To determine the Consumer Price Index (CPI) for 2014 and the inflation rate, we will first calculate the total cost of the consumer basket for the base year (2012) and for the year 2014. The CPI is calculated using the formula:
\[ \text{CPI} = \left(\frac{\text{Cost of Basket in Current Year}}{\text{Cost of Basket in Base Year}}\right) \times 100 \]
Let’s calculate the Cost of Basket for each year:
Step 1: Calculate the Cost of Basket for Each Year
Base Year (2012):
- Apples: 3 apples * $2/apple = $6
- Oranges: 2 oranges * $3/orange = $6
- Total cost for 2012 = $6 + $6 = $12
For 2014:
- Apples: 1 apple * $5/apple = $5
- Oranges: 2 oranges * $5/orange = $10
- Total cost for 2014 = $5 + $10 = $15
Step 2: Calculate the CPI for 2014
Using the formula for CPI:
\[ \text{CPI} = \left(\frac{15}{12}\right) \times 100 = 125 \]
Step 3: Calculate the Inflation Rate
The inflation rate is calculated using the formula:
\[ \text{Inflation Rate} = \left(\frac{\text{CPI}{\text{current}} - \text{CPI}{\text{previous}}}{\text{CPI}_{\text{previous}}}\right) \times 100 \]
In this case, we will consider CPI for the previous year 2013, which we will calculate now.
For 2013:
- Apples: 2 apples * $3/apple = $6
- Oranges: 1 orange * $4/orange = $4
- Total cost for 2013 = $6 + $4 = $10
Now, calculate CPI for 2013:
\[ \text{CPI}_{2013} = \left(\frac{10}{12}\right) \times 100 \approx 83.33 \]
Now calculate the inflation rate from 2013 to 2014:
\[ \text{Inflation Rate} = \left(\frac{125 - 83.33}{83.33}\right) \times 100 \approx 50.00% \]
Conclusion
Based on the calculations:
- CPI for 2014 is 125
- Inflation Rate is approximately 50.00%
Thus, the correct answer is:
E. 125 CPI, 50.60 percent inflation
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