An investment account loses 20% of its value in January, gains 25% in February, and then loses 10% in March. What is the overall percent change in the account value over the three months?
- A 10% decrease (correct answer)
- A 5% decrease
- No change
- A 5% increase
Explanation: When you encounter percent change problems involving multiple periods, remember that these changes compound—they don't simply add or subtract. You must apply each percentage change to the result of the previous change. Let's start with an initial value of $100 to make the calculations clear. In January, the account loses 20%, so it becomes $100 × 0.80 = $80. In February, it gains 25% of its current value: $80 × 1.25 = $100. Finally, in March, it loses 10% of the February value: $100 × 0.90 = $90. The account went from $100 to $90, representing a $10 decrease on the original $100, which is a 10% decrease overall. Looking at the wrong answers: Choice B (5% decrease) likely comes from incorrectly adding the percentages: -20% + 25% - 10% = -5%. However, this ignores the compounding effect. Choice C (no change) might result from noticing that after February, the account returned to its original value, but this overlooks March's 10% loss. Choice D (5% increase) could come from miscalculating the percentage arithmetic or applying the changes in the wrong order. The key strategy here is to always work with the actual values step by step rather than trying to shortcut with percentage arithmetic. Set up a simple example with $100 as your starting point, apply each change sequentially, and then calculate the overall percent change from beginning to end.