It is known that the inflation rate over next three years is expected to be 5% in the first year, 10% in the second and 15% in the third. In such a case, average expected annual inflation rate is
A)5.00%.
B)9.92%.
C)10.00%.
D)10.08%.
E)15.00%.

Question

Quizplus · Accepted Answer

The average expected annual inflation rate is calculated using the geometric mean, not the arithmetic mean, due to the compounding nature of inflation. The formula for the geometric mean is $\sqrt[n]{x_1 \cdot x_2 \cdot \ldots \cdot x_n}$, where $x_1, x_2, \ldots, x_n$ are the inflation factors (1 + inflation rate) for each year, and $n$ is the number of years. For the given rates, the inflation factors are 1.05, 1.10, and 1.15 for the first, second, and third years, respectively. The geometric mean is $\sqrt[3]{1.05 \cdot 1.10 \cdot 1.15}$ - 1, which equals approximately 0.0992 or 9.92% when converted to a percentage.

It Is Known That the Inflation Rate Over Next Three