Monica has decided that she wants to build enough retirement wealth that, if invested at $10$ percent per year, will provide her with $$5,500$ of monthly income for $25$ years. To date, she has saved nothing, but she still has $30$ years until she retires.

How much money does she need to contribute per month to reach her goal? First compute how much money she will need at retirement, then compute the monthly contribution to reach that goal. $($Do not round intermediate calculations and round your final answer to $2$ decimal places.$)$