The correct answer is $\boxed{\text{C}. P = 1,133.78}$.
The price of a bond is the present value of all future cash flows, discounted at the bond’s yield. In this case, the future cash flows are the semiannual coupon payments of $\frac{6}{2} = 3\%$ of the face value, $P = 1,000$, plus the face value itself, redeemed at maturity in 204. The yield is $4\%$ per year, compounded semiannually.
The present value of a single cash flow of $C$ in $n$ years, discounted at a rate of $r$ per year, compounded $m$ times per year, is given by the formula
$$PV = \frac{C}{(1 + r/m)^n}$$
In this case, we have $C = 3\% \times 1,000 = 30$, $n = 204 – 2001 = 3$, $r = 4\%/2 = 2\%$, and $m = 2$. So the present value of each coupon payment is
$$PV_C = \frac{30}{(1 + 0.02/2)^3} = 24.92981$$
The present value of the face value is
$$PV_F = \frac{1,000}{(1 + 0.02/2)^6} = 758.3549$$
The total present value of the bond is therefore
$$PV = PV_C + PV_F = 24.92981 + 758.3549 = 1,133.78$$
Therefore, the price of the bond is $\boxed{\text{C}. P = 1,133.78}$.