An American call option expiring in $3-$years has an exercise price of E$1,500\mathrm{.}00$ on the Eswatini stock market and currently trades at E$1,940\mathrm{.}00.$ It is anticipated that the stock will rise by a factor of $1\mathrm{.}10$ and fell by a factor of $0\mathrm{.}80.$ If the interest rate is $6\%$; find the upward prices of the option until its expiry and the pay$-$offs a binomial tree.