Question

The price of a stock decreased by $20\%$ in 2001, and then decreased by $20\%$ in 2002. What percent increase in 2003 will restore the price to its value at the beginning of 2001? Express your answer to the nearest hundredth.

Answer 1

To recover its initial value after decreasing by 20% in 2001 and 2002, the stock needs to increase by 56.25% in 2003.

Step-by-step explanation:

The question involves calculating the percentage increase required to recover from two consecutive years of stock price depreciation. Let's assume the initial value of the stock is $100 (for simplicity). After a 20% decrease in 2001, the value is reduced to $80. In 2002, the stock then decreases by another 20%, which brings the value down to $64, as 20% of $80 is $16, and $80 minus $16 is $64.

To return to the original $100 value in 2003, the stock must increase by the difference between $100 and $64, which is $36. The required percentage increase is found by dividing $36 by the starting value of 2003, which is $64, and then multiplying by 100 to get the percentage.

$36 / $64 × 100% = 56.25%

Therefore, the stock needs to increase by 56.25% in 2003 to restore its original value at the beginning of 2001.

Answer 2

2001—80/100 x
2002— 64/100 x
now we need to get x from 64/100 x