Consider an option that expires in 72 days. The bid and ask discounts on the T-bill are 7.44 and 7.20, respectively. Find the appropriate risk-free rate.

The following option quotes are observed for XYZ stock on Jul 3. Use this table for questions 2 through 6. Current stock price is 165.13. The expirations are Jul 17, Aug 21, and Oct 16. The risk-free rates are 0.0516, 0.0550, and 0.0588, respectively.

	Calls			Puts
Strike	Jul	Aug	Oct	Jul	Aug	Oct
155	10.50	11.80	14.00	0.20	1.25	2.75
160	6.00	8.10	11.10	0.75	2.75	4.50
165	2.70	5.20	8.10	2.35	4.70	6.70
170	0.80	3.20	6.00	5.80	7.50	9.00

5. Examine the following pairs of American calls which differ only by exercise price. Determine whether the rules regarding relationship between American calls that differ only by exercise price are violated.

a. August 155 and 160

b. October 160 and 165