Henry is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}92\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2033.$

$($a$)$ If Henry purchased this bond on $5$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}15\%$ p$.$a$.$ compounded half$-$yearly.

a$.$

$98\mathrm{.}9370$

b$.$

$99\mathrm{.}0136$

c$.$

$98\mathrm{.}9356$

d$.$

$97\mathrm{.}4783$