Due to a recession, expected inflation this year is only 4.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 4.25%. Assume that the expectations theory holds and the real risk-free rate (r*) is 3.5%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 0.5%, what inflation rate is expected after Year 1

The inflation rate expected after Year 1 is 5%

Explanation:

In order to calculate the inflation rate expected after Year 1 we would have to make the following calculations:

Yield on 1 year treasury bond r1=r+inflation rate=3.5%+4.25%=7.75%

r3=r1+0.5%=7.75%+0.5%=8.25%

But r3=r+IP3

Therefore, 8.25%=3.5%+IP3

IP3=4.75%

So, inflation rate expected after Year 1=(4.25%+I+I)/3=4.75%

(4.25%+I+I)=14.25%

2(I)=10%

I=5%

The inflation rate expected after Year 1 is 5%

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