Janine is $46$ and has a good job at a biotechnology company. Janine estimates that she will need $$886,000$ in her total retirement nest egg by the time she is $65$ in order to have retirement income of $$27,000$ a year. $($She expects that Social Security will pay her an additional $$17,000$ a year.$)$ She currently has $$4,500$ 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 $65.$ How much will Janine$$s IRA be worth when she needs to start withdrawing money from it when she retires?