A two-year 4% Treasury Note has 12 months to expiry. The Note pays semiannual coupons (hence there are two coupon payments left). Assume that you know the following: Price of the 6-month T-Bill is 98.6527 The 6-month forward rate is F(6m; 12m) = 3:25% (a) According to the pure-expectations theory of the term structure of interest rates, how should the 6-month spot rate evolve? (b) What is the arbitrage-free price of the 4% T-Note? © What is the yield to maturity of the 4% T-Note? Hint: The solution involves finding roots of a quadratic equation. Only one of the roots has economic meaning. (d) Calculate duration and modifed duration of the 4% T-Note.

**My answers:**** a)** The interest rate curve will be decreasing.

**b)**The current market price for 6m is 98,6527; thus, the price of the 1y is 95,6798 (102/(1+0.0325)^2,

Therefore,the arbitrage free price is: 2(coupon) x 98,6527/100 + 2 x 95,6798/100 + 100 x 95,6798 = **99,5665**

**c)** How should I construct a quadratic equation ? ie **(2/(1+yt) + 2/(2/(1+yt)^2 + 100/(1+yt)^2=99,5665**

**d)** Should I calculate the duration & MD for the whole 2 years using just the 4% or else… ? I appreciate !