You plan to work for $40$ years, and then retire for the following $30$ years. You decide that you want to build enough retirement wealth that, if invested at $7$ percent per year $($APR$),$ will provide you with $$4,500$ of monthly income for $30$ years. To date, you have saved nothing. How much money will you need to contribute per month during your working years to reach your goal? $($Hint: first compute how much money you will need at retirement, then compute the monthly contribution in working years to reach that goal.