St is the price of a non-dividend-paying stock at time t. St follows a lognormal model. You are given

(i) S0 = 45.

(ii) The continuously compounded expected rate of return is 0.15.

(iii) The volatility is 0.2.

Asking:

(a) The probability that the stock price is less than 40 at time t is 0.10. Determine all possible values for t. [You may use 1 (0.10) = 1.28155.]

(b) Let pt be the probability that St is less than 40. Determine the value of t for which pt is maximized overall positive t