On January $2,2021,$ Twilight Hospital purchased a $$96,400$ special radiology scanner from Crane Inc. The scanner had a useful life of $4$ years and was estimated to have no disposal value at the end of its useful life. The straight$-$line method of depreciation is used on this scanner. Annual operating costs with this scanner are $$106,000.$

Approximately one year later, the hospital is approached by Dyno Technology salesperson, Jacob Cullen, who indicated that purchasing the scanner in $2021$ from Crane Inc. was a mistake. He points out that Dyno has a scanner that will save Twilight Hospital $$25,000$ a year in operating expenses over its $3-$year useful life. Jacob notes that the new scanner will cost $$110,000$ and has the same capabilities as the scanner purchased last year. The hospital agrees that both scanners are of equal quality. The new scanner will have no disposal value. Jacob agrees to buy the old scanner from Twilight Hospital for $$45,500.$

$($a$)$

If Twilight Hospital sells its old scanner on January $2,2022,$ compute the gain or loss on the sale.