Jay purchased a Treasury bond with a coupon rate of $2\mathrm{.}71\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2029.$

$($b$)$ In fact, Yuri changes his plan and Jay plans to sell this bond on $11$ January $2022.$ What was Jay's sale price $($rounded to four decimal places$)?$

Assume a yield of $2\mathrm{.}14\%$ p$.$a$.$ compounded half$-$yearly.

a$.104\mathrm{.}6539$

b$.103\mathrm{.}5459$

c$.103\mathrm{.}3039$

d$.104\mathrm{.}8959$