Question 1202620
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please help me solve this problem .
The price of a stock appreciated by 24.70% of its value last month 
and then depreciated by 24.70% this month. By what percent did the stock 
appreciate or depreciate over the 2-month period? 
Express your answer as a positive or negative value 
based on the direction of the percentage change.
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<pre>
Let x be the starting price of the stock.

Then, according to the problem, the price of the stock appreciated 
to (1+0.247)x = 1.247x last month, and after that, depreciated to 
(1-0.247)*(1.247x) = 0.753*1.247x = 0.938991x.


So, the stock started from the price x and ended at the price 0.938991x.


It means that the stock depreciated in two months, and the percent 
of depreciation is 1-0.938991 = 0.061009 = 6.1009%.


Since the value of the stock decreased, the percentage change 
is negative  6.1009%,  or  -6.1009%.    <U>ANSWER</U>



Now, when you know the answer, I will show you another way to calculate it:

    (1+0.247)*(1-0.247) = 1 - 0.247^2 = 1 - 0.061009 = 0.938991.


Here you clearly see how consecutive increase and then decrease at the same rate
leads to decreasing the initial price.
</pre>

Solved, &nbsp;with explanations.


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If you want to see other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/percentage/lessons/Percentage-problems-on-chains-of-discounts.lesson>Percentage problems on chains of discounts</A> 

in this site.



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The formula in the post by @josgarithmetic is not precisely correct, 
so you better IGNORE his post, for your safety.


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He just edited his post after seeing my note.