On January $1,2019,$ Hess Co$.$ purchased a patent for $$1,904,000.$ The patent is being amortized over its remaining legal life of $15$ years expiring on January $1,2034.$ During $2022,$ Hess determined that the economic benefits of the patent would not last longer than ten years from the date of acquisition. What amount should be reported in the balance sheet for the patent, net of accumulated amortization, at December $31,2022?$

$$1,142,400$

$$1,344,000$

$$1,305,600$

$$1,396,400$