please do Only A and B in 40 minutes will upvote

Problem 1. (60/100) The on-the-run issue for ABC Company is shown below: Using the bootstrapping methodology, the spot rates are: Assuming an interest rate volatility of 10% for the 1 -year rate, the binomial interest rate tree for valuing a bond with maturity of up to three years is shown below: a) Demonstrate using the 3 -year on-the-run issue that the binomial interest rate tree above is in fact an arbitrage free tree. b) Consider a 2 -year on-the-run issue, demonstrate that the binomial interest rate tree above is also an arbitrage free tree c) Using the spot rate given above, what is the arbitrage-free value of a 3-year 8.5% coupon issue of ABC Company d) Using the binomial tree, determine the value of an 8.5%3-year option freebond e) Suppose that the 3 -year 8.5% is callable starting in year 1 at par (100). What is the value of this 3 -year 8.5% coupon callable bond? f) What is the value of embedded call option for the 3 -year 8.5% callable issue