Due to a recession, expected inflation this year is only 3.75%. However, the inflation rate in Year 2 and thereafter is expected to be constant at some level above 3.75%. 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

5.25%

Explanation:

To calculate the inflation for the year 3, we will have to calculate the yield on 1 Year treasury bond.

The yield is calculated using the following formula:

Nominal Yield on Bond = Real risk free rate + Inflation for the year

Here

Inflation for Year One is 3.75%

Real Risk-Free Rate is 3.5%

Nominal yield on bond is Y for year 1

By putting values, we have:

Y = 3.5% + 3.75% = 7.25%

For 3 years treasury bond,

Nominal Yield on Treasury Bond for 3 years = Yield on year 1 + Inflation

Y3 = 7.25% + 1.5% = 8.75 %

Now if we deduct the real risk free rate from the 3 year yield on the treasury bond, then the resultant rate would be the inflation rate for the year 3.

Inflation Rate for Year 3 = Y3 - Real Risk-Free Rate

Inflation Rate for Year 3 = 8.75% - 3.5%

Inflation Rate for Year 3 = 5.25%