Log-normally distributed stock price

If the stock price is log-normally distributed, the continuously compounded 2-year return is 36% and the 2-year volatility is $0.4 \times \sqrt{2}=0.565685$ . Thus, we have $S_2=1000$ currency units $\times e^{(0.18-\frac{(0.4)^2}{2})\times 2+\sigma \sqrt{2}Z}$ $S_2$ = Expected stock price after 2 years.

The expected value of $S_2=1000$ currency units $\times e^{(0.18\times 2)}=1433.33$ currency units. The stock price below which the stock price will remain for 50% of the time is 1000 currency units $\times e^{(0.18-0.5 \times (0.4)^2)\times 2}=1221.40$ currency units. This is because median of the log-normally distributed random variable is less than its mean.