Consider the following statements. Choose the correct statement. A$.$ Given the time to maturity, the duration of a zero$-$coupon bond is lower when the discount rate is higher. B$.$ Given the time to maturity, the duration of a zero$-$coupon bond is lower when the discount rate is lower. C$.$ Given the time to maturity, the duration of a zero$-$coupon bond is lower when the discount rate is equal to the risk$-$free rate. D$.$ The zero$-$coupon bond's duration is independent of the discount rate E$.$ None of the options are correct