1.Using the term structure in Problem 29, what is the present value of an investment that pays $100 at the end of each of years 1, 2, and 3? If you wanted to value this investment correctly using the annuity formula, which discount rate should you use?
2.What is the shape of the yield curve given the term structure in Problem 29? What expectations are investors likely to have about future interest rates?
3.Suppose the current one-year interest rate is 6%. One year from now, you believe the economy will start to slow and the one-year interest rate will fall to 5%. In two years, you expect the economy to be in the midst of a recession, causing the Federal Reserve to cut interest rates drastically and the one-year interest rate to fall to 2%. The one-year interest rate will then rise to 3% the following year, and continue to rise by 1% per year until it returns to 6%, where it will remain from then on.
a. If you were certain regarding these future interest rate changes, what two-year interest rate would be consistent with these expectations?
b. What current term structure of interest rates, for terms of 1 to 10 years, would be consistent with these expectations?
c. Plot the yield curve in this case. How does the one-year interest rate compare to the 10-year interest rate?