Perform all calculations with excel:

ABC Corporation is currently trading at $$40,$ with volatility $\backslash$sigma $=30\%,$ r$=5\%,$ and no dividends. Assume that the ABC stock price can be modeled according to a three period binomial approach with T$=9$ months and n$=3,$ so that the stock price moves every $3$ months.

$1.$ Build out the binomial tree for ABC.

$2.$ What is the value of an American put option with strike price $40?$

$3.$ What is the value of a European call option with strike price $50?$