A

$3$

$5$

$$year old employee who has just been hired will contribute part of their paycheck monthly to a

$4$

$0$

$1$

$($

k

$)$

$.$

$$The employee's starting salary is $

$7$

$5$

$0$

$0$

$0$

$$a year. An annual raise of

$4$

$.$

$6$

$4$

$\%$

$$is given to every employee each year. The employee plans to work for the company until they retire at age

$6$

$2$

$$and start withdrawing from their

$4$

$0$

$1$

$($

k

$)$

$3$

$0$

$\%$

$$of their ending salary each year they are retired. The employee expects to be retired for

$3$

$5$

$$years$.$ They will withdraw the money in monthly installments. The

$4$

$0$

$1$

$($

k

$)$

$$earns

$7$

$.$

$1$

$7$

$\%$

$$per year compounded monthly. c

$)$

$$Using your answer to part b

$)$

$,$

$$how much does the employee needs to save in their

$4$

$0$

$1$

$($

k

$)$

$$before they retire at age

$6$

$2$

$?$

$$Round to two decimals. d

$)$

$$Using your answer to part c

$)$

$,$

$$how much does the employee's monthly

$4$

$0$

$1$

$($

k

$)$

$$contributions need to be

$?$

$$Round to two decimals. e

$)$

$$Using your answers to part c

$)$

$$and d

$)$

$,$

$$how many years would it take the employee to save the money they need to retire if they doubled their monthly contributions? Round to two decimals.