If the national economy shrank to an annual rate of 9% per year for four consecutive years, then the economy shrank by 36% over the four-year period. The economy actually shrank b

Question

If the national economy shrank to an annual rate of 3% per year for four consecutive years, then the economy shrank by 9% over the four-year period. The economy actually shrank b

Answer 1

The statements in the question are not correct. Consider the first statement. If the economy shrank by 9% each year for 4 consecutive years, it shrank to (0.91)⁴ times its initial level.

(0.91)⁴ = 0.686 (with roundoff)

So it shrank to 68.6% of its initial level, which means it shrank by 31.4%, not 36%. A similar analysis can be applied to the second statement.

Where did this question come from?