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For the period from Year $6$ through Year $7,$ Charlie Company had net sales of $$500,000$ and a gross profit of $$200,000.$ During the first quarter of Year $8,$ the company made purchases of $$19,500$ and recorded sales of $$47,500.$ The inventory value at the beginning of the year was $$15,500.$ What is the estimated cost of Charlie's inventory on March $31,$ Year $8,$ using the gross profit method?

a$.$ $$22,500$

b$.$ $$6,500$

c$.$ $$6,000$

d$.$ $$15,000$