Question

Suppose that the consumer price index of a country was 278.29 at Year X and 86.50 at the end of Year Y. What was the country’s inflation rate during Year Y.

Answer 1

To calculate the inflation rate between Year X and Year Y, we can use the following formula:

\[
\text{Inflation Rate} = \left( \frac{\text{CPI}_{\text{end}} - \text{CPI}_{\text{start}}}{\text{CPI}_{\text{start}}} \right) \times 100
\]

Here, \(\text{CPI}_{\text{start}}\) is the consumer price index at the beginning of the period (Year X) and \(\text{CPI}_{\text{end}}\) is the consumer price index at the end of the period (Year Y).

From the problem, we have:

- \(\text{CPI}_{\text{start}} = 278.29\) (at Year X)
- \(\text{CPI}_{\text{end}} = 86.50\) (at the end of Year Y)

Plugging in the values:

\[
\text{Inflation Rate} = \left( \frac{86.50 - 278.29}{278.29} \right) \times 100
\]

Calculating the difference:

\[
86.50 - 278.29 = -191.79
\]

Now substituting back into the formula:

\[
\text{Inflation Rate} = \left( \frac{-191.79}{278.29} \right) \times 100
\]

Calculating the division:

\[
\frac{-191.79}{278.29} \approx -0.689
\]

Now, converting to percentage:

\[
\text{Inflation Rate} \approx -0.689 \times 100 \approx -68.9\%
\]

Thus, the country's inflation rate during Year Y was approximately **-68.9%**, indicating deflation.