PLEASE ONLY ANSWER PART 3 Thanks

2. Consider a 1-year zero-coupon bond with $1,000 face value. Assume todays 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. Keep at least 4 decimal digits. All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually.

3. Use all the information in problem 2 plus assume that every 6 months the 6-month forward rate can either increase or decrease by 1%. I.e., todays 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%. Like in lectures, 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. Keep at least 4 decimal digits. You may use the results of Problem 2 if you find any of them useful