How to calculate historical data knowing only yearly percentage increase and data for year 2015?

Question

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?

Answer 1

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: $$(1+\frac{2.5}{100})^{1-5}\times 678 \text{ Million}\approx614 \text{ Million}$$

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Or for all of them..

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

Answer 2

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...