When the price index rises from 100 to 120, it indicates an increase in the overall price level, meaning that the purchasing power of money decreases.
To determine the change in purchasing power, you can use the formula:
\[ \text{Purchasing Power} = \frac{1}{\text{Price Index}} \]
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Initial Purchasing Power (when the price index is 100): \[ \text{Purchasing Power} = \frac{1}{100} = 0.01 \]
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New Purchasing Power (when the price index is 120): \[ \text{Purchasing Power} = \frac{1}{120} \approx 0.00833 \]
To find the change in purchasing power, we can calculate the difference:
\[ \text{Change in Purchasing Power} = 0.01 - 0.00833 \approx 0.00167 \]
Now, applying percentage change:
\[ \text{Percentage Change} = \frac{\text{Change}}{\text{Original}} \times 100 = \frac{0.00167}{0.01} \times 100 \approx 16.67% \]
This shows a decrease in purchasing power by about 16.67%.
Given the options, the correct answer is:
will fall by one-sixth (approximately 16.67% decrease).
1 answer