Question

(Real

interest​ rates: approximation

method​)

The CFO of your firm has asked you for an approximate answer to this​ question: What was the increase in real purchasing power associated with both​ 3-month Treasury bills and​ 30-year Treasury​ bonds? Assume that the current​ 3-month Treasury bill rate is

5.26

​percent, the​ 30-year Treasury bond rate is

7.71

​percent, and the inflation rate is

2.09

percent.​ Also, the chief financial officer wants a short explanation should the​ 3-month real rate turn out to be less than the​ 30-year real rate.

The inferred real interest rate of Treasury bills is

​%.

​(Round to two decimal​ places.)The inferred real interest rate of Treasury bonds is

​%.

​(Round to two decimal​ places.)

Should the​ 3-month real interest rate turn out to be less than the​ 30-year real interest​ rate?  ​(Select the best choice​ below.)

A.

​Yes, the​ 30-year real interest rate should exceed the​ 3-month real interest rate because of the maturity premium demanded by investors.

B.

​Yes, the​ 30-year real interest rate should exceed the​ 3-month real interest rate because the two securities are sold in different markets.

C.

​Yes, the​ 30-year real interest rate should exceed the​ 3-month real interest rate because inflation only affects the​ long-term security.

D.

​Yes, the​ 30-year real interest rate should exceed the​ 3-month real interest rate because the goverment demands lower rates for lending short term

Answer 1

The real interest on treasury bill = (Nominal interest rate - inflation rate) /(1+ inflation rate) = (0.0526-0.0209)/(1+0.0209) = 0.03105 = 3.105% = 3.11%

The real interest rate on treasury bond = ( 0.0771-0.0209)/(1+0.0209) = 0.0550 = 5.50%

Should the​ 3-month real interest rate turn out to be less than the​ 30-year real interest​ rate?

Answer: Option A:​Yes, the​ 30-year real interest rate should exceed the​ 3-month real interest rate because of the maturity premium demanded by investors.