A three$-$year$-$old machine that has a cost of $$14,000,$ an estimated residual value of $$3,000,$ and an estimated useful life of $22,000$ machine hours. The company uses units$-$of$-$production depreciation and ran the machine $1,400$ hours in year $1$; $3,100$ hours in year $2$; and $3,100$ hours in year $3.$

Calculate the carrying amount at the end of the third year.