Using Black's approximation to find the current fair values of a 13-month American call option with a strike price of 126.67 on a dividend paying stock trading at a current market price of 126.67, interest rate of 11.33 percent per year, continuously compounded and volatility of 0.83 (as a number, not percent). The stock will go ex-dividend every 3 months starting from time zero and the amount of each quarterly dividend is 4% of the current stock price. Obtain the following fair values of options needed to find Black's approximate American call value:
1. European call option with maturity at first ex-dividend date
2. European call option with maturity at second ex-dividend date
3. European call option with maturity at third ex-dividend date
4. European call option with maturity at fourth ex-dividend date
5. European call option with maturity 13 months
6. Current fair value of American call using Black's approximation
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