$($Solving a comprehensive problem$)$ Use the end$-$of$-$year stock price data in the popup window, $,$ to answer the following questions for the Harris and Pinwheel companies.

a$.$ Compute the annual rates of return for each time period and for both firms.

b$.$ Calculate both the arithmetic and the geometric mean rates of return for the entire three$-$year period using your annual rates of return from part a$.($Note: you may assume that neither firm pays any dividends.$)$

c$.$ Compute a three$-$year rate of return spanning the entire period $($i$.$e$.,$ using the ending price for period $1$ and ending price for period $4).$

d$.$ Since the rate of return calculated in part $c$ is a three$-$year rate of return, convert it to an annual rate of return by using the following equation:

$(1+[$ Three$-$Year $],[$ Rate $of$ Return $])=([$ Annual Rate $],[,of$ Return $]{)}^3$

e$.$ How is the annual rate of return calculated in part d related to the geometric rate of return? When you are evaluating the performance of an investment that has been held for several years, what type of average rate of return $($arithmetic or geometric$)$ should you use? Why?