Consider a binomial tree pricing model regarding a call option on a future. The current future price is $40. In up state, the future price becomes 60; in down state, it becomes $30. The strike price of the call option is $50. The gross risk-free return R is 1.2.

i) longing a future, the payoff in the both up, down states would be?

ii) Payoff of call option in the up and down states would be?

iii) by obtaining future and the risk-free bond to form synthetic call option on the future.

iv) If the transaction cost is $1 to long a unit future, and a transaction cost of $2 to short a unit future. What would be upper bound and lower bound of the call premium to maintain no arbitrage principle?