Question

state whether the following statement is true or false, and explain why. if the statement is false, state the true change.
the price of a stock falls by 23%, then later rises by 23%. after the two changes in value, the price is unchanged.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the statement is true because the percentages of the increase and decrease in the value of the stock are the same, so there is no net change in the price.
b. the statement is false because the reference values for the increase and decrease in the value of the stock are not the same. the true change in the price is %.
(simplify your answer. type an integer or decimal rounded to the nearest hundredth as needed.)

Explanation:

Step1: Define initial stock price

Let initial price = $P$

Step2: Calculate price after 23% fall

New price = $P \times (1 - 0.23) = 0.77P$

Step3: Calculate price after 23% rise

Final price = $0.77P \times (1 + 0.23) = 0.77P \times 1.23$
$= 0.9471P$

Step4: Calculate total percentage change

Change = $\frac{0.9471P - P}{P} \times 100\% = (0.9471 - 1) \times 100\% = -5.29\%$

Answer:

B. The statement is false because the reference values for the increase and decrease in the value of the stock are not the same. The true change in the price is -5.29%.