Question

consumer price index

consumer price index
year | xxx1 | xxx2
housing | 1450 | 1560
food | 400 | 440
transportation | 450 | 510
medical | 520 | 560
education | 470 | 530
apparel | 320 | 360
recreation | 200 | 210
other | 270 | 290

calculate the inflation rate from year 1 to year 2 using the consumer price index.
?%

round to the nearest tenth of a percent.

Explanation:

Step1: Calculate total CPI for year 1

Sum all CPI components for year 1: \(1450 + 400 + 450 + 520 + 470 + 320 + 200 + 270\)
\(= 1450 + 400 = 1850\); \(1850 + 450 = 2300\); \(2300 + 520 = 2820\); \(2820 + 470 = 3290\); \(3290 + 320 = 3610\); \(3610 + 200 = 3810\); \(3810 + 270 = 4080\)

Step2: Calculate total CPI for year 2

Sum all CPI components for year 2: \(1560 + 440 + 510 + 560 + 530 + 360 + 210 + 290\)
\(= 1560 + 440 = 2000\); \(2000 + 510 = 2510\); \(2510 + 560 = 3070\); \(3070 + 530 = 3600\); \(3600 + 360 = 3960\); \(3960 + 210 = 4170\); \(4170 + 290 = 4460\)

Step3: Use inflation rate formula

Inflation rate formula: \(\text{Inflation Rate} = \frac{\text{CPI}_2 - \text{CPI}_1}{\text{CPI}_1} \times 100\%\)
Substitute \(\text{CPI}_1 = 4080\), \(\text{CPI}_2 = 4460\):
\(\frac{4460 - 4080}{4080} \times 100\% = \frac{380}{4080} \times 100\% \approx 9.3\%\)

Answer:

\(9.3\%\)