Bella Inc. started the month with $5$ items in inverntory with a total cost of $$5,000.$ It purchased $10$ items for $$12,000$ on January $10.$ After inspecting the inventory purchased on January $10,$ management determined that it was not satisfied with the quality of the items. The supplier applied a $10\%$ price reduction on the total purchase. Using the LIFO method and assuming that $8$ items were sold on January $15,$ what is the amount of cost of goods sold for January?

$$8,640$

$$8,240$

$$8,427$

$$7,740$