If a stock price goes up by 5% one day, then goes down by 5% the next day, is the final price higher, lower, or the same as the original price?

Let’s denote the original stock price as S₀. The stock price increases by 5% on the first day, so the new price, S₁, can be calculated as:

S₁ = S₀(1 + 0.05) = 1.05S₀

On the next day, the stock price goes down by 5%. We will now calculate the final price, S₂, based on the updated price S₁:

S₂ = S₁(1 − 0.05) = 1.05S₀(1 − 0.05)

S₂ = 1.05S₀ × 0.95

S₂ = (1.05 × 0.95)S₀

S₂ = 0.9975S₀

As we can see, the final price S₂ is 99.75% of the original price S₀. Therefore, the stock price is lower than the original price after the two-day period.

For example, if the original stock price S₀ was $100, the final price S₂ would be:

S₂ = 0.9975 × 100 = 99.75

In this example, the stock price goes up to $105 on the first day and then drops to $99.75 on the second day — resulting in a net loss compared to the original price.