Due to a recession, expected inflation this year is only 2%. However, the inflat

Question

Due to a recession, expected inflation this year is only 2%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 2%. Assume that expectations theory holds and the real risk-free rate is r* = 3.25%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 2.25%, what inflation rate is expected after Year 1? Round your answer to two decimal places.

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Explanation / Answer

p(1)%=2.5% p(2)%=p(3)%=x% >2.5% r(1)%=r(2)%=r(3)%=3.25% Format: y(duration;year) : y(1;1)= [p(1)+r(1)] = [p(1)+r(1)] y(1;2)= [p(2)+r(2)] = [x%+3.25%] y(1;3)= [p(3)+r(3)] = [x%+3.25%] y(1;2)=y(1;3)=z% y(3;n)= [y(1;1)+3%] = [p(1)+r(1)+x%] Equation: (1+y(1;1)%)•(1+y(1;2)%)•(1+y(1;3)%) = (1+y(3;n)%)³ Solution: y(1;1) = (1+2.5%)•(1+3.25%) -1 = 0.0583125 = 5.83125% y(3;n) = (1+5.83125%)•(1+3%) -1 = 0.090061875 = 9.0061875% 1.0583125•(1+z%)•(1+z%) = 1.090061875³ (1+z%)²=1.090061875³/1.0583125 1+z%˜v1.223881938068371 ˜ 1.10629197686 z˜0.10629197686 ˜ 10.629197686% x = (1+z%)/(1+r%) -1 ˜ 1.10629197686 /1.0325 - 1 ˜ 0.071469 ˜ 7.14% p(2)=p(3)˜7.14% Or simply: (1+y%)(1+z%)²=((1+y%)(1+3%))³ y%=(1+2.5%)(1+3.25%) -1 z%=(1+x%)(1+3.25%) -1 (1.025•1.0325)((1+x%)•1.0325)² =(1.025•1.0325•1.03)³ (1+x%)² = (1.025•1.0325•1.03)³ / (1.025•1.0325³) (1+x%)² = 1.025²•1.03³ 1+x% = 1.025•v1.03³ = 1.025•1.03•v1.03 ˜ 1.07146923 p% = x% ˜ 7.14692%

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