Question

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?

Answer 1

I see you already received your answer, hope tomorrow goes an excellent route :)

Answer 2

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

`x - 0.172x = 0.828x`

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.

`100 - 82.80 = 17.20`

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

`17.20 / 82.80 = 0.2077`

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

`x - 0.828x`

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

`((x - 0.828x))/(0.828x) = (0.172x)/(0.828x) = 0.2077`

Or 20.77%