Jacob is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}9\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2033.$

$($b$)$ If Jacob purchased this bond on $2$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}02\%$ p$.$a$.$ compounded half$-$yearly. Jacob needs to pay $27\mathrm{.}7\%$ on coupon payment as tax payment and tax are paid immediately.

a$.$

$91\mathrm{.}0844$

b$.$

$90\mathrm{.}0372$

c$.$

$91\mathrm{.}3968$

d$.$

$91\mathrm{.}0829$