Aromia is $22,$ and she estimates that she will need $$1,500,000$ in her total retirement nest egg by the time she is $65$ in order to have retirement income of $$50,000$ a year. $($She expects that Social Security will pay her an additional $$20,000$ a year.$)$ Aromia believes that putting money into a Roth IRA that is expected to grow at an annual rate of $8$ percent is the way to go$.$ She plans to leave it untouched until she retires at age $65.$ How much does Aromia need to put in the IRA each month to reach her goal?