On July $1,20$X$1,$ Kat Company paid $$5,100,000$ for all of the common stock of Pillar, Inc. Pillar$$s identifiable net assets had a fair value of $$4,845,000$ at that date. After acquisition, Pillar was identified as a reporting unit and the goodwill from the acquisition was assigned to that reporting unit.

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Over the remainder of the year, the new unit experienced significant operating losses, suggesting the need for testing of the goodwill for impairment. The fair value of the reporting unit was estimated to be $$3,408,500$ at December $31.$ Pillar's year$-$end balance sheet showed net assets of $$3,570,000,$ including the goodwill.

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Determine the amount of the goodwill impairment, if any, that occurred in $20$X$1.$

Question $1$ options:

$110,500$

$255,000$

$0$

$161,500$