According to an article in the NY Times \"Sales of water in standard lightweight

Question

According to an article in the NY Times "Sales of water in standard lightweight plastic bottles grew at a rate of more than 14 percent every quarter from 1993 to 2006."

(i) How many quarters are there from the beginning of 1993 to the beginning of 2006?
Express your answer as an integer.
________ quarters

(ii) For sales to increase 14% per quarter from the beginning of 1993 to the beginning of 2006, how much of an overall increase is that? ( Hint: think of compounding for several time periods! )
Express your answer rounded correctly to the nearest whole number, not in percent form!
_________ times

Explanation / Answer

i)Each year has got 4 quarters, therefore from beginning of 1993 to beginning of 2006 there are 13 years = 52 quarters.

ii) Now if the sales is x at beginning of 1993, sales after 1st quarter = x(1+14/100)

sales after 2nd quarte = x(1+14/100)(1+14/100) = x(1+14/100)2

similarly, sales after 52nd quarter = x(1+14/100)52 = 910.0227918x

therefore, overall increase = (910.0227918x - x )/x = 909.0227918 = 909

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