The duration for a $5-$year, zero coupon, $$1,000$ face value bond is $\_\_\_\_\_\_$ years if its yield to maturity is $9\mathrm{.}2\%.$ Group of answer choices $4\mathrm{.}5$ years $5\mathrm{.}0$ years $2\mathrm{.}2$ years $3\mathrm{.}8$ years