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 $2033.$

$($c$)$ 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 and capital gain as tax payment. Assume that all tax payments are paid immediately.

a$.$

$87\mathrm{.}7395$

b$.$

$89\mathrm{.}0282$

c$.$

$72\mathrm{.}3437$

d$.$

$100\mathrm{.}0195$