Profit growth

The profit of a company increased by 25% during the year 1992, increased by 40% during the year 1993, decreased by 20% in the year 1994 and increased by 10% during the year 1995. Find the average growth in the profit level over the four years periods?

Correct result:

p =  11.3987 %

Solution:

$$\begin{gathered} q=(1+{\displaystyle \frac{25}{100}})\cdot (1+{\displaystyle \frac{40}{100}})\cdot (1-{\displaystyle \frac{20}{100}})\cdot (1+{\displaystyle \frac{10}{100}})={\displaystyle \frac{77}{50}}=1.54 \\ {p}_1=100\cdot (q-1)=100\cdot (1.54-1)=54\mathrm{\%} \\ {q}_2=q^{1\mathrm{/}4}=\sqrt[4]{1.54}\doteq 1.114 \\ p=100\cdot (q_2-1)=100\cdot (1.114-1)=11.3987\mathrm{\%} \end{gathered}$$

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One example about progression in percentage and depressed in percentage

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