Approximating Geometric Brownian Motion numerically

Question

I am trying to generate a numerical solution to the SDE for Geometric Brownian Motion.

The stochastic process is given by $S_t = \exp(\sigma W_t + \mu t)$, and by Ito's lemma, we have that the SDE is given by:

$dS_t = \sigma S_t dW_t + (\mu + \frac{1}{2} \sigma^2) S_t dt$.

For some reason, I can't get my code to work. I tried following the procedure to a T, but my code is only plotting a straight (horizontal) line. Can anyone tell me what is wrong?

    # This program is to practice solving SDEs numerically:
# For the stochastic process of Geometric Brownian Motion,
#     S_t = S_0 exp( sigma * W_t + mu * t)
# The SDE is given by:
#     dS_t = sigma * S_t * dW_t + (mu + 1\2 sigma^2) * S_t * dt
# We will apply the Euler-Maruyama scheme to solve the SDE

import numpy as np
import math
import matplotlib.pyplot as plt

#parameters
mu = 0.75
sigma = 0.30

#time-scheme
t_init = 0
t_end = 2
s_init = 0
N = 1000

dt = float(t_end - t_init) / N
sqrtdt = np.sqrt(dt)
t = np.arange(t_init, t_end, dt)

s = np.zeros(N)
s[0] = s_init

for i in xrange(1, t.size):
    dW = np.random.normal(loc = 0.0, scale = 1.0) * sqrtdt
    s[i] = s[i-1] + (sigma * s[i-1] * dW) + (mu + 0.5 * math.pow(sigma, 2.0)) * s[i-1] * dt

plt.plot(t, s)
plt.show()