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The consumer price index (CPI), published by the Australian Bureau of Statistics, measures household inflation. In the June quarter of 2022, the CPI index was 126.1 and the percentage change from the corresponding quarter of the previous year was 6.1%. Given this information, the CPI index in the June quarter of 2021 was:  121.3   122.1   118.8                        119.7

Question

The consumer price index (CPI), published by the Australian Bureau of Statistics, measures household inflation. In the June quarter of 2022, the CPI index was 126.1 and the percentage change from the corresponding quarter of the previous year was 6.1%. Given this information, the CPI index in the June quarter of 2021 was:  121.3   122.1   118.8                        119.7

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Solution

To find the CPI index in the June quarter of 2021, we need to understand that the percentage change from the previous year is calculated as:

( (CPI in 2022 - CPI in 2021) / CPI in 2021 ) * 100%

We know the CPI in 2022 is 126.1 and the percentage change is 6.1%. We can rearrange the formula to solve for the CPI in 2021:

CPI in 2021 = CPI in 2022 / (1 + (percentage change / 100))

Substituting the given values:

CPI in 2021 = 126.1 / (1 + (6.1 / 100))

CPI in 2021 = 126.1 / 1.061

CPI in 2021 = 118.8

So, the CPI index in the June quarter of 2021 was 118.8.

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