Suppose you observe a binomial tree of $6-$month risk$-$free spot rates and the spot rates shown below.

A$.$ Using true probability, what is the current price of a $12-$month zero coupon bond at $t_0$ if the bond has a face value of $$800?(18$pt$)$

B$.$ Using the annualized spot rate in the table, what is the current price of a $12-$month zero coupon bond at $t_0$ if the bond has a face value of $$800?(($:$4pt\}$

C$.$ What is the risk neutral probability $P_{RN}?(4$pt$)$

D$.$ Assume that the bond is callable in six month with a call price of $$784,$ what is the price of the call option at $t_0?(6$pt$)$

E$.$ Assume that the bond is puttable in six month with a put price of $$784,$ what is the price of the put option at $t_0?(6$pt$)$

$\backslash$table$[[$Period$,$Years,Annualized Spot Rate$],[1,0\mathrm{.}5,4\%$