n May $1,2023,$ Bailey Corp. acquired $90\%$ of the outstanding common stock of Carter Company for $$750,000$ cash. At the purchase date, Carter's balance sheet showed assets of $$500,000,$ liabilities of $$150,000,$ and stockholders' equity of $$350,000.$ The fair value of Carter's identifiable net assets is estimated to be $$440,000.$

Compute the amount of goodwill recorded by Bailey in the acquisition.

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