On January $1,2023,$ Bertrand, Incorporated, paid $$62,500$ for a $40$ percent interest in Chestnut Corporation's common stock. This investee had assets with a book value of $$220,500$ and liabilities of $$87,000.$ A patent held by Chestnut having a $$8,100$ book value was actually worth $$20,100.$ This patent had a six$-$year remaining life. Any further excess cost associated with this acquisition was attributed to an indefinite$-$lived asset. During $2023,$ Chestnut earned income of $$42,000$ and declared and paid dividends of $$14,000.$ In $2024,$ it had income of $$57,000$ and dividends of $$19,000.$ During $2024,$ the fair value of Bertrand's investment in Chestnut had risen from $$74,100$ to $$81,000.$

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 $2024?$

$\backslash$table$[[$a$.$ Investment in Chestnut account as per the equity method,$51,400],[$b$.$ Income from the investment in Chestnut as per fair$-$value accounting,$