Question

consumer price index
year xxx1 xxx2
housing 1320 1380
food 400 450
transportation 200 230
medical 460 550
education 550 650
apparel 190 170
recreation 150 110
other 300 330
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 the CPI values for year 1: \(1320 + 400 + 200 + 460 + 550 + 190 + 150 + 300\)
\(= 1320+400 = 1720\); \(1720+200 = 1920\); \(1920+460 = 2380\); \(2380+550 = 2930\); \(2930+190 = 3120\); \(3120+150 = 3270\); \(3270+300 = 3570\)

Step2: Calculate total CPI for year 2

Sum all the CPI values for year 2: \(1380 + 450 + 230 + 550 + 650 + 170 + 110 + 330\)
\(= 1380+450 = 1830\); \(1830+230 = 2060\); \(2060+550 = 2610\); \(2610+650 = 3260\); \(3260+170 = 3430\); \(3430+110 = 3540\); \(3540+330 = 3870\)

Step3: Use inflation rate formula

Inflation rate formula: \(\text{Inflation Rate} = \frac{\text{CPI}_2 - \text{CPI}_1}{\text{CPI}_1} \times 100\%\)
Substitute \(\text{CPI}_1 = 3570\) and \(\text{CPI}_2 = 3870\):
\(\frac{3870 - 3570}{3570} \times 100\%=\frac{300}{3570} \times 100\%\)
\(\approx 0.0840 \times 100\% = 8.4\%\) (rounded to nearest tenth)

Answer:

\(8.4\)