Question

A Treasury bill is a discount bond issued by the U.S. Treasury. Suppose that on January 1, 2012, a one-year Treasury bill with $1000 face value is sold at $970.87. Investors expect that the inflation rate will be 2% during 2012, but at the end of the year, the inflation turns out to have been 1%. What is the nominal interest rate on the bill (measured as the yield to maturity), the expected real interest rate, and the actual real interest rate?

Answer 1

Consider the given problem here the “FV = Face Value” of the “T-bill” is “1000” and the “Actual Price or Present Value” is “970.87”. It’s a one year discounted bond, => the following condition should hold.

=> PV*(1+i) = FV, here FV = Face Value, PV = Present Value and “i” the nominal rate of interest.

=> (1+ i) = FV/PV = 1000/970.87 = 1.03, => i = 0.03 = 3%

So, the nominal rate of interest is “3%”.

We have also given that the "expected inflation" is “2%” and the "actual inflation" is “1%”. So, the “expected real interest rate” is the difference between “nominal rate of interest” and the “expected inflation”, => “expected real interest rate” is “3% - 2% = 1%”.

Now, the “actual real interest rate” is the difference between “nominal rate of interest” and the “actual inflation”, => “actual real interest rate” is “3% - 1% = 2%”.

So, according to the given information “the nominal rate of return” is “3%”, the “expected real rate of return” is “1%” and the “actual real rate of return” is “2%”.