Today is $15$ May $2022.$ Emma has just purchased a Treasury bond with a face value of $$100,$ maturing at par and paying coupon at j$2=3\mathrm{.}4\%$ p$.$a$.$ The purchase price was $$100\mathrm{.}065.$ The maturity date of this bond is $15$ May $2024.$

For the purposes of this question only, assume that Emmas purchase price was not $$100\mathrm{.}065,$ and that we don$$t know her purchase price. Calculate the duration of this Treasury bond. Assume that Emma's purchase yield rate was j$2=5\mathrm{.}2\%$ p$.$a$.$ Give your answer in terms of years, rounded to three decimal places. a$.1\mathrm{.}8930$ years b$.1\mathrm{.}8988$ years c$.1\mathrm{.}9465$ years d$.1\mathrm{.}9494$ years