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The library at a certain university reported that journal prices had increased by 160% over a period of 10 years. The report concluded that this represented a price increase of 16% each year. If journal prices had indeed increased by 16% each year, what percentage increase would that give over 10 years? (Round your answer as a percentage to the nearest whole number.)

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Answer:

  • report author's interpretation: 160%
  • report reader's interpretation: 341%

Step-by-step explanation:

Whenever you work with percentages, you need to understand what the base quantity is.

By saying that an increase of 160% over 10 years is an increase of 16% per year, the report's author has effectively said the base being used is the price in the first year.

When a reader of the report reads that the prices has increased 16% per year, the usual assumption would be that the base is the previous year's price. That is the assumption you're asked to make when you're asked to compute the result of an increase of 16% per year.

Under the assumption that the increase is 16% year on year, the multiplier over a period of 10 years is ...

  (1 +16%)^10 ≈ 4.411

So, the increase is ...

  (new -original)/original × 100%

  (4.411 -1)/1 × 100% = 341.1%

The percentage increase in 10 years from a 16% year-on-year increase would be 341%.

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Additional comment

Since the journal prices did indeed increase 16% each year (on average, based on the original price), the actual increase over 10 years is 160%, not 341%. Expressed as a year-on-year increase, that increase of 160% would average about 10.03% per year.

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