YearYear Priceat Year$-$End$2020$$ $120$$ $5202115052022110520231205$XYZ$\text{'}$s stock price and dividend history are as follows:An investor buys three shares of XYZ at the beginning of $2020,$ buys another two shares at the beginning of $2021,$ sells one share at the beginning of $2022,$ and sells all four remaining shares at the beginning of $2023.$Required:a$.$ What are the arithmetic and geometric average time$-$weighted rates of return for the investor?Note: Round your year$-$by$-$year rates of return and final answers to $2$ decimal places. Do not round other calculations.b$.$ What is the dollar$-$weighted rate of return? $($Hint Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January $1,2020,$ to January $1,2023.$ If your calculator cannot calculate internal rate of return, you will nave to use trial and error.$)$