On January $1,2023,$ Bertrand, Incorporated, paid $$60,000$ for a $40$ percent interest in Chestnut Corporation's common stock. This investee had assets with a book value of $$200,000$ and liabilities of $$75,000.$ A patent held by Chestnut having a $$5,000$ book value was actually worth $$20,000.$ This patent had a six$-$year remaining life. Any further excess cost associated with this acquisition was attributed to an indefinite$-$lived asset. During $2023,$ Chestnut earned income of $$30,000$ and declared and paid dividends of $$10,000.$ In $2024,$ it had income of $$50,000$ and dividends of $$15,000.$ During $2024,$ the fair value of Bertrand's investment in Chestnut had risen from $$68,000$ to $$75,000.$

Required:

Assuming Bertrand uses the equity method, what balance should appear in the Investment in Chestnut account as of December $31,2024?$

Assuming Bertrand uses fair$-$value accounting, what income from the investment in Chestnut should be reported for $2024?$