The current price of NLT stock is $$20$ and the stock price will increase by $15\%$ or decline by $10\%$ at the end of each month. NLT pays no dividends. The continuous risk$-$free interest rate is $6\%$ p$.$a$.,$ which will remain constant forever. Construct a two$-$step binomial tree to describe the price evolvement of the stock and calculate the price of a $12-$month American call option on NLT stock with a strike price of $$20\mathrm{.}50$