Suppose the stock is currently trading at $$72$ and the strike price

of the put option is $$75.$ Suppose the up$-$factor u $=1\mathrm{.}356$ and the

down$-$factor d $=0\mathrm{.}541$ and the option matures in two periods $($i$.$e$.,$

a two$-$period binomial tree$).$ If the interest rate in each period is

$3\%,$ calculate price of the put option for both the European style

and the American style.