Suppose that you have a bond that offers a coupon rate of $10\%$ paid semiannually $($or $5\%$ paid every $6$ months$).$ The face value of the bond is $$1,000,$ it matures in four years, its yield to maturity is $8\%.$

The duration of the bond is $\_\_\_\_\_\_\_$ years.

Group of answer choices

$3\mathrm{.}37$

$3\mathrm{.}41$

$3\mathrm{.}50$

$3\mathrm{.}60$

Please show all work and answer.