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Due to a recession, expected inflation this year is only 2.75%. However, the inflation rate in...

Due to a recession, expected inflation this year is only 2.75%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 2.75%. Assume that the expectations theory holds and the real risk-free rate (r*) is 3%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 3%, what inflation rate is expected after Year 1? Round your answer to two decimal places.

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Answer #1

Yield on 1-year Treasury Bond = Real Risk-free Rate + Inflation Premium on 1-year Treasury Bond
Yield on 1-year Treasury Bond = 3.00% + 2.75%
Yield on 1-year Treasury Bond = 5.75%

Yield on 3-year Treasury Bond = Real Risk-free Rate + Inflation Premium on 3-year Treasury Bond
Yield on 3-year Treasury Bond = 3.00% + Inflation Premium on 3-year Treasury Bond

Yield on 3-year Treasury Bond = Yield on 1-year Treasury Bond + 3.00%
3.00% + Inflation Premium on 3-year Treasury Bond = 5.75% + 3.00%
Inflation Premium on 3-year Treasury Bond = 5.75%

Inflation Premium on 3-year Treasury Bond = Average Inflation over next 3 years
5.75% = [2.75% + 2 * Inflation for Year 2 and thereafter] / 3
17.25% = 2.75% + 2 * Inflation for Year 2 and thereafter
14.50% = 2 * Inflation for Year 2 and thereafter
Inflation for Year 2 and thereafter = 7.25%

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