A depreciable asset costing $$75,000$ is purchased on September $1,$ Year $1.$ The asset is estimated to have a salvage value of $$10,000$ and an estimated useful life of $4$ years. Double$-$declining$-$balance depreciation is used. If the asset is sold on December $31,$ Year $3$ for $$13,000,$ the journal entry to record the sale will include:

A$-$A credit to gain on sale for $$8,000.$

B$-$A debit to loss on sale for $$2,625.$

C$-$A credit to accumulated depreciation for $$59,375.$

D$-$A debit to loss on sale for $$3,042.$

E$-$A credit to gain on sale for $$4,979.$