Ruby is $25$ and has a good job at a biotechnology company. She currently has $$10,000$ in an IRA, an important part of her retirement nest egg. She believes her IRA will grow at an annual rate of $8$ percent, and she plans to leave it untouched until she retires at age $65.$ Ruby estimates that she will need $$875,000$ in her total retirement nest egg by the time she is $65$ in order to have retirement income of $$20,000$ a year $($she expects that Social Security will pay her an additional $$15,000$ a year$).$ Using Exhibit $1-$A$,$ Exhibit $1-$B$,$ Exhibit $1-$C$,$ Exhibit $1-$D$,$ answer the following questions.

a$.$ How much will Ruby's IRA be worth when she needs to start withdrawing money from it when she retires? $($Round discount factor to $3$ decimal places and final answer to the nearest whole dollar.$)$

Worth of IRA

b$.$ How much money will she have to accumulate in her company's $401($k$)$ plan over the next $40$ years in order to reach her retirement income goal? $($Round discount factor to $3$ decimal places and final answer to the nearest whole dollar.$)$

Money to accumulate