Percent change/shrinkage

Question

I had previously submitted my homework question and received the correct answer. However, they did not explain how they reached that answer. My original homework question was: If the national economy shrank at an annual rate of 7% per year for three consecutive years, then the economy shrank by 21% over the three-year period. Is this statement true or false. If false, how much did the economy shrink over the three-year period? 

I received the correct answer of 19.56% but I have no idea how they got that answer. Any clarification would be appreciated. 

Answer 1

Let's use $1000 as the starting point.

If it shrank 7% for 3 years, after one year it would be

$930 which is 1000-70 (70 is 7 % of 1000)

 

After 2 years, it would be 930 - 65.1 (65.1 is 7% of 930) or 864.9

 

After 3 years, it would be 864.9 - 60.54 (60.54 is 7 % of 864.9) so you will end up with $804.36

 

Total decrease is $195.64.

 

Divide that by original which is $1000 and you get 19.56 %