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perpetuity pays $$100$ each and every year forever. The duration of this perpetuity will be if its yield is $9\mathrm{.}5\%.$

Multiple Choice

$11\mathrm{.}53$

$9\mathrm{.}50$

$7\mathrm{.}50$

$8\mathrm{.}68$

Given its time to maturity, the duration of a zero$-$coupon bond is $$

Multiple Choice

higher when the discount rate is lower

lowest when the discount rate is equal to the risk$-$free rate

higher when the discount rate is higher

the same regardless of the discount rate