Henry is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}6\%$ 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 $3\mathrm{.}25\%$ p$.$a$.$ compounded half$-$yearly

a$.93\mathrm{.}0867$

b$.94\mathrm{.}5994$

c$.94\mathrm{.}3858$

d$.94\mathrm{.}3844$

$($b$)$ If Henry purchased this bond on $7$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}25\%$ p$.$a$.$ compounded half$-$yearly. Henry needs to pay $25\mathrm{.}5\%$ on coupon payment as tax payment and tax are paid immediately.

a$.86\mathrm{.}1075$

b$.87\mathrm{.}0739$

c$.87\mathrm{.}5067$

d$.87\mathrm{.}0753$

$($c$)$ If Henry purchased this bond on $7$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}25\%$ p$.$a$.$ compounded half$-$yearly. Henry needs to pay $25\mathrm{.}5\%$ on coupon payment and capital gain as tax payment. Assume that all tax payments are paid immediately.

a$.83\mathrm{.}3107$

b$.70\mathrm{.}3174$

c$.84\mathrm{.}4733$

d$.94\mathrm{.}3629$

$($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 $3\mathrm{.}25\%$ p$.$a$.$ compounded half$-$yearly. Henry needs to pay $25\mathrm{.}5\%$ on coupon payment and capital gain as tax payment. Assume that all tax payments are delayed by half year.

a$.84\mathrm{.}6631$

b$.70\mathrm{.}7023$

c$.94\mathrm{.}3634$

d$.83\mathrm{.}4979$