$($Calculating the geometric and arithmetic average rates of return$)$ The common stock of the Brangus Cattle Company had the following end$-$of$-$year stock prices over the last five years and paid no cash dividends:

Time Brangus Cattle Company

$1$ $$15$

$210$

$312$

$423$

$525$

$1.$ Calculate the annual rate of return for each year from this information.

$2.$ What is the arithmetic average rate of return earned by investing in the company$$s stock over this period?

$3.$ What is the geometric average rate of return earned by investing in the company$$s stock over this period?

$4.$ Which type of average rate of return $($the arithmetic or geometric$)$ better describes the average annual rate of return earned over the period? Why?

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