As of December $31,$ Frappe Company has a balance of $$5,000$ in accounts receivable. Of this amount, $$500$ is past due and the remainder is not yet due. Frappe has a DEBIT balance of $$15$ in the Allowance for Doubtful Accounts. Frappe Company estimates its bad debt losses using the aging of receivables method, with estimated bad debt loss rates equal to $1\%$ of accounts not yet due and $10\%$ of past due accounts. How will the Bad Debt Expense account be included in the required adjusting journal entry at year$-$end?

a$.$ Debit Bad Debt Expense $$95$

b$.$ Credit Bad Debt Expense $$80$

c$.$ Debit Bad Debt Expense $$110$

d$.$ Credit Bad Debt Expense $$80$