If the national economy shrank at an annual rate of 2​% per year for three consecutive​ years, then the economy shrank by 6​% over the three​-year period.

Question

State whether the following statement is true or false, and explain why. If the statement is false, state the true change.
If the national economy shrank at an annual rate of 2% per year for three consecutive years, then the economy shrank by 6% over the three-year period.

Answer 1

No it didn't, though the 6% figure isn't all that far off. Still, merely adding the percentage for each year isn't how it works. We would find the truth by realizing that losing 2% means keeping 98% of it. Each year, you are multiplying the current value by .98, which means you are taking it down by .98³ = .9412 . That means the actual percentage of decrease over the three years is 1 - .9412 = .0588  or  5.88% . Over a short span like this, the discrepancy is minimal, but over a longer time span, you would have seen a growing divergence between reality and the idea of adding up percentages.