Jay purchased a Treasury bond with a coupon rate of $3\mathrm{.}19\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2029.$

$($a$)$ Yuri plans to purchase Jay's Treasury bond on $10$ September $2021.$

What price will Yuri pay $($round to four decimal places$)?$ Assume a yield of $2\mathrm{.}66\%$ p$.$a$.$ compounded half$-$yearly. Round your answer to four decimal places.

a$.103\mathrm{.}5449$

b$.104\mathrm{.}0074$

c$.105\mathrm{.}3694$

d$.103\mathrm{.}5430$

$($b$)$ In fact, Yuri changes his plan and Jay plans to sell this bond on $9$

January $2022.$ What was Jay's sale price $($rounded to four decimal

places$)?$ Assume a yield of $2\mathrm{.}66\%$ p$.$a$.$ compounded half$-$yearly.

a$.103\mathrm{.}0918$

b$.104\mathrm{.}8903$

c$.103\mathrm{.}0065$

d$.104\mathrm{.}4629$