One year ago you put $500 into a newly opened savings account earning 4 percent interest. On that day the consumer price index was 120. Today, the same consumer price index is 132.
1. The realized real rate of interest on your savings account was -2.0 percent.
2. $52 would have been sufficient to compensate you for the increase in prices that occurred during the year.
3. If the savings account had been indexed by the local CPI you would have about $572 in your account instead of the $520 you now have.
4. All of the above statements are true.
Choose the correct option.
The correct answer is 3. Without indexing, you earned $20 interest ($500 times .04). With indexing, given the 10 percent rise in the CPI, you would now have in your account the inflation-adjusted principal of $550 ($500 times 1.10) plus interest amounting to $22 ($20 times 1.10). Option 1 is clearly wrong---the realized real rate of interest is approximately equal to the nominal rate of interest (4 percent) minus the actual inflation rate (10 percent). This difference equals minus 6 percent.
Had you been quick off the mark, not calculating all the options, you might have chosen 2. It is indeed true that the difference in your account balance would have been $52. But that does not mean that $52 would have been sufficient to compensate you for the inflation that occurred. Suppose that people typically spend half their income on housing whereas you live with your parents for free. You don't consume the same mix of goods that other people consume. The index of the goods you buy is not well represented by the CPI.