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Question 1202620: 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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Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39629)   (Show Source):
You can put this solution on YOUR website! depreciated by 24.7% based on what?
Based on month to month?
for the initial price, p
If this is what you have as the description, then simplify it.
Answer by ikleyn(52873)  (Show Source):
You can put this solution on YOUR website! .
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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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%. ANSWER
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.
Solved, with explanations.
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If you want to see other similar (and different) solved problems, look into the lesson
- Percentage problems on chains of discounts
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.
..................
He just edited his post after seeing my note.
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