On January $1,2023,$ Bertrand, Incorporated, paid $$72,000$ for a $40$ percent interest in Chestnut Corporation$$s common stock. This investee had assets with a book value of $$260,500$ and liabilities of $$115,500.$ A patent held by Chestnut having a $$10,200$ book value was actually worth $$23,700.$ 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 $$39,000$ and declared and paid dividends of $$13,000.$ In $2024,$ it had income of $$61,500$ and dividends of $$18,000.$ During $2024,$ the fair value of Bertrand$$s investment in Chestnut had risen from $$84,500$ to $$92,700.$

Required:

a$.$ Assuming Bertrand uses the equity method, what is the amount of goodwill $($if any$)$ related to this investment?

b$.$ Assuming Bertrand uses the equity method, what balance should appear in the Investment in Chestnut account as of December $31,2023($one year later$)?$

c$.$ Assuming Bertrand uses the equity method, what balance should appear in the Investment in Chestnut account as of December $31,2024($two years later$)?[$Hint: start with ending balance from prior year as your beginning balance for current year and repeat the formula.$]$

d$.$ Assuming Bertrand uses fair$-$value accounting, what income from the investment in Chestnut should be reported for $2024($include both fair value appreciation and dividend income$)??$