Loop Inc. has a patent on new boxing training equipment. The patent was purchased from smith Inc. on January $1,$ Year $1$ for $$150,000.$ It is estimated that the patent will have an economic useful life to the company of $5$ years, but has a remaining legal life of $7$ years. At the beginning of Year $3,$ Loop Inc. successfully defended the patent with a total legal fee of $$12,000,$ which made the firm to extend the useful life by two additional years. How much is the amortization expense for the patent in Year $3.$