Herry 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 $2033.$

$($c$)$ 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 paid immediately.

Show full working steps for capital gain tax payment.

a$.71\mathrm{.}0797$

b$.89\mathrm{.}2385$

c$.98\mathrm{.}4075$

d$.87\mathrm{.}9075$