# 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?

Result

p =  11.399 %

#### Solution:

$q=(1+\dfrac{ 25 }{ 100 } ) \cdot \ (1+\dfrac{ 40 }{ 100 } ) \cdot \ (1-\dfrac{ 20 }{ 100 } ) \cdot \ (1+\dfrac{ 10 }{ 100 } )=\dfrac{ 77 }{ 50 }=1.54 \ \\ \ \\ p_{1}=100 \cdot \ (q-1)=100 \cdot \ (1.54-1)=54 \ \% \ \\ \ \\ q_{2}=q^{ 1/4 }=\sqrt[4]{ 1.54 } \doteq 1.114 \ \\ \ \\ p=100 \cdot \ (q_{2}-1)=100 \cdot \ (1.114-1) \doteq 11.3987 \ \% \doteq 11.399 \%$

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