13. Reconsider exercise 12. Show that if the date-1 exercise price is X, the date-2 exercise price is X*(1 + r), and the date-3 exercise price is X*(1 + r)2, you will not exercise the option early.[5]

[5]It can also be shown that this property holds if the exercise prices grow more slowly than the interest rate. Thus for the problem considered in section 14.7, there will be early exercise of the American call only when the exercise prices grow at a rate faster than the interest rate.