Pitino acquired $90$ percent of Brey's outstanding shares on January $1,2022,$ in exchange for $$486,000$ in cash. The subsidiary's stockholders' equity accounts totaled $$470,000,$ and the noncontrolling interest had a fair value of $$54,000$ on that day. However, a building $($with a ten$-$year remaining life$)$ in Brey's accounting records was undervalued by $$45,000.$ Pitino assigned the rest of the excess fair value over book value to Brey's patented technology $($four$-$year remaining life$).$

Brey reported net income from its own operations of $$80,000$ in $2022$ and $$96,000$ in $2023.$ Brey declared dividends of $$27,000$ in $2022$ and $$31,000$ in $2023.$ a$.$ What was the annual amortization resulting from the acquisition$-$date fair$-$value allocations?