Question

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 4.34 ​percent, the​ 30-year Treasury bond rate is 7.33 ​percent, and the inflation rate is 2.78 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

Answer 1

3-month real rate: 1.56%

30 years real rate: 4.42%

Step-by-step explanation:

We will calcualte the future value of the bond and adjust by inflation:

`Principal \: (1+ r)^(time) = Amount`

3.months TB:

Principal 100.00

time 1 quarter

rate 0.01085 (4.34% divide into 4 quarter)

`100 \: (1+ 0.01085)^(1) = Amount`

Amount 101.09

Adjusted for 2.78 annual inflation

`(Nominal)/((1 + inflation)^(time) ) = PV`

Nominal 101.09

time 1 quarter

Inflation 0.0278/4 = 0,00695

`(101.085)/((1 + 0.00695)^(1) ) = PV`

PV 100.39

100.39 / 100 - 1 = 0.39% quarterly rate:

0.39 x 4 = 1.56% real rate.

Because the time is low and difference in rate is lower there is no subtancial difference between the accurate method and the simplier method : nominal - inflation = 4.34 - 2.78 = 1.56

Now we do the same for the 30 years TB

`Principal \: (1+ r)^(time) = Amount`

Principal 100.00

time 30.00

rate 0.07330

`100 \: (1+ 0.0733)^(30) = Amount`

Amount 834.90

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 834.90

time 30.00

rate 0.0278

`(834.898884531252)/((1 + 0.0278)^(30) ) = PV`

PV 366.75

now we calculate the rate:

30√366.75/100 - 1 = 0.04427 = 4.42%