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Difficulty: MediumPercentages, Percent Change, and Interest

A technology company's annual revenue increased by 40%40\% from 2021 to 2022, and then decreased by 15%15\% from 2022 to 2023. If the company's annual revenue in 2023 was $476,000\$476,000, what was its annual revenue in 2021?

  1. A
    $336,000\$336,000
  2. B
    $380,800\$380,800
  3. $400,000\$400,000Answer
  4. D
    $404,600\$404,600
  5. E
    $560,000\$560,000

Answer

$400,000\$400,000
The correct answer is $400,000\$400,000. Expressing the multi-step percentage change relative to the initial 2021 revenue RR gives an intermediate 2022 value of 1.40R1.40R and a final 2023 value of 1.40R×0.85=1.19R1.40R \times 0.85 = 1.19R. Solving 1.19R=476,0001.19R = 476,000 yields R=400,000R = 400,000.

Step-by-Step Solution

1
Define the unknown variable and express successive percentage changes algebraically.
Let RR be the 2021 annual revenue. The 2022 revenue is R×(1+0.40)=1.40RR \times (1 + 0.40) = 1.40R. The 2023 revenue is 1.40R×(1−0.15)=1.40R×0.851.40R \times (1 - 0.15) = 1.40R \times 0.85.
Sequential percentage adjustments apply to the newly resulting base values rather than the initial value.
2
Calculate the net multiplier for the two-year change.
1.40×0.85=1.191.40 \times 0.85 = 1.19. Thus, the 2023 revenue equals 1.19R1.19R.
Multiplying the growth factor (1.401.40) by the decay factor (0.850.85) gives the overall percentage relationship between 2021 and 2023.
3
Solve for the initial revenue RR using the given 2023 revenue.
1.19R=476,000  ⟹  R=476,0001.19=400,0001.19R = 476,000 \implies R = \frac{476,000}{1.19} = 400,000.
Dividing the final amount by the combined multiplier determines the original starting revenue.

Key Concept

Successive Percent Change and Base Shift
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Topics

Percentages, Percent Change, and Interest

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