$($Solving a comprehensive$$ problem$)$ Use the$$ end$-$of$-$year stock price data in the popup$$ window, LOADING...$,$ 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:

left parenthesis $1$ plus Start $2$ By $1$ Matrix $1$st Row $1$st Column Three dash Year $2$nd Row $1$st Column Rate of Return EndMatrix right parenthesis equals left parenthesis $1$ plus Start $2$ By $1$ Matrix $1$st Row $1$st Column Annual Rate $2$nd Row $1$st Column of Return EndMatrix right parenthesis cubed

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?