From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 20 percent. What percent of the stock’s 2007 starting price was the price of the stock at the end of 2009?

A. 80
B. 90
C. 95
D. 100
E. 108

Kudos for a correct solution.
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at Beginning of 2007, Stock = s

at End of 2007, Stock = s+(20/100)s = 1.2*s [Rose by 20%]

at End of 2008, Stock = 1.2*s - (25/100)1.2*s = 0.75*1.2*s [Dropped by 25%]

at End of 2009, Stock = 0.75*1.2*s + (20/100)0.75*1.2*s = 1.2*0.75*1.2*s = 1.08*s [Rose by 20%]

i.e. Stock at the end of 2009 = (108/100) of Stock at the beginning of 2007 = 108% of Stock at the beginning of 2007


Answer: Option E
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Lets take Magic Number 100 as stock price before 2007.

After 2007's 20 % increase, Stock Price = 100 + 20 = 120
After 2008's 30 % decrease, Stock Price = 120 - (25/100)*120 = 120 - 30 = 90
After 2009's 20 % increase , stock Price = 90 + (20/100) * 90 = 90 + 18 = 108

Final price is 8% more than Original Price or 108% of original price.

Hence Option E should be correct

Let price of stock at beginning of 2007 be $100
At end of 2007 , price pf stock= 100*120/100=120
At end of 2008, price of stock=120*75/100=90
At end of 2009, price of stock=90*120/100=108
Therefore, reqd %=108/100*100=108%
Answer E

800score Official Solution:

This problem is most easily solved by picking a number for the price at the beginning of 2007, and then determining what the prices would be in 2008 and 2009, given that starting number.

Since we are dealing with percents, let’s start with $100 for the price at the beginning of 2007. By the end of 2007, the price had risen 20 percent, up to $120. In 2008, the price dropped 25 percent, but it dropped from $120, not from the original $100. So the price at the end of 2008 was:
$120 – 0.25 × ($120) = $120 – $30 = $90.

In 2009, the stock price rose by 20 percent, but it rose from $90, not from $100 or $120. So the price at the end of 2009 was:
$90 + 0.20 × ($90) = $90 + $18 = $108.

Now, since our starting value was $100, the question is really asking was percent $108 is of $100:
$108 is 108% of $100.

The correct answer is choice (E).
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