The geometric rate of growth of sales for a company for the first three years was 25% and for the next three years was 40%. Is the claim of average growth being 65% valid? Give analytic reason in support of your answer.
Answers
Answer:
Average growth = 72.66 %
Step-by-step explanation:
The geometric rate of growth of sales for a company for the first three years was 25% and for the next three years was 40%. Is the claim of average growth being 65% valid? Give analytic reason in support of your answer.
Let say company was on x at start
after 1 year with 25% growth = x + (25/100)x = 1.25
after 2 year with 25% growth = 1.25x + (25/100)(1.25x) = 1.5625x
after 3 year with 25% growth = 1.5625x + (25/100)(1.5625x) = 1.953125x
after 4 Year with 40% growth = 1.953125x + (40/100)1.953125x = 2.734375x
after 5 Year with 40% growth = 2.734375x + (40/100)2.734375x = 3.828125x
after 6 Year with 40% growth = 3.828125x + (40/100)3.828125x = 5.359375x
Total growth in 6 years = 5.359375x - x = 4.359375x
Growth % in 6 years = 4.359375x/x * 100 = 435.9375 %
Average growth per year = 435.9375/6 = 72.66 %
72.66% > 65 %