$($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:

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 vears, what type of averaqe rate of return $($arithmetic or qeometric$)$ should

$\backslash$table$[[$Time$,\backslash$table$[[$Value of$],[$Harris Stock$]],\backslash$table$[[$Annual Rate$],[$of Return$]],\backslash$table$[[$Value of$],[$Pinwheel Stock$]],\backslash$table$[[$Annual Rate$],[$of Return$]]],[1,$$$10,,$$$22,],[2,6,\%,33,],[3,13,\%,31,],[4,13,\%,24,]]$