ATM call delta with a 3% dividend yield

Consider the same one-year at-the-money European call with $r = 6\%$, but now the stock pays a continuous dividend yield of $3\%$. Is delta above or below $0.5$?

Still above $0.5$. Now $\Delta = e^{-qT}N(d_1)$ with $d_1 = \frac{0.03}{\sigma} + \frac{\sigma}{2}$. That is at least $2\sqrt{0.015} \approx 0.245$ for every $\sigma$, so $N(d_1) \ge 0.597$ and $\Delta \ge 0.97 \times 0.597 \approx 0.58$. The dividend discount $e^{-0.03}$ is not enough to pull it below one half.