Discuss QUESTION #4 supr ose you expect the rate of inflation to be 5% next year

Question

Discuss QUESTION #4 supr ose you expect the rate of inflation to be 5% next year, then fall to 3% or the following year, and then-decrease to 2% for each ofthe following years. Suppose r is to reman constant at 2%ard the maturuv risk premium is 0 for the 1" year, and will increase by .10% for each following year, up to a limit of 1 0% Calculate the rate of interest (r) on the following term bonds: 1) List and explain each component of the formula to calculate the rate of interest (r) 2) Calculate the rate of interest with the above information for a 1-year bond 3) Calculate the rate of interest with the above information for a 5-year bond ) Calculate the rate of interest with the above information for a 10-year bond 5) Calculate the rate of interest with the above information for a 15-year bond 6) Calculate the rate of interest with the above information for a 20-year bond 2

Explanation / Answer

Expected inflation is to be 5 % next year, then fall to 3 % for the following year, and then to decrease to 2 % for each of the following years.

r * = 2 %

Maturity Risk Premium (MRP) is O for the 1st year and it will increase by 0. 10 % for each of the following year upto a limit of 1%

Calculate the Rate of Interest (r) for the 1 - Year Treasury Bond:

Real - rate of interst is 2 % (It is expected to remains constant for the further years also)

Inflation is expected to be:

Year 1

5.00%

Year 2

3.00%

Year 3

2.00%

Maturity Risk Premium is " 0 " for the 1st year

r = r * + IP + MRP + DRP + LP

k = 0. 02 + 0. 05 + 0 + 0 + 0

= 0.07 or 7%

Therefore, the rate of interest (r) for a 1 - year bond is 7 %

Calculate the Rate of Interest (r) for the 5-Year Treasury Bond:

Averaged inflation =0.05 +0.03 + 0.02 +0.02 +0.02

=0.028

Maturity Risk Premium (MRP) is 0 for the year and it will increase by 0.10% for each following year up to a limit of 1.0%

Therefore,the 1 year MRP is 0%

   MRP

Average MRP = (0.00 + 0.001+0.002 + 0.003 + 0.004)/5

=0.002

r=r*+IP+MRP+DRP+LP

K= 0.02+0.028+0.002+0+0

= 0.05 (or)5%

Therefore, the Rate of Interest (r) for the 5-year Treasurybond is 5%

Calculate the Rate of Interest (r) for the 10-Year Treasury Bond:

Average inflation = (005+0.03+ 0.02+0.02+0.02+0.02+0.02+0.02+

0.02+0.02)/10

=0.024

   MRP

Average MRP( MRP% ) =(0.00+0.001+0.002 +0.003+0.004 +0.005+0.006+0.007+0.008+

0.009)/5

= 0.005

r=r*+IP+ MRP+ DRP+LP

K=0.02 + 0.024 + 0.005 +0 + 0

= 0.049 (or) 4.9%

Therefore, the Rate of Interest (r) for the 10-year Treasury bond is 4.9%

Calculate the Rate of Interest (r) for the 15-Year Treasury Bond:

Average inflation =0.02266

Average MRP for 15 years is 0.006

r=r*+IP+MRP+DRP+LP

k =0.02 +0.02266 +0.006+0+0

= 0.04866 (or)4.87%

Therefore, the Rate of Interest (r) for the 15-year Treasury bond is 4.87%

Calculate the Rate of Interest (r) for the 20-Year Treasury Bond:

Average inflation = 0.022

Average MRP for 20 years is 0.00725

r=r*+IP+MRP+DRP+LP

k: =0.02+0.022+0.00725+0+0

= 0.04925 (or) 4.925%

Therefore, the Rate of Interest (r) for the 20-year Treasury Bond is 4.925%

Year 1

5.00%

Year 2

3.00%

Year 3

2.00%

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