To find the Consumer Price Index (CPI) for the years 2010 and 2021, we will use the following formula:
[tex]\[ \text{CPI in a given year} = \left( \frac{\text{Cost of the basket in the given year}}{\text{Cost of the basket in the base year}} \right) \times 100 \][/tex]
Here, the base year is 2010, and the cost of the basket in the base year is [tex]$6,150.00.
### CPI for 2010:
Since 2010 is the base year, the cost of the basket in 2010 is used as the denominator and numerator in the formula:
\[ \text{CPI for 2010} = \left( \frac{6,150.00}{6,150.00} \right) \times 100 \]
Simplifying this:
\[ \text{CPI for 2010} = 1 \times 100 = 100.00 \]
So, the CPI for 2010 is 100.00.
### CPI for 2021:
To find the CPI for 2021, we use the cost of the basket in 2021, which is $[/tex]6,500.00, and compare it to the base year cost:
[tex]\[ \text{CPI for 2021} = \left( \frac{6,500.00}{6,150.00} \right) \times 100 \][/tex]
Calculating this:
[tex]\[ \text{CPI for 2021} = \left( \frac{6,500.00}{6,150.00} \right) \times 100 \approx 1.0569 \times 100 = 105.69 \][/tex]
So, the CPI for 2021 is 105.69.
Therefore, the final CPIs are:
- CPI for 2010: 100.00
- CPI for 2021: 105.69
