Question

The value of stocks can vary dramatically. Suppose a stock decreases in value by 50% one year. The next year it increases by 50%. By how many percent has the value of the stock decreased over the two year period?

Answer 1

Answer: The stock is decreased by 25% over the two year period.

Step-by-step explanation:

Since we have given that

Decrease in value in one year = 50% = x

Increase in value in second year = 50% = y

So, Net change in stock over the two year period is given by

$x-y-\dfrac{xy}{100}\\\\=-50+50-\dfrac{50\times 50}{100}\\\\=0-\dfrac{2500}{100}\\\\=-25\%$

Hence, the stock is decreased by 25% over the two year period.

Answer 2

Answer:

Step-by-step explanation:

Let the initial value of stock is t.

The value of stock after one year = 50% of the value of stock initially

                                                        =  50 t / 100 = t / 2

The value of stock after one more year = increases by 50%

                                                                 = t/2 + 50% of t/2

                                                                 = t/2 + t/4  = 3t/4

Decreased value after 2 years = t - 3t/4 = t/4

Percentage decrease = decreased value x 100 / initial value

                                    = t/4t x 100 = 25%

Thus, the value of stock is decreased by 25% in two years.