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Question 532596: Find the percent increase if hourly wages grew from $1.50 per hour to $6.60 per hour in 30 years?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! If you are just asking what the percentage change is, then the general, all-purpose percentage change formula applies:
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((EndingValue-BeginningValue)/BeginningValue) * 100
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In formal typesetting, the equation is:
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The values you need are given in the problem:
Ending Value = 6.60
Beginning Value = 1.50
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Note that you do not need:
Number of Years = 30
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If you need a calculator, you can copy the unformatted version (above) into the Google search box. It will calculate the value for you:
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((6.6-1.5)/1.5) * 100 = 340
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That means there was a 340% change.
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We can check this by multiplying: 3.4*1.5 = 5.1. Adding the $1.50 we started with = $6.60.
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So, there has been a 340% increase in hourly wages from $1.50 to $6.60 which amounts to $5.10 per hour.
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That sounds pretty good, until you consider that we have ignored the number of years.
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Of course, to find the percentage change in absolute terms, you don't care how long it has taken. If you need a tree to grow from 2 ft. to 40 ft tall, you have to wait for the tree to do it. The percentage change is the same. (40-2)/2 * 100 = 1900%. If it takes 50 years, so be it. If you plant two trees, it will not happen in half the time. You just end up with two trees.
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However, you might wonder if a 340% increase is a "good investment" given the 30 years involved. In that case, you would, in fact, be asking what the "compound annual growth rate" is for the hypothetical hourly wages.
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The word "compound" is critical because it mean that the annual increase affects the most recent value, not the beginning value. For example, if wages had grown to $4.00 per hour at some point, then a 10% increase would be 10% of $4.00 = 40 cents, not 10% of $1.50 = 15 cents.
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The compound annual growth rate is commonly known as CAGR. CAGR (pronounced "cagger", which rhymes with Jagger) is an important financial ratio. CAGR equals
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(EndingValue/BeginningValue)^((1/NumberOfYears)) -1
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In formal typesetting the equation is:
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The values you need are given in the problem:
Ending Value = 6.60
Beginning Value = 1.50
Number of Years = 30
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Plug these values into the equation and you have your answer. Again, you can use a calculator.
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((6.6 / 1.5)^(1 / 30)) - 1 = 0.0506266735
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So, CAGR = .0506266735
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That is the compound average growth rate. However, that is not the average percentage change.
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You need to remember that to talk about percentages you need to multiply the calculated rate of change by 100.
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So, the compound average percentage change is about 5%.
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Notice that this result is vastly different from the 340%/30 = 11.33%. This value gives what amounts to the average "simple" percentage change. The "simple" rate of changes is always relative to the beginning value. It tends to be misleading. The worker experienced only a 5% increase per year, not 11%.
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To recap, over 30 years wages rose from $1.50/hr to $6.60/hr. In absolute terms, that is a 340% increase. From a compound annual rate of growth perspective, the percentage change was 5%.
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Done.
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