For a call option on a non-dividend-paying stock, the lower bound is

$$c \ge \max\left(S_0 - Ke^{-rT},\ 0\right)$$

Here:

• $S_0 = 19$
• $K = 20$
• $r = 5\%$
• $T = 0.5$ years

Compute the intrinsic present-value comparison:

$$19 - 20e^{-0.05 \times 0.5} = 19 - 20e^{-0.025} \approx 19 - 19.5062 = -0.5062$$

Because this value is negative, the lower bound is zero (0).