If CPI in 2016 was 300, and CPI in 2017 was 312, what is the annual rate of inflation?

Question

BlackTom AI · Accepted Answer

Inflation rate = (CPI_new − CPI_old) / CPI_old × 100%.

1. Relevant knowledge points and concepts
- The annual inflation rate is the percentage change in the Consumer Price Index (CPI) from one year to the next.
- Use the percentage change formula: (new − old) / old × 100%.

2. Step-by-step reasoning
- Plug the CPIs into the formula with CPI_old = 300 (2016) and CPI_new = 312 (2017).

3. Calculations with intermediate steps
- Difference: 312 − 300 = 12
- Proportion: 12 / 300 = 0.04
- Convert to percent: 0.04 × 100% = 4%

(Alternate view: 312 / 300 = 1.04 → subtract 1 to get 0.04 → 0.04 × 100% = 4%.)

4. Why the correct answer is correct
- The CPI increased by 12 points on a base of 300. That 12-point increase is 12/300 = 0.04 of the base, which is 4% of the 2016 CPI. Therefore the annual inflation rate from 2016 to 2017 is 4%.

5. Why the other options are incorrect
- a. 1.04%: Confuses the factor 1.04 (which represents a 104% level) with a percentage change; 1.04 as a percentage change would be 104%, not 1.04%. Here the change is 4%, not 1.04%.
- b. 12%: Treats the 12-point change as if the base were 100 instead of 300. The correct base is 300, so the change is 12/300 = 4%, not 12%.
- c. 3.12%: This misplaces the decimal (0.0312 instead of 0.04). There is no valid division of 12 by 300 that yields 0.0312, so this is a calculation error.

6. Conclusion
- The correct annual rate of inflation is 4%, matching answer d. 4%.

If CPI in 2016 was 300, and CPI in 2017 was 312, what is the annual rate of inflation?单项选择题

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