Consider a one$-$step binomial tree on stock with a current price of $$200$ that can go either up to $$220$ or down to $$180$ in $2$ years. The stock does not pay dividend. The continuously compounding interest rate is $4\%($per year$).$ We want to price the $2-$year $$200-$strike European call option on this tree. $($i$)$ What's the option payoff at expiry if the stock price ends up at $$220?$

$($ii$)$ What's the payoff if the stock price ends at $$180?($iii$)$ Use the tree to compute the value and delta of the option. $($iv$)$ What's the risk$-$neutral probability of the stock price going up to the $$220$ node of the tree?

$($v$)$ What's the riskneutral probability of going down to the $$180$ node?

$($Round answers to $2$ decimals$)$