $$1,200,000$ for inheritance when they die at age $85,$ how much would they need to contribute to the account at the end of each of the next $25$ years? $($Assume everything else stays the same.$)$

c$.$ Diane and James 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. Create in

Excel a two$-$input Data Table that tests the sensitivity of their annual deposit

amount by varying the expected returns from $4\%$ to $12\%$ in $1\%$ increments and

varying the inheritance level from $0$ to $$1,600,000$ in $$200,000$ 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.