On January $1,2023,$ Bertrand, Incorporated, paid $$86,900$ for a $40$ percent interest in Chestnut Corporation's common stock. This investee had assets with a book value of $$229,500$ and liabilities of $$79,500.$ A patent held by Chestnut having a $$11,500$ book value was actually worth $$50,500.$ This patent had a six$-$year remaining life. Any further excess cost associated with this acquisition was attributed to an indefinite$-$lived asset. During $2023,$ Chestnut earned income of $$53,500$ and declared and paid dividends of $$18,000.$ In $2024,$ it had income of $$51,000$ and dividends of $$23,000.$ During $2024,$ the fair value of Bertrand's investment in Chestnut had risen from $$99,600$ to $$102,400.$

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 $2024?$

Answer is complete but not entirely correct.

$\backslash$table$[[$a$.$ Investment in Chestnut account as per the equity method,$$,121,500x$