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 have to

use trial and error.$)$

Note: Round your answer to $4$ decimal places. Negative amount should be indicated by a minus sign.