Jay purchased a Treasury bond with a coupon rate of $4\mathrm{.}33\%$ 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 $5$ January $2022.$ What was Jay's sale price $($rounded to four decimal places$)?$ Assume a yield of $3\mathrm{.}4\%$ p$.$a$.$ compounded half$-$yearly.

Question $6$

a$\mathrm{.}107\mathrm{.}5826$

b$\mathrm{.}107\mathrm{.}2238$

c$\mathrm{.}105\mathrm{.}0727$

d$\mathrm{.}105\mathrm{.}4315$