3y inflation

The price of the cookie rise in the first year by 2%, the second year fell by 6%, and in the third year increased by 17%.

Calculate the average annual increase in the price of the cookie.

Correct answer:

p =  3.91 %

Step-by-step explanation:

$$\begin{gathered} r_1=100\%+2\%=1+\frac{2}{100}=1.02 \\ {r}_2=100\%-6\%=1-\frac{6}{100}=0.94 \\ {r}_3=100\%+17\%=1+\frac{17}{100}=1.17 \\ r=r_1\cdot r_2\cdot r_3=1.02\cdot 0.94\cdot 1.17\doteq 1.1218 \\ r=r_0^3 \\ {r}_0=r^{1/3}=\sqrt[3]{1.1218}\doteq 1.0391 \\ p=100\cdot (r_0-1)=100\cdot (1.0391-1)=3.91\% \end{gathered}$$

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