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.