Suppose that you own a one-year bond indexed by the CPI paying a real interest rate of 4 percent. A 10 percent rise in the CPI that happens to be fully anticipated occurs.
1. You will receive 114.4 percent of the face value of the bond at the end of one year.
2. You will be paid interest at a contracted interest rate of 14 percent because when there is anticipated inflation the market interest rate always equals the real interest rate plus the expected rate of inflation.
3. Because you willingly purchased the bond fully expecting the inflation, the indexing fully compensates you for it.
4. All of the above are true.
Choose the correct option.
Option 1 is correct. Indexing guarantees you repayment of principal plus interest equal to 4 percent of the principal, both adjusted by the percentage growth of the CPI. For every dollar of principal you will therefore receive (1.04)(1.10) = 1.144 dollars. All of the other choices are wrong---4 percent, not 14 percent, is the contracted interest rate, and indexing by the CPI only compensates you for the inflation if you consume the exact bundle of goods used in constructing the CPI.
If you chose 2 you might not have realized that the usual method of compensating for anticipated inflation---adding a premium to the interest rate equal to the expected inflation rate---is unnecessary when there is indexing. The indexing provisions take care of both anticipated and unanticipated inflation. True, you would have received the same amount in this particular case had there been no indexing, because the nominal interest rate would have then been 14 percent, but this is only because the inflation that occurs happens to be fully anticipated.
In the case of option 3, it is true that by choosing to purchase the bond you entered into the contract voluntarily. You therefore must have thought that this was the best form in which to hold that portion of your wealth. But you might still have been better off had the anticipated inflation not occurred. You would then have received 4 percent real interest independently of whether you happen to consume the same bundle of goods as was used in constructing the CPI.