Assume the following: binomial process; current annualized spot rate on risk-free bond with maturity of 0.25 years of \(S_{0}=4 \%\); up and down parameters for period equal in length to 0.5 years of \(u\) \(=1.1, d=1 /1.1\); length of binomial period 0.5 years (six-month steps); probability of the spot rate increase in one period of \(q=\)B0.5 .

a. Generate a three-period binomial interest-rate tree of spot rates.

b. Using the binomial tree, calculate the values at each node of a T-bill with a \(\$ 100\) face value and maturity of 0.25 years.

c. Assuming a flat yield curve, calculate the values at each node of a futures contract on the above T-bill with the expiration on the futures being at the end of the third period (1.5 years).