$($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:

$(\frac{\text{T}\text{h}\text{r}\text{e}\text{e}-\text{Y}\text{e}\text{a}\text{r}}{\text{R}\text{a}\text{t}\text{e}of\text{R}\text{e}\text{t}\text{u}\text{r}\text{n}})=(\frac{\text{A}\text{n}\text{n}\text{u}\text{a}\text{l}\text{R}\text{a}\text{t}\text{e}}{of\text{R}\text{e}\text{t}\text{u}\text{r}\text{n}}{)}^3$

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?

Data table

$\backslash$table$[[$Time$,$Harris,Pinwheel$],[1,$$$11,$$$18$