For a two$-$period binomial model, you are given:

$($i$)$ Each period is one year:

$($ii$)$ The current price for a nondividend$-$paying stock is $20.$

$($iii$)u=1\mathrm{.}2840$

$($iv$)d=0\mathrm{.}8607,$

$($v$)$ The continuously compounded risk$-$free interest rate is $5\%.$ Calculate the price of a European call option on the stock with a strike price of $22.$