The bond pays four semiannual coupon payments of `4` each, plus \`100` principal at maturity.

Because the spot rates are given with continuous compounding, each cash flow is discounted using:

$$PV = CF \times e^{-rt}$$

Cash flows and discounting

• 0.5 years: `$4` discounted at 3.0% $$4e^{-0.03(0.5)} = 4e^{-0.015} \approx 3.9404$$
• 1.0 year: `$4` discounted at 4.0% $$4e^{-0.04(1.0)} = 4e^{-0.04} \approx 3.8432$$
• 1.5 years: `$4` discounted at 4.6% $$4e^{-0.046(1.5)} = 4e^{-0.069} \approx 3.7333$$
• 2.0 years: `$104` discounted at 5.0% $$104e^{-0.05(2.0)} = 104e^{-0.10} \approx 94.1022$$

Total price

$$3.9404 + 3.8432 + 3.7333 + 94.1022 \approx 105.62$$

So the nearest theoretical price is `$105.62`, which is D.