Consider a stock with a current price and possible prices in $1$ year given by the binomial tree below, and

a $1-$year call option on this stock with an exercise price given below.

Assume a $1-$year risk$-$free rate $($annual compounding$)$ given below.

What are the payoffs to the call option in the $2$ states at time $1?$

Payoffs

What fraction of a share of stock do you need to replicate the call option?

How much do you need to borrow to replicate the call option $($use a positive number to indicate borrowing$)?$

What is the current value of the call option?