Henry is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}94\%$ and face value of $$100.$ The maturity date of the bond is $15$ September $2033.$

$($d$)$ If Henry purchased this bond on $3$ March $2024,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}3\%$ p$.$a$.$ compounded half$-$yearly. Henry needs to pay $27\mathrm{.}8\%$ on coupon payment and capital gain as tax payment. Assume that all tax payments are delayed by half year.

a$.71\mathrm{.}5239$

b$.88\mathrm{.}0916$

c$.98\mathrm{.}4084$

d$.89\mathrm{.}4255$