Consider an American call option on a stock. The stock price is \(\$ 50\), the time to maturity is 15 months, the risk-free rate of interest is \(8 \%\) per annum, the exercise price is \(\$ 55\), and the volatility is \(25 \%\). Dividends of \(\$ 1.50\) are expected in 4 months and 10 months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Calculate the price of the option.