Question

f) The price of petrol per litre has risen by 5%, 10%, 12%, 15% and 18% in each of five year successive years. Determine the geometric mean rise. (5 Marks)

Answer 1

The geometric mean rise is used for estimating average growth of some values and can be calculated using the formula

$$GM=\sqrt[n]{x_1\cdot x_2\cdot x_3\cdot ... \cdot x_{n}},$$

which in our case (for the costs becoming 1.05, 1.1, ..., 1.18 times more expensive) gives

$$GM=\sqrt[5]{1.05\cdot 1.10\cdot 1.12\cdot 1.15 \cdot 1.18}=1.119.$$

Therefore, every year the petrol costs 1.119 times more on the average than in the previous year (it adds 11.9% of its price for the past year).