Due to a recession, expected inflation this year is only 3.25%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.25%. Assume that the expectations theory holds and the real risk-free rate (r*) is 2.5%. If the yield on 3-year Treasury bonds equals the 1-year yield plus 1.5%, what inflation rate is expected after Year 1?

5.5%

Explanation:

The computation of the inflation rate is expected after Year 1 is shown below:-

the Yield on year 1 treasury bond

Let us assume the inflation rate be I

r1 = risk free rate + Inflation rate

= 2.5% + 2.25%

= 5.75%

r3 = r1 + 0.50%

= 5.75% + 1.50%

= 7.25%

Now,

r3 = risk free rate + IP3

= 7.25% = 2.5% + IP3

IP3 = 4.75%

Year 1 Inflation = 4.75%

Year 2 Inflation = I

Year 3 Inflation = 2

So, inflation rate is expected after Year 1 = (3.25% + I + I) ÷ 3 = 4.75%

(3.25% + I + I) = 14.25%

2(I) = 11%

I = 5.5%

the answerr would be 1