Profit growth

A company's profit increased by 25% during 1992, increased by 40% during 1993, decreased by 20% in 1994, and increased by 10% during 1995. Find the average growth in the profit level over the four years.

Correct answer:

p =  11.3987 %

Step-by-step explanation:

$$\begin{gathered} q_1=100\%+25\%=1+\frac{25}{100}=1.25 \\ {q}_2=100\%+40\%=1+\frac{40}{100}=1.4 \\ {q}_3=100\%-20\%=1-\frac{20}{100}=0.8 \\ {q}_4=100\%+10\%=1+\frac{10}{100}=1.1 \\ q=q_1\cdot q_2\cdot q_3\cdot q_4=1.25\cdot 1.4\cdot 0.8\cdot 1.1=\frac{77}{50}=1.54 \\ {p}_1=100\cdot (q-1)=100\cdot (1.54-1)=54\% \\ {q}_5=q^{1/4}=\sqrt[4]{1.54}\doteq 1.114 \\ p=100\cdot (q_5-1)=100\cdot (1.114-1)\%=11.3987\% \end{gathered}$$

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