Perform all calculations in 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. For $6$ and $7,$ you may use Excel or a programming language, but be sure to include the code if you use the latter.

$1.$ 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 $50?$