Relationship between Price index and purchasing power value?

If the price index rises from 100 to 120, the purchasing power value of the dollar;

will raise or fall?

I think I will fall by one-sixth.
It this right?

Answer:
You are right. Let us say the value of money or purchasing power was X when the Price Indes was 100.
NOw Price Index rises to 120, So the value of money or puchasing power will fall from X to [ {X divided by 120} multiplied by 100]. That the value of money will change in percentage terms by
[X - (100X/120)} / X which is equal to
1- 1/1.2 = 1 - 5/6 = 1/6 = 0ne-sixth16% approx. ( slughtly higher).
Purchading power or value of money falls because with 20% rise in prices you can buy 1/6 lower qauntity of goods and services on an average.

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