A four-step Cox-Ross-Rubinstein binomial tree is used to price a one-year American put option on an index when the index level is 500 , the strike price is 500 , the dividend yield is $2 \%$, the risk-free rate is $5 \%$, and the volatility is $25 \%$ per annum. What is the option price, delta, gamma, and theta? Explain how you would calculate vega and rho.