Problem $15\mathrm{.}15.$Consider an American call option on a stock. The stock price is $$70,$ the time to maturity is eight months, the risk$-$free rate of interest is $10\%$ per annum, the exercise price is $$65,$ and the volatility is $32\%.$ A dividend of $$1$ is expected after three months and again after six months. Show that it can never be optimal to exercise the option on either of the two dividend dates. Use Python code to calculate the price of the option.