$.$ On January $1,2019,$ Vespa, Inc., paid $$500,000$ for a $45\%$ interest in Winn Corp.$$s common stock.$$ Winn had assets with a book value of $$250,000$ and liabilities of $$10,000.$ A copyright held by Winn had a $$5,000$ book value but was actually worth $$60,000.$ A manufacturing plant held by Winn had a book value of $$100,000$ and a fair value of $$225,000.$ The copyright will be amortized over $5$ years while the plant had a $50$ year remaining life.$$ Any further excess cost was associated with goodwill.$$ During $2019,$ Winn earned income of $$80,000$ and paid dividends of $$10,000.$ During $2020,$ it had income of $$90,000$ and dividends of $$12,000.$ During $2020,$ the fair value of Winn had risen from $$1,500,000$ to $$2,000,000.$

a$.$ Assuming the equity method, what balance should appear in the investment in Winn account as of Dec. $31,2020?$

b$.$ Assuming Vespa uses fair$-$value accounting, what income from the investment in Winn should be reported in $2019$ and $2020?$ What is the value of the investment account and the end of both years?