Price of the call option before the announcement of the dividend:
$c_{\text{before}} = S_0 \times N(d_1) - K \times e^{-r \times T} \times N(d_2)$

When dividends are expected, the stock price must be reduced by the present value of the dividends.
Present Value of Dividends ($PV_{\text{div}}$): $PV_{\text{div}} = 3 \times e^{-0.05 \times (6/12)} + 3 \times e^{-0.05 \times (12/12)}$ $PV_{\text{div}} = 3 \times e^{-0.025} + 3 \times e^{-0.05}$ $PV_{\text{div}} = 3 \times 0.97531 + 3 \times 0.95123 = 2.92593 + 2.85369 = 5.77962$

The new price of the call option will be: $c_{\text{after}} = (S_0 - PV_{\text{div}}) \times N(d_1) - K \times e^{-r \times T} \times N(d_2)$

Assuming $N(d_1)$ and $N(d_2)$ are unchanged as stated: Change in option price = $c_{\text{after}} - c_{\text{before}} = -PV_{\text{div}} \times N(d_1)$ Change = $-5.77962 \times 0.7654 = -4.4237$

Thus, the price of the option will decrease by approximately USD 4.42.