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How do I calculate historical yearly market worth knowing only its yearly growth rate and its martket worth for year 2015?

Example:

According to MarketLine, the global home improvement market is expected to grow at 2.5% yearly rate between 2010-2015 and is predicted to be worth almost $678 billion by 2015

I need to find X for each year since 2010 until 2014. I have yearly 2.5% percentage increase and 678,000,000,000 for year 2015.

How do I calculate historical worth for respective years?

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2 Answers 2

up vote 3 down vote accepted

Note that if $P$ was the markets initial value in the year of $2010$ then we must have: $$P(1+\frac{2.5}{100})^5=678 \text{ Million}$$

So the value of the global home improvement market at year $2010+n$ where $n=0,1,2,3,4,5$ is:

$$(1+\frac{2.5}{100})^{n-5}\times 678 \text{ Million}$$

For example, in $2011$ we have that the value of the global home improvement market is: $$(1+\frac{2.5}{100})^{1-5}\times 678 \text{ Million}\approx614 \text{ Million}$$


Or for all of them..

$$\text{Year } 2010 \approx 599 \text{ Million}$$ $$\text{Year } 2011 \approx 614 \text{ Million}$$ $$\text{Year } 2012 \approx 630 \text{ Million}$$ $$\text{Year } 2013 \approx 645 \text{ Million}$$ $$\text{Year } 2014 \approx 661 \text{ Million}$$ $$\text{Year } 2015 \approx 678 \text{ Million}$$

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Thanks Ethan. Can Windows calculator be used to calculate market's worth for each year? –  Boris_yo Jun 8 at 9:44
    
@Boris_yo Yes, anything capable of representing the product of two fractions as a floating point in decimal form should work (you could probably even do this by hand pretty quick with any multiplication and division algorithm, e.g. long multiplication/division) but I will save you the time - See my updated answer for the results for each year rounded to the nearest millionth. –  Ethan Jun 8 at 10:16
    
Appreciate your help. The initial data was provided here but partially because full report costs money. Do you think I can take that data and complement it with statistical graph using numbers for 5 years you helped me to calculate and give credit back to the source? I want to upload it to presentation hosting website. Would it be legit? –  Boris_yo Jun 8 at 13:32
1  
@Boris_yo Yes, but I would make sure you show your work. Under the assumption that the value in $2015$ is correct and that it grew at an exactly $2.5$% rate then all this data is accurate to the nearest millionth. What you're really doing is just calculating some compound interest and then doing a bit of algebra. I know Khan Academy has several videos that go through this process and give explanations along the way, if you're interested. –  Ethan Jun 8 at 22:13
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@Boris_yo I think it sounds good just make sure you explain how you got the work. If you are able to prove it mathematically to the readers, then their only real option for refutation is to question the accuracy of the original data provided by MarketLine. –  Ethan Jun 9 at 5:39

Obviously you can't find the actual data, because the "yearly growth rate" is only a rough guess. But if you, take it as accurate, start at the value for $2015$, divide it by $1.025$ for the $2014$ value, and continue...

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