Building an n = 10-period binomial model for the short-rate, r{i,j}

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Building an n = 10-period binomial model for the short-rate, r{i,j}. The lattice parameters are: r{0,0} = 5% , u = 1.1, d = 0.9 and q = 1-q = 1/2.

Q1) Compute the price of a zero-coupon bond (ZCB) that matures at time t = 10 and that has face value 100.

Q2) Compute the price of a forward contract on the same ZCB of the previous question where the forward contract matures at time t = 4.

Q3) Compute the initial price of a futures contract on the same ZCB of the previous two questions. The futures contract has an expiration of t=4.

NOTE: Give your answer rounded to 2 decimal places. For example, if you compute the answer to be 73.2367%, submit 73.24.