\(Log(S_T| S_t)\) has the following distribution \(N(log S_t + (r- 0.5\sigma^2)(T-t), \sigma^2(T-t)) \)
The expectation of a lognormal distribution, \(X\) with parameters \(\mu, \sigma^2\) is given by \(E[X] = \exp(\mu + 0.5 \sigma^2)\). Now try substituting and you will get the same answer.
Last edited: Aug 30, 2017
