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 $2033.$

$($a$)$ 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.

a

$100\mathrm{.}0605$

b$.$

$98\mathrm{.}6121$

c$.$

$100\mathrm{.}1011$

d$.$

$100\mathrm{.}0589$