Tina invested $30,000 in a stock. In the first year, the stock increased in value by 10%. In the second year, the stock decreased in value by 20%. What percentage gain is requird in the third year for Tina's stock to return to its original value?
13.6%
Let x be the factor by which the value changes in the third year. If you end up with the same amount after three years,
1.1 * 1.2 * x = 1
x = 0.7576
That would require a 24.24% LOSS in the third year
To find the required percentage gain in the third year for Tina's stock to return to its original value, we need to determine the net gain/loss from the first two years and then calculate the percentage gain needed in the third year.
First, let's calculate the value of the stock after the first year:
Increase in value = 10% of $30,000 = $30,000 * 0.10 = $3,000
Value after the first year = $30,000 + $3,000 = $33,000
Next, let's calculate the value of the stock after the second year:
Decrease in value = 20% of $33,000 = $33,000 * 0.20 = $6,600
Value after the second year = $33,000 - $6,600 = $26,400
Now, let's find out the required percentage gain in the third year for the stock to return to its original value:
Original value = $30,000
Current value after the second year = $26,400
Difference in value = Original value - Current value = $30,000 - $26,400 = $3,600
Percentage gain needed = (Difference in value / Current value) * 100
Percentage gain needed = ($3,600 / $26,400) * 100
Using a calculator or performing the division, we find:
Percentage gain needed = 13.6%
Therefore, Tina's stock needs to gain 13.6% in the third year for it to return to its original value.