Why does the justification for exercising an American call early not hold up when considering an American put?
The following option prices were observed for a stock on July 6 of a particular year. Use this information to solve problems 11 through 16. Unless otherwise indicated, ignore dividends on the stock. The stock is priced at 165.13. The expirations are July 17, August 21, and October 16. The risk-free rates are 0.0516, 0.0550, and 0.0588, respectively.

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CALLS PUTS STRIKE JUL AUG OCT JUL AUG OCT 155 160 165 170 10.50 1.80 14.00 0.20 125 2.75 6.00 8.10 1.10 0.75 2.75 4.50 2.70 5.20 8.10 2.35 4.70 6.70 0.80 3.20 6.00 5.80 7.50 9.00