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

Answer:

3-month real rate: 1.56%

30 years real rate: 4.42%

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

$\frac{Nominal}{(1 + inflation)^{time} } = PV$  

Nominal 101.09

time   1 quarter

Inflation 0.0278/4 =  0,00695

$\frac{101.085}{(1 + 0.00695)^{1} } = PV$  

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

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity  834.90

time   30.00

rate   0.0278

$\frac{834.898884531252}{(1 + 0.0278)^{30} } = PV$  

PV   366.75

now we calculate the rate:

30√366.75/100 -  1 =  0.04427   = 4.42%