An ordinary annuity pays $100\%$ compounded monthly.

$($A$)$ A person deposits $$$$100$ monthly for $30$ years and then makes equal monthly withdrawals for the next $15$ years, reducing the balance to zero. What are the monthly$$ withdrawals? How much interest is earned during the entire$45-$year process?

$($B$)$ If the person wants to make withdrawals of $1,500$ per month for the last $15$ years, how much must be deposited monthly for the first $30$ years? Round to the nearest cent