Tucker Inc. buys $20\%$ of the common shares of Brothers on $1/1/2023$ for $$1,000.$ The book value $($i$.$e$.,$ net assets$)$ of Brothers at the time of the purchase was $$4,500.$ The fair value of Brothers$$s net assets at the time of the purchase was $$4,800.$ During $2023,$ Brothers paid $$100$ in dividends and had net income of $$500.$ The total market value of Brothers at $12/31/2023$ was $$5,500.$

$1)$ Assume the Brothers investment is accounted for using fair value through net income.

a$.$ For $2023,$ how much income is recognized by Tucker as a result of the investment in Brothers? $($Include all types of income.$)$

b$.$ As of $12/31/2023,$ what is on Tucker$$s balance sheet for the investment in Brothers? $($Include all balance sheet balances directly related to the investment.$)$

$2)$ Alternatively, assume Tucker determines that it has significant influence over Brothers as a result of the investment in Brothers. Accordingly, Tucker uses the equity method of accounting. Assume that fair market value increments $($i$.$e$.,$ the difference between the fair and book value of Brothers$$ assets$)$ are depreciated using straight$-$line over $5$ years.

a$.$ For $2023,$ how much income from affiliates is recognized by Tucker as a result of the investment in Brothers?

b$.$ As of $12/31/2023,$ what is on Tucker$$s balance sheet for the asset account Investment $-$ Brothers?