CMA Foundation · Fundamentals of Business Economics and Management · Money and Banking
In an economy the price index rises from 125 to 200 over several years. Taking the value of money as the reciprocal of the price index, by what percentage has the purchasing power of money fallen?
Purchasing power has fallen by 37.5%. The value of money is the reciprocal of the price index, so it moves from 1/125 to 1/200, which is 125/200 = 62.5% of the original. The decline is therefore 100 − 62.5 = 37.5%, not the 60% rise in prices.
- A60%
- B37.5%Correct
- C75%
- D40%
Explanation
Value of money initially = 1/125 and later = 1/200. The fall = (1/125 − 1/200)/(1/125) = 1 − 125/200 = 1 − 0.625 = 37.5%. The 60% figure is the rise in prices (75/125), the wrong base. Check: 0.625 × 125 = 78.1... equals 1/200 scaled correctly to 62.5% of the original.
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