According to put-call parity for a dividend-paying stock, the relationship between European call and put prices is: $c + K \times e^{-rT} = p + S_0 - PV(\text{Dividends})$

Given: Call option price c = \`1.5$ Strike price $K = \$42`$ Current stock price S_0 = \`38$ Expected dividend $D = \$0.75`$ in 2 months (or $2/12$years) Maturity$T = 6$months (or `$0.5$ years) Risk-free rate $r = 6\%$ or $0.06`$

First, calculate the present value of the dividend: PV(\text{Dividends}) = 0.75 \times e^{-0.06 \times (2/12)} = 0.75 \times e^{-0.01} = 0.75 \times 0.99005 = \`0.74`25$

Calculate the present value of the strike price: PV(K) = 42 \times e^{-0.06 \times 0.5} = 42 \times e^{-0.03} = 42 \times 0.970445 = \`40.75`87$

Now, rearrange the put-call parity formula to solve for the put price ($p$): $p = c + K \times e^{-rT} - S_0 + PV(\text{Dividends})$ $p = 1.5 + 40.7587 - 38 + 0.7425$ $p = 42.2587 - 38 + 0.7425 = 4.2587 + 0.7425 = 5.0012$

The closest option is `$5.00`.