Buffalo Corporation operates in an industry that has a high rate of bad debts. Before any year$-$end adjustments, the balance in

Buffalo's Accounts Receivable account was $$591,800$ and Allowance for Doubtful Accounts had a credit balance of $$43,510.$ The

year$-$end balance reported in the balance sheet for Allowance for Doubtful Accounts will be based on the aging schedule shown below.

$($a$)$ What is the appropriate balance for Allowance for Doubtful Accounts at year$-$end?