Banana hospital has annual patient service revenues of $$62,666,000.$ It has two major third$-$party payers, and some of its patient are self$-$payers. The hospital$$s patient accounts manager estimates that $15\%$ of the hospitals$$ billings are paid $($received by the hospital$)$ on day $30,55\%$ are paid on day $60,$ and $30\%$ are paid on day $90.$

$1.$ What is Banana hospital$$s average collection period $($ACP$)?$

$2.$ What would be the hospital$$s new receivables balance if a newly proposed electronic claims system resulted in collecting from third$-$party payers in $15,45$ and $75$ days, instead of $30,60$and $90$ days?