Herry is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}67\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2033.$

$($a$)$ If Henry purchased this bond on $7$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}45\%$ p$.$a$.$ compounded half$-$yearly.

a$.93\mathrm{.}1478$

b$.91\mathrm{.}8152$

c$.93\mathrm{.}1492$

d$.93\mathrm{.}3990$

$($d$)$ If Henry purchased this bond on $7$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}45\%$ p$.$a$.$ compounded half$-$yearly. Henry needs to pay $26\mathrm{.}5\%$ on coupon payment and capital gain as tax payment. Assume that all tax payments are delayed by half year.

a$.68\mathrm{.}8832$

b$.93\mathrm{.}1245$

c$.82\mathrm{.}6798$

d$.81\mathrm{.}4957$