Problem:
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 $65, and the volatility is 32%. A dividend of $1 is expected after 3 months and another dividend of $2 after 6 months.
Required:
Find the value of this American call option using Black's Approximation of BSM Model.
Note: Explain all steps comprehensively.