$(b)$ A stock price currently trades $at$ $$100.Itis$ known that next year $it$ will $be$ either $$110or$

$$90.$ The yield curve $is$ flat, and the risk$-$free rate $of$ interest with annual compounding $is$

$10\%$ per annum. Using the binomial model, calculate the value $of$ a derivative, whose payoff

$is$ max$\{2(S_T-$$$95),3($$$102-S_T)\},$ where $S_{T}is$ the stock price next year.