Please show all work so I can learn. Thanks!

Consider a binominal model for a futures contract. You are given:

i) Each period is 1 year.

ii) The price of a one-year at the money call option on the futures contract is 6.3415.

iii) The risk-neutral probability of an up move is ¹/₃

iv) The initial futures price is 100

v) The continuously compounded risk-free interest rate is 5%

Calculate d.

(Note: resolve this contract as a call option, treating the initial futures price as the strike and the final futures price as the final price)

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A) 0.5

B) 0.6

C) 0.7

D) 0.8

E) 0.9