Bond A and Bond $B$ both make interest payments annually, and have $$1,000$ face values. Bonds A and $B$ also have identical coupon rates, and both have the same yield to maturity. The only difference between the two bonds is that Bond A will mature in five years, while Bond $B$ will mature in seven years. Which of the following must be true about the relationship between the prices of the two bonds?

A$.$ Bond A must have a higher price than Bond $B,$ since owners of Bond A will receive the large $$1,000$ face value payment at an earlier date than Bond $B$ investors.

B$.$ Bond $B$ must have a higher price than Bond $A,$ since owners of Bond $B$ receive a larger number of coupons $($i$.$e$.,$ interest payments$)$ than Bond A investors.

C$.$ There is not enough information to know which bond is more valuable. However, if the bonds are premium bonds, then Bond A will be more valuable than Bond $B.$

D$.$ There is not enough information to know which bond is more valuable. However, if the bonds are premium bonds, then Bond $B$ will be more valuable than Bond $A.$

E$.$ There is not enough information to know which bond is more valuable. Knowing whether these are premium or discount bonds does not help us determine their relative value if we do not know the exact yield to maturity.

Answer: D

Explain why the answer is D