Question

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? Round your answer to two decimal places.

Answer 1

Answer:

inflation rate after 1 year is 5.00%

Explanation:

expected inflation  = 4.25%

risk-free rate (r) =  3.5%

Treasury bonds = 1-year yield plus 0.5%

to find out

what inflation rate is expected after Year 1

solution

we say that yield on 1st year treasury bond is here

r1 = r + inflation rate = 3.5 + 4.25 = 7.75 %

and in 3rd year bond bond value is

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

and

r3 = r + inflation3

so  inflation3  = 8.25 - 3.5 = 4.75 %

so

for 1st year inflation is = 4.25 %

and for 2nd year inflation is = I

and for 3rd year inflation is = I

so mean of these

$\frac{4.28 + I + I}{3} = 4.75$

so I = 5.00 %

so

inflation rate after 1 year is 5.00%