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

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:

3.months TB:

Principal100.00

time1 quarter

rate0.01085 (4.34% divide into 4 quarter)

Amount101.09

Adjusted for 2.78 annual inflation

Nominal 101.09

time   1 quarter

Inflation 0.0278/4 =  0,00695

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

Principal100.00

time30.00

rate0.07330

Amount834.90

Maturity  834.90

time   30.00

rate   0.0278

PV   366.75

now we calculate the rate:

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