Marsh Inc. had the following$$ end$-$of$-$year stock prices over the last five years and paid no cash$$ dividends:

Time

Marsh

$1$

$$$$8$

$2$

$10$

$3$

$20$

$4$

$5$

$5$

$8$

$($Click on the icon in order to copy its contents into a spreadsheet.$)$

a$.$ Calculate the annual rate of return for each year from the above information.

b$.$ What is the arithmetic average rate of return earned by investing in$$ Marsh's stock over this$$ period?

c$.$ What is the geometric average rate of return earned by investing in$$ Marsh's stock over this$$ period?

d$.$ Considering the beginning and ending stock prices for the$$ five$-$year period are the$$ same, which type of average rate of return$($the arithmetic or$$ geometric$)$ better describes the average annual rate of return earned over the$$ period?