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

$2020$ $$153$ $$4\mathrm{.}76$

$2021$ $$202$ $$4\mathrm{.}76$

$2022$ $$174$ $$4\mathrm{.}76$

$2023$ $$140$ $$4\mathrm{.}76$

An investor buys three shares of CLX 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 $2023.$

$(1)$ What are the arithmetic average time$-$weighted rates of return for the investor?

$2\mathrm{.}28\%$

$(2)$ What are the geometric average time$-$weighted rates of return for the investor?

$[$ Select $]$

$(3)$ What is the dollar$-$weighted rate of return?

$[$ Select $]$