On January $1,2023,$ Bertrand, Incorporated, paid $$73,900$ for a $40$ percent interest in Chestnut Corporation's common stock. This investee had assets with a book value of $$251,500$ and liabilities of $$122,500.$ A patent held by Chestnut having a $$8,100$ book value was actually worth $$30,600.$ This patent had a six$-$year remaining life. Any further excess cost associated with this acquisition was attributed to an indefinite$-$lived asset. During $2023,$ Chestnut earned income of $$49,500$ and declared and paid dividends of $$17,000.$ In $2024,$ it had income of $$64,500$ and dividends of $$22,000.$ During $2024,$ the fair value of Bertrand's investment in Chestnut had risen from $$88,700$ to $$94,900.$

Required:

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

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

a$.$ Investment in Chestnut account as per the equity method

b$.$ Income from the investment in Chestnut as per fair$-$value accounting