Binomial Pricing Model

Consider American options on a stock index which pays dividends at the continuously compounded rate of 3% per year. The volatility of the index is 20% per year. Assume a current index value of 100, and a continuously compounded riskless rate of 2% per year. The options expire in two months.

(a) Use the binomial option pricing model with t = 1/12 (one month) to estimate the price of an American call option with an exercise price of 100. Will the option be exercised early? If so, when?

(b) Use the binomial option pricing model with t = 1/12 (one month) to estimate the price of an American put option with an exercise price of 100. Will the option be exercised early? If so, when?