Suppose a basket of goods and services has been selected to calculate the CPI and Year 1 has been selected as the base year. In Year 1, the basket's cost was $50; in Year 2, the basket's cost was $52; and in Year 3, the basket's cost was $55. The value of the CPI in Year 3 was

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To evaluate the CPI for Year 3 with Year 1 as the base, we compare the cost of the basket in Year 3 to the cost in the base year and multiply by 100.
Option 1: 104.0. This would come from (Year 2 cost / Year 1 cost) × 100, since 52/50 × 100 = 104.0. While this is the Year 2 index, it does not represent Year 3.
Option 2: 90.9. This value would arise if the Year 3 cost were 45.5 while the base year cost is 50 (45.5/50 × 100 = 90.9). But the given Year 3 cost is 55, so this is not correct for Year 3.
Option 3: 110.0. This is computed as (Year 3 cost / Year 1 cost) × 100 = (55 / 50) × 100 = 1.1 × 100 = 110.0. This uses the base year cost of 50 and Year 3 cost of 55, matching the definition of the CPI with Year 1 as base.
Option 4: 105.0. This would correspond to a Year 3 cost of 52.5 (since 52.5/50 × 100 = 105.0), which does not align with the given Year 3 cost of 55. Hence this option misrepresents the data.
In summary, the correct CPI for Year 3, using Year 1 as the base year with base cost 50, is derived from 55 divided by 50, scaled by 100, yielding 110.0. The other options either reflect Year 2 data, a mismatch with the base-year definition, or incorrect arithmetic based on the provided costs.

Suppose a basket of goods and services has been selected to calculate the CPI and Year 1 has been selected as the base year. In Year 1, the basket's cost was $50; in Year 2, the basket's cost was $52; and in Year 3, the basket's cost was $55. The value of the CPI in Year 3 was

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