The Badenhorst company using the perpetual inventory system purchased inventory worth $$500,000$ on account with credit terms of $\frac{3}{15},\frac{n}{45}.$ Defective inventory of $$50,00$ days later, and the accounts were appropriately adjusted. If the company paid the invoice $25$ days later, the journal entry to record the payment would be

A$)$ $$500,000$ debit to Accounts Payable and $$500,000$ credit to Cash

B$)$ $$450,000$ debit to Accounts Payable and $$450,000$ credit to Cash

C$)$ $$500,000$ debit to Accounts Payable, $$486,500$ credit to Cash, and $$13,500$ credit to Merchandise Inventory

D$)$ $$463,500$ debit to Accounts Payable, $$13,500$ credit to Merchandise Inventory, and $$450,000$ credit to Cash