A price decreases by 20% and then increases by 20%. Is the final price equal to the original price?

• A. No; the final price is 100% of the original
• B. Yes; the final price is equal to the original
• C. No; final price is 96% of the original (a 4% decrease)
• D. No; final price is 80% of the original

Answer: (C)

Understanding how percent changes compound is key. A 20% drop leaves you with 80% of the original price. Then increasing that new amount by 20% adds 20% of 0.8 of the original, which is 0.16 of the original. So the final price is 0.80P + 0.16P = 0.96P, meaning it’s 96% of the original (a 4% decrease). The reason is that percent changes apply to the current value, and multiplying the factors 0.8 and 1.2 yields 0.96, regardless of order.