Final answer:
The purchasing power of the dollar will fall by one-sixth, or about 16.67%, when the price index rises from 100 to 120 due to inflation.
Step-by-step explanation:
When the price index rises from 100 to 120, it indicates that there has been inflation, meaning the overall level of prices for goods and services in the economy has increased. This means that the purchasing power of the dollar will decrease, because you now need more dollars to buy the same basket of goods. The question of how much the purchasing power falls is a matter of calculating the percentage decrease. In this case, the purchasing power of the dollar will fall by one-sixth, or approximately 16.67 percent. This is because the price index has increased by 20 percent (from 100 to 120), and the inverse of this increase (1/1.20) reflects the decrease in purchasing power.