Which of the Following Statements Is False

Which of the following statements is false?

A) If a bond trades at a premium, its yield to maturity will exceed its coupon rate.
B) A bond that trades at a premium is said to trade above par.
C) When a coupon-paying bond is trading at a premium, an investor's return from the coupons is diminished by receiving a face value less than the price paid for the bond.
D) Holding fixed the bond's yield to maturity, for a bond not trading at par, the present value of the bond's remaining cash flows changes as the time to maturity decreases.