XYZ$\text{'}$s stock price and dividend history are as follows:

Year Beginning$-$of$-$Year Price Dividend Paid at Year$-$End

$2019$ $ $180$ $ $4$

$20202004$

$20211704$

$20221804$

An investor buys three shares of XYZ at the beginning of $2019,$ buys another two shares at the beginning of $2020,$ sells one share at the beginning of $2021,$ and sells all four remaining shares at the beginning of $2022.$

Required:

a$.$ What are the arithmetic and geometric average time$-$weighted rates of return for the investor? $($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 $1,2019,$ to January $1,2022.$ If your calculator cannot calculate IRR, you will have to use trial and error or a spreadsheet program.$)($Round your answer to $4$ decimal places. Negative amount should be indicated by a minus sign.$)$