The current price of a stock is $$22,$ and at the end of one year its price will be either $$29$ or $$15.$ The annual risk$-$free rate is $8\mathrm{.}0\%,$ based on daily compounding. A $1-$year call option on the stock, with an exercise price of $$20,$ is available. Based on the binominal model, what is the option's value?