State whether the following statement is true or​ false, and explain why. If the statement is​ false, state the true change.

Question

If the national economy shrank at an annual rate of 11​% per year for four consecutive​ years, then the economy shrank by 44​% over the four​-year period.

A. The statement is false because each year there is a different reference value. The economy actually shrank by ____% over the four​-year period.

B.

The statement is true because 4×11​% is 44%.

Answer 1

Hi Brianna:

This is a classic example of compound interest, interest accumulates on interest.

Therefore, 4 consecutive years of 11%must accumulate to MORE than 44%.

Statement B is FALSE.

The economy actually shrunk by (1 - 11%)⁴ = 0.89⁴ =0.6274 = 62.74% (which quite a bit more than 44%).