GRE General TestQuantitative ReasoningHard
A financial analyst is evaluating an investment. The value of the investment increased by 20% in the first year and then decreased by 10% in the second year. If the initial investment was $10,000, what is its value at the end of the second year?
- A$10,800
- B$11,200
- C$11,000
- D$12,000
Show answer & explanationAnswer & explanation
Correct answer: A. $10,800
After the first year, the value is $10,000 * (1 + 0.20) = $10,000 * 1.20 = $12,000. In the second year, it decreases by 10% from this new value: $12,000 * (1 - 0.10) = $12,000 * 0.90 = $10,800.
Why the other options are wrong
- B. This is a plausible distractor, perhaps from incorrectly summing percentage changes.
- C. This would be the value if the net change was +10% of the original ($10,000 * 1.10).
- D. This is the value only after the first year's increase, not including the second year's decrease.
Successive Percentage Changes
Applying multiple percentage increases or decreases sequentially to a value, where each subsequent change is based on the new current value.
- Changes are multiplicative, not additive.
- Order of operations matters.
- Final value = Initial Value * (1 ± r1) * (1 ± r2) * ...
Memory trick: Multiply by (1+gain), then by (1-loss), for the final value, without cross!