how do i get the actual economy shrinkage?

Question

If the national economy shrank at an annual rate of 4% per year for four consecutive years, then the economy shrank by 9% over the four-year period.

The actual question is looking for a true or false answer, I am looking for the formula to obtain that it is false but how.

Answer 1

If it shrank by 4% each year, then at the end of a year it is (100 - 4)% = 96% of what it was at the start of the year, which is 0.96 times as much.  Keep this up 4 years in a row, assuming you started at 100%, and get

 

E = (100%)(0.96)⁴ ≅ 84.93%

 

Note that is not 9% lower than 100%.

 

FALSE