The price of shares of ABC stock was

$$60$ on January $1,2018$

$$70$ on January $1,2019$; and

$$60$ on January $1,2020.$

Paul bought one share of ABC on January $1,2018,$ four more on January $1,2019,$ and sold all five shares on January $1,2020.$

$1.$ What is the annual arithmetic $($time$-$weighted$)$ average return on ABC stock during the two$-$year period?

$2.$ What is the annual geometric $($time$-$weighted$)$ average return on ABC stock during the two$-$year period?

$3.$ What is Paul's annual dollar$-$weighted average return during the two$-$year period? $($To find the return, use Excel, a financial calculator, or trial and error. Using approximation is okay. Hint $-$ Look for an integer between $-12\%$ and $-9\%).$

$4.$ Why is Paul's annual dollar$-$weighted average return lower than the arithmetic and geometric time$-$weighted annual average return of ABC?