$($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?

Question content area bottom

Part $1$

a$.$ Enter the annual rate of return for each year for Harris in the table below.$($Round to two decimal$$ places.$)$

Time

Value of

Harris Stock

Annual Rate

of Return

Value of

Pinwheel Stock

Annual Rate

of Return

$1$

$$$$8$

$$$$18$

$2$

$9$

$$

enter your response here

$\%$

$36$

$3$

$11$

$$

enter your response here

$\%$

$28$

$4$

$15$

$$

enter your response here

$\%$

$24$

Part $2$

Enter the annual rate of return for each year for Pinwheel in the table below.$($Round to two decimal$$ places.$)$

Time

Value of

Harris Stock

Annual Rate

of Return

Value of

Pinwheel Stock

Annual Rate

of Return

$1$

$$$$8$

$$$$18$

$2$

$9$

$12\mathrm{.}50$

$\%$

$36$

$$

enter your response here

$\%$

$3$

$11$

$22\mathrm{.}22$

$\%$

$28$

$$

enter your response here

$\%$

$4$

$15$

$36\mathrm{.}36$

$\%$

$24$

$$

enter your response here

$\%$

Part $3$

b$.$ The arithmetic average rate of return earned by investing in Harris stock over this period is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $4$

The arithmetic average rate of return earned by investing in Pinwheel stock over this period is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $5$

The geometric average rate of return earned by investing in Harris stock over this period is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $6$

The geometric average rate of return earned by investing in Pinwheel stock over this period is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $7$

c$.$ The $$three$-$year rate of return spanning the entire period for Harris is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $8$

The $$three$-$year rate of return spanning the entire period for Pinwheel is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $9$

d$.$ The annual rate of return converted from the$$ three$-$year rate in part c for Harris is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $10$

The annual rate of return converted from the$$ three$-$year rate in part c for Pinwheel is

$$

enter your response here$\%.($Round to two decimal$$ places.$)$

Part $11$

e$.$ How is the annual rate of return calculated in part d related to the geometric rate of$$ return?$($Select the best choice$$ below.$)$

A$.$

The annual rate of return calculated in part d is nothing but the arithmetic average rate of return calculated in a different way.

B$.$

The annual rate of return calculated in part d is the same as the geometric rate of return in this problem but this is only a coincidence.

C$.$

The annual rate of return calculated in part d is nothing but the geometric average rate of return calculated in a different way.

D$.$

The annual rate of return calculated in part d is not related to the geometric average rate of return.

Part $12$

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$$ use? Why?$($Select the best choice$$ below.$)$

A$.$

The arithmetic rate of return should be used. It better describes the average annual rate of return over a period because it compounds at the same rate while the geometric rate of return is best used for a single period.

B$.$

The geometric rate of return should be used. It better describes the average annual rate of return over a period because it compounds at the same rate while the arithmetic rate of return is best used for a single period.

C$.$

Geometric average return better describes the average annual rate of return over a period because it is a simple$$ average, so it an