note: all interest rates are annual interest rates with semi-annual compounding. all coupon rates are annual rates paid semi-annually.

practice problem 1: consider a 1-year zero-coupon bond with $1,000 face value. assume today's 6-month forward rate is 6% and in six months the new 6-month forward rate can be either 5% or 7%. assume also that the current price of the 6-month call option with a strike price of $970 on this bond is $2.17. find the 1-year spot rate today. (please keep at least 4 decimal digits)

practice problem 2: use all the information in practice problem 1 plus assume that every 6 months the 6-month forward rate can either increase or decrease by 1%. i.e., today's 6-month forward rate is 6%; in 6 months the 6-month forward rate can be either 5% or 7%; and in 1 year the 6- month forward rate can be either 4%, 6%, or 8%. assume also that the 1.5-year spot rate is 6.25%. assume that the risk-neutral probability depends on the time period but not on the exact node. find the price of a 1-year call option with a strike price of $960 on the 1.5-year zero-coupon bond. (please keep at least 4 decimal digits, also you may use the results of problem 2 if you find any of them useful)

(telfer school of management, 2020)

Hey dear! I just need answer in problem 2. please answer right way. i will give thumbs up.