$($Calculating the geometric and arithmetic average rates of return$)($Related to

Checkpoint $7\mathrm{.}2$ on page $208)$ Marsh Inc. had the following end$-$of$-$year stock prices

over the last five years and paid no cash dividends:

Time Marsh

$1$ $$10$

$212$

$318$

$47$

$510$

a$.$ Calculate the annual rates of return for each year from this 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 that the beginning and ending stock prices for the five$-$year period

are the same, which type of average rate of return $($the arithmetic or geomet