4. You are given the following data for U.S. Treasuries. You may assume that all attributes are the same across bonds, except the term to maturity. All bonds are zero coupon bonds. (SHOW YOUR WORK FOR FULL CREDIT-ALL PARTS)

One period until maturity: P1t=$925.92593 and F=$1000

Two periods until maturity: P2t=$889.99644 and F=$1000

Three periods until maturity: P3t=$888.99636 and F=$1000

Four periods until maturity: P4t=$854.80419 and F=$1000

a. For each bond above, determine the Yield to Maturity (interest rate; round to two decimal places).

b. Using the Expectations Theory of Interest Rates, what do your results imply about future short-term interest rates? Explain your reasoning (DISCUSSION ONLY).

c. Use the Expectations Theory of Interest Rates to determine the sequence of expected short term interest rates using the approximation method. That is, find the following values: i1t+1e, i1t+2e, and i1t+3e.

d. Use the Expectations Theory of Interest Rates to determine the sequence of expected short term interest rates using the exact method. That is, find the following values: i1t+1e, i1t+2e, and i1t+3e.