Question

On Monday, a stock market index goes up \(5.00 \% .\) On Tuesday, the index goes down \(5.00 \% .\) What is the net percentage change in the index for the two days?

Short answer

Answer: -0.25%

Step-by-step solution

Find the index value after the first day

Let the initial value of the index be \(x\). After the first day, it goes up by 5%. So the new value of the index is: \(x * (1 + 5\%) = x * 1.05\)

Find the index value after the second day

On the second day, the index goes down by 5%. We apply the 5% decrease to the value we got from Step 1: \((x * 1.05) * (1 - 5\%) = (x * 1.05) * 0.95\)

Simplify the index value

Now we can simplify the expression from Step 2: \((x * 1.05) * 0.95 = x * 1.05 * 0.95 = x * 0.9975\)

Calculate the net percentage change

To find the net percentage change, we consider the difference between the final value and the initial value, divided by the initial value: \(\frac{(x*0.9975) - x}{x}\). We can simplify this expression: \(\frac{0.9975x - x}{x} = \frac{-0.0025x}{x}= -0.0025 =-0.25\%\) So, the net percentage change in the index for the two days is -0.25%.