All yields in this problem are quoted as semi-annually compounded APRs. The following coupon paying bonds are being traded in the market:

4% coupon-paying bond with maturity of 6 months and semi-annual coupons. Its yield to maturity is 2%.

6% coupon-paying bond with maturity of 1 year and semi-annual coupons. Its yield to maturity is 2.5%. 5% coupon-paying bond with maturity of 18 months and annual coupons. Its yield to maturity is 3%.

A zero-coupon bond with maturity of 2 years. Its yield to maturity is 4%.

a) What are the zero coupon bond prices with face values of $100 and maturities 0.5, 1, 1.5, and 2 years respectively?

b) What are the spot rates with maturities 0.5, 1, 1.5, and 2 years respectively? Plot the yield curve.

c) A two-year bond with face value $1000 and a coupon rate of 8% paid semiannually. What is the price of this bond?

d) Show that if the price of the bond is higher than computed in part c), then there exists an arbitrage opportunity. Provide an arbitrage strategy (i.e., specify the portfolio and the resulting cash flows).

e) Suppose the expectation hypothesis holds. What is the price of the coupon paying bond in part c) 1 year from now?