All interest rates are annual rates with continuous compounding, and all bonds have a face value of $100. The current one-year rate is 7% and the current price of a three-year zero-coupon bond is $60. One year from now, the one-year interest rate is either 5% with probability 1/4, or 2% with probability 3/4, and remains fixed thereafter. Do all your calculations to at least two decimal places.

i. Draw a binomial tree showing the evolution of the one-year rate over the next two years and the evolution of the price of the three-year zero-coupon bond.

ii. Find the price of a 3-year callable zero-coupon bond with face value $100, that gives the issuer the option to buy back the bond in one year for $75. Without calculating a replicating strategy, determine the no-arbitrage price of this bond. How does this price compare to the price of the three-year zero?

iii. Now price the callable bond using replication.