On January $1,2023,$ Bertrand, Incorporated, paid $$85,700$ for a $40$ percent interest in Chestnut Corporation$$s common stock. This investee had assets with a book value of $$256,000$ and liabilities of $$83,500.$ A patent held by Chestnut having a $$9,800$ book value was actually worth $$20,300.$ 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 $$48,000$ and declared and paid dividends of $$16,000.$ In $2024,$ it had income of $$52,000$ and dividends of $$21,000.$ During $2024,$ the fair value of Bertrand$$s investment in Chestnut had risen from $$99,100$ to $$105,100.$

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 $2024?$