Jessie is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}01\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2033.$

$($a$)$ If Henry purchased this bond on $3$ 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$.$

$84\mathrm{.}9212$

b$.$

$85\mathrm{.}9250$

c$.$

$85\mathrm{.}9235$

d$.$

$86\mathrm{.}3861$