25. The following table shows the price of a specific stereo receiver for a five-year period. Using Year 1 as the base year, calculate the price index for each year.
Year Price Price index
(answers using
Year 1 = 100)
1 $112 ___
2 144 ___
3 160 ___
4 176 ___
5 200 ___
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100
200
300
400
500
To calculate the price index for each year, we need to compare the price in each year to the price in the base year (Year 1).
1. For Year 1, the price index is always set to 100 since it is the base year.
2. To calculate the price index for Year 2, divide the price in Year 2 by the price in Year 1 and multiply by 100:
Price index (Year 2) = (Price in Year 2 / Price in Year 1) * 100 = (144 / 112) * 100 = 128.57
3. To calculate the price index for Year 3, divide the price in Year 3 by the price in Year 1 and multiply by 100:
Price index (Year 3) = (Price in Year 3 / Price in Year 1) * 100 = (160 / 112) * 100 = 142.86
4. To calculate the price index for Year 4, divide the price in Year 4 by the price in Year 1 and multiply by 100:
Price index (Year 4) = (Price in Year 4 / Price in Year 1) * 100 = (176 / 112) * 100 = 157.14
5. To calculate the price index for Year 5, divide the price in Year 5 by the price in Year 1 and multiply by 100:
Price index (Year 5) = (Price in Year 5 / Price in Year 1) * 100 = (200 / 112) * 100 = 178.57
Therefore, using Year 1 as the base year, the price index for each year is as follows:
Year 1: 100
Year 2: 128.57
Year 3: 142.86
Year 4: 157.14
Year 5: 178.57
To calculate the price index for each year, you need to follow these steps:
1. Determine the price of the stereo receiver in Year 1 (base year). In this case, it is given as $112.
2. For each subsequent year, divide the price of the stereo receiver by the price in Year 1 and multiply by 100 to express the price index using Year 1 as the base year.
Here's how you can calculate the price index for each year:
Year 1:
Price index = (Price in Year 1 / Price in Year 1) * 100
The price index for Year 1 is [(112 / 112) * 100] = 100.
Year 2:
Price index = (Price in Year 2 / Price in Year 1) * 100
The price index for Year 2 is [(144 / 112) * 100] = 128.57 (rounded to two decimal places).
Year 3:
Price index = (Price in Year 3 / Price in Year 1) * 100
The price index for Year 3 is [(160 / 112) * 100] = 142.86 (rounded to two decimal places).
Year 4:
Price index = (Price in Year 4 / Price in Year 1) * 100
The price index for Year 4 is [(176 / 112) * 100] = 157.14 (rounded to two decimal places).
Year 5:
Price index = (Price in Year 5 / Price in Year 1) * 100
The price index for Year 5 is [(200 / 112) * 100] = 178.57 (rounded to two decimal places).
So, the price index for each year are as follows:
Year 1: 100
Year 2: 128.57
Year 3: 142.86
Year 4: 157.14
Year 5: 178.57