The following table summarizes current prices of various default-free bonds with different maturities. Interest is paid semi-annually.

Year to maturity	Counpon rate(%)	Spot price()
0.5	0.0	96.15
1.0	0.0	92.19
1.5	8.5	99.45
2.0	9.0	99.64

3.1 Compute the yield to maturity (YTM) and the theoretical spot rate for each of the four bonds. (14%)

3.2 Based on your answer in 3.1, compute, under the pure expectations theory, the forward rate on the six-month default-free bond six months from now. (4%)

3.3 Suppose you wanted to lock in an interest rate for an investment that beginsin one year and matures in one year. Under the pure expectations theory, what rate would you obtain if there are no arbitrage opportunities? Show your calculations. (3%)

3.4 Explain each of the following theories for the term structure of interest rates and discuss how each of them could explain an upward slope of the yield curve. (1) Pure expectations (unbiased) (2) Liquidity preference (term premium) (3) Market segmentation 12.3%