A CPI has three groups. Food: weight 40, price index 120. Housing: weight 35, price index 110. Other: weight 25, price index 104. The base year index is 100. What is the CPI, and by how much have prices risen since the base year?
- Weight × index: 40 × 120 = 4,800; 35 × 110 = 3,850; 25 × 104 = 2,600.
- Sum = 4,800 + 3,850 + 2,600 = 11,250; sum of weights = 100.
- CPI = 11,250 ÷ 100 = 112.5.
Answer: The CPI is 112.5, so prices have risen by 12.5% since the base year.