Today is $15$ May $2022.$ Saamiya 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 $2024$

Use linear interpolation to calculate the yield rate. Give your answer in j$2$ form, rounded to three decimal places. Hint: $1\mathrm{.}65\%$ per half year and $1\mathrm{.}9\%$ per half year are the lower bound and the upper bound for the linear interpolation.

a$.1\mathrm{.}683\%$ p$.$a$.$

b$.3\mathrm{.}201\%$ p$.$a$.$

c$.3\mathrm{.}366\%$ p$.$a$.$

d$.3\mathrm{.}550\%$ p$.$a$.$

e$.$ None of the above