On January $1,2024,$ Benjamin Company acquires $80\%$ of Coaster Company for $$1,600,000$ in cash consideration. The remaining $20$ percent noncontrolling interest shares had an acquisition$-$date estimated fair value of $$400,000.$ Coaster's acquisition$-$date total book value was $$1,500,000.$ The fair value of Coaster's recorded assets and liabilities equaled their carrying amounts. However, Coaster had two unrecorded assets$-$a trademark with an indefinite life and estimated fair value of $$80,000$ and several customer relationships estimated to be worth $$320,000$ with four$-$year remaining lives. Any remaining acquisition$-$date fair value in the Coaster acquisition was considered goodwill. During $2024,$ Coaster reported $$300,000$ net income and declared and paid dividends totaling $$20,000.$ Also in $2024,$ Benjamin reported $$850,000$ net income, but neither declared nor paid dividends. What amount of noncontrolling interest should appear in the owners' equity section of Benjamin's consolidated balance sheet at December $31,2024?$ $$440,000.$ $$460,000.$ $$430,000.$ $$450,000.$