Suppose that on January 1, 2018, the price of a one-year Treasury bill is $970.87. Investors expect that the inflation rate will be 2% during 2018, but at the end of the year, the inflation rate turns out to have been 1%. What are the nominal interest rate on the bill (measured as the yield to maturity), the expected real interest rate, and the real interest rate?

Nominal interest rate or YTM is 3 %.

Expected real interest rate is 1 %.

Actual Real interest rate is 2 %.  

Explanation:

Given data

Price of Treasury bill = $ 970.87 = Present value of bond

Future value = $ 1000

Expected inflation rate = 2%

Real inflation = 1 %

Yield to Maturity = nominal interest rate = ?

Yield to maturity is the internal rate of return that investor earns if he purchases bond today and held it till the maturity of bond.

Yield to maturity is denoted by YTM.

YTM = (Future value - Present value) / Present value  

YTM = ($ 1000 - $ 970.87) / $ 970.87.  

YTM = 3 % = Nominal interest rate.  

Expected real interest rate = Nominal interest rate - Expected inflation rate

Expected real interest rate = 3 % - 2 % = 1 %.

Actual real interest rate = Nominal interest rate - Actual inflation rate

Actual real interest rate = 3 % - 1 % = 2 %.

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