A company uses gross method for accounting for cash discounts and began the period with $$100$ balance in its acocunts receivable account and $$8$ credit balance in its allowance for doubtful accounts. During the period, the company made sales on account for $$200.$ It collected $$220$ cash from outstanding accounts and recorded $$30$ of sales discounts in the collection. During the period, the company wrote off $$20$ of accounts that it considered uncollectible. The company also reinstated $$5$ of accounts from a prior period $($but it did not collect cash during the current period$).$

Calculate the balance of allowance for doubtful accounts after recording the transactions during the period.