Parents deposit $$9,000$ into a savings account at the end of each year for $22$ years to help their child pay for college. The savings account pays $6\%$ interest per year, compounded monthly. The child withdrawals an equal sum twice per year while in college $($years $19$ through $22).$ After the last withdrawal at the end of year $22,$ there is $$10,000$ remaining in the account. How much was each semi$-$annual withdrawal in year $19$ through $22?$ Express your answer in $ to the nearest $$100.$