Skip to content

CMA Foundation · Fundamentals of Business Mathematics and Statistics · Arithmetic Progression and Geometric Progression

A firm's sales grew by 20% in the first year and by 80% in the second year. What is the equivalent constant yearly growth rate over the two years (approximately the geometric mean of growth factors 1.2 and 1.8)?

The equivalent constant growth rate is about 46.9% per year. Compound growth uses the geometric mean of growth factors: the square root of 1.2 times 1.8, which is the square root of 2.16, about 1.47. The arithmetic mean of 50% overstates it.

  1. A50%
  2. B46.9%Correct
  3. C40%
  4. D30%

Explanation

Growth factors are 1.2 and 1.8, product 2.16. The square root of 2.16 is about 1.4697, so the rate is about 46.9%. The 50% option is the simple average of 20% and 80%... actually 50% is the arithmetic mean, which overstates the compound rate.

Did you get it right without looking?

One question tells you little. A timed set on Arithmetic Progression and Geometric Progression shows your real accuracy, how long you take and where you lose marks.

Practise Arithmetic Progression and Geometric ProgressionFree diagnostic mock

More Arithmetic Progression and Geometric Progression questions