You bought some stock, and then the stock price went down by 17.2% from the purchase price. By what percentage would the price have to increase for the investment to be back to the original value?

Step-by-step explanation:

Let's pick some easy numbers for illustration.

Let x equal our initial stock purchase, and, say it was $100.

x = $100

The problem says it's value dropped by 17.2%. If x = 100 is 100% of our stock value the 17.2% less is

[tex]x - 0.172x = 0.828x[/tex]

So now our stock is worth 0.828(100) = $82.80.

Now how much of an increase do we need to get back to $100.

[tex]100 - 82.80 = 17.20[/tex]

So our base is $82.80 because our stock price dropped, we want to know what percent increase is $17.20 of $82.80

[tex]17.20 \div 82.80 = 0.2077[/tex]

Or 20.77% increase to get back to original price.

To make this generic, since $100 is not supplied information, substitute x for 100 and 0.828x for the amount of money dropped.

x = original stock value

[tex]x - 0.828x [/tex]

Is the amount of value lost, and to be regained in the second part of the question.

To find out what portion the decrease is of the new value

[tex] \frac{(x - 0.828x)}{0.828x} = \frac{0.172x}{0.828x} = 0.2077 [/tex]

Or 20.77%

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