Problem 7(6 points): Find the price of a six-month European put option with a strike $970 on a six-month 1,000 face zero-coupon bond (i.e., on a bond that will have 6 month till maturity left at the time when the option matures). Assume 1-year spot rate is 6.2%, six-month rate is 6%, and 6 months from now the six-month rate can be either 8% or 4%. Keep at least 6 decimal digits for all calculations