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Taken from here.

Say the Treasury issues an inflation-protected security with a $1,000 face value and a 3 percent coupon. In the first year, the investor receives $30 in two semiannual payments. That year, the CPI increases by 4 percent. As a result, the face value adjusts upward to $1,040.

In Year 2, the investor receives the same 3 percent coupon but this time it’s based on the new, adjusted face value of $1,040. The result: instead of receiving an interest payment of $30, the investor receives interest of $31.20 (.03 times $1,040). In Year 3, inflation drops to 2 percent. The face value rises from $1,040 to $1060.80, and the investor receives interest of $31.82.

I'm mostly confused about this line In Year 3, inflation drops to 2 percent. The face value rises from $1,040 to $1060.80, and the investor receives interest of $31.82. Without knowing what the inflation rate was previous to "drop[ing] to 2 percent", how is the change in the principal of this TIPS calculated in this example?

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    But the previous inflation rate is known. It is 4%. The CPI is an index that tracks inflation. Saying the CPI increased by 4 percent is the same as saying that the rate of inflation is 4%. – Acccumulation Jan 30 at 20:23
  • @Acccumulation yes this was my confusion. I didn’t realized CPI and inflation rate could be taken synonymously. Thank you for clearing it up! – CCC Jan 30 at 20:25
  • @Jalep Strictly, CPI itself and the inflation rate are not synonymous: rather, the rate of inflation is (roughly) the change in the value of CPI over a given period. – TripeHound Jan 31 at 14:27
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According to the example, the inflation during year 2 (and measured at the beginning of year 3) was 2 percent. During year 1 it was 4 percent.

2 percent of $1,040 is $20.80. When you add the $20.80 to the previous face value of $1,040 you get $1,060.80.

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