Calculating an IRA Accumulation. Janine is $27$ and has a good job at a biotechnology company. She currently has $$5,000$ in an IRA, an important part of her retirement nest egg. She believes her IRA will grow at an annual rate of $6$ percent, and she plans to leave it untouched until she retires at age $67.$ Janine estimates that she will need $$850,000$ in her total retirement nest egg by the time she is $67$ 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$).$ How much will Janine's IRA be worth when she needs to start withdrawing money from it when she retires? $($Hint: Use Exhibit A$-1$ in the appendix to Chapter $1.)$

Years to retirement $=40$

Her current IRA $=$$$5,000$

Annual growth rate $=6\%$

Future Value $($compounded sum$)$ after $40$ years @$6\%$ growth $=$$$$