Consider an American call option on a stock. The stock price is $70, the time to maturity is 8 months, the risk-free rate of interest is 10% per annum, the exercise price is $5, and the volatility is 32%. A dividend of $1 is expected after 3 months and again after 6 months. Show that it can never be optimal to exercise the option on either of the two dividend date. Use DerivaGem to calculate the price of the option.