please explain why the answer if F. thank you.

2. Bonds A and B both have $1,000 face values, yields to maturity of 4.5%, coupon rates of 6%, and make semi-annual coupon payments. Bond B will mature two years later than bond A. Which of the following statements must be true about the two bonds? A. Bond A can be sold for a higher price than bond B. B. Bond B can be sold for a higher price than bond A. C. If interest rates (yields to maturity) rise, bond A will fall by a greater amount, as a percentage of its initial price, than bond B. D. If interest rates (yields to maturity) rise, bond B will fall by a greater amount, as a percentage of its initial price, than bond A. E. Both A and C are true. F. Both B and D are true