To determine the Consumer Price Index (CPI) for year 2, we need to follow several steps. We start by calculating the cost of the basket in both year 1 and year 2, and then use these costs to find the CPI for year 2. Here is the step-by-step solution:
1. Calculate the cost of the basket in year 1:
- Number of toothbrushes: 5
- Number of tubes of toothpaste: 2
- Price of one toothbrush in year 1: [tex]$1.00
- Price of one tube of toothpaste in year 1: $[/tex]2.00
The total cost of the basket in year 1 is:
[tex]\[
\text{Cost in year 1} = (5 \times 1.00) + (2 \times 2.00)
\][/tex]
[tex]\[
\text{Cost in year 1} = 5.00 + 4.00 = 9.00
\][/tex]
2. Calculate the cost of the basket in year 2:
- Number of toothbrushes: 5
- Number of tubes of toothpaste: 2
- Price of one toothbrush in year 2: [tex]$1.25
- Price of one tube of toothpaste in year 2: $[/tex]2.10
The total cost of the basket in year 2 is:
[tex]\[
\text{Cost in year 2} = (5 \times 1.25) + (2 \times 2.10)
\][/tex]
[tex]\[
\text{Cost in year 2} = 6.25 + 4.20 = 10.45
\][/tex]
3. Calculate the CPI for year 2:
The CPI is calculated using the formula:
[tex]\[
\text{CPI} = \left(\frac{\text{Cost in year 2}}{\text{Cost in year 1}}\right) \times 100
\][/tex]
Substituting the values we have:
[tex]\[
\text{CPI} = \left(\frac{10.45}{9.00}\right) \times 100
\][/tex]
[tex]\[
\text{CPI} = 1.1611111 \times 100 = 116.11
\][/tex]
Therefore, the correct answer is:
D. 116.11
