Inflation

Once upon a time, the tsar owned a money printer and printed and printed. Printing money prices went up in the first year 2.7 %, in the second 2.1%, in the third 3.6%, and in the fourth 5.4%.

Then tsar failed in the election.

Calculate the average annual inflation rate (price increase percentage) during these four years.

Correct answer:

i =  3.4 %

Step-by-step explanation:

$$\begin{gathered} r_1=100\%+2.7\%=1+\frac{2.7}{100}=1.027 \\ {r}_2=100\%+2.1\%=1+\frac{2.1}{100}=1.021 \\ {r}_3=100\%+3.6\%=1+\frac{3.6}{100}=1.036 \\ {r}_4=100\%+5.4\%=1+\frac{5.4}{100}=1.054 \\ r=r_1\cdot r_2\cdot r_3\cdot r_4=1.027\cdot 1.021\cdot 1.036\cdot 1.054\doteq 1.145 \\ {r}_0=r^{1/4}=\sqrt[4]{1.145}\doteq 1.0344 \\ i=100\cdot (r_0-1)=100\cdot (1.0344-1)=3.4\% \end{gathered}$$

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