$xYZ$ stock price and dividend history are as follows:

An investor buys four shares of XYZ at the beginning of $2018,$ buys another two shares at the beginning of $2019,$ sells one share at the

beginning of $2020,$ and sells all five remaining shares at the beginning of $2021.$

Required:

a$.$ What are the arithmetic and geometric average time$-$weighted rates of return for the investor? $($Do not round intermediate

calculations. Round your answers to $2$ decimal places.$)$

b$-1.$ Prepare a chart of cash flows for the four dates corresponding to the turns of the year for January $1,2018,$ to January $1,2021.$

$($Negative amounts should be indicated by a minus sign.$)$

b$-2.$ What is the dollar$-$weighted rate of return? $($Hint: If your calculator cannot calculate internal rate of return, you will have to use a

spreadsheet or trial and error.$)($Negative value should be indicated by a minus sign. Round your answer to $4$ decimal places.$)$