# Example TIPS and how inflation rate affects its principal

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?

• 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%. Commented Jan 30, 2019 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!
– jed
Commented Jan 30, 2019 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. Commented Jan 31, 2019 at 14:27