Barbara Kardashian is a new accountant with Flint Discount Retail Company. Flint purchased merchandise on account for $$9,000.$ The credit terms are $\frac{1}{10},\frac{n}{30}.$ Barbara has talked with the company's banker and knows that she could earn $10\%$ on any money invested in the company's savings account.

Should Barbara pay the invoice within the discount period or should she keep the $$9,000$ in the savings account and pay at the end of the credit period? $($Use $360$ days for calculation.$)$