Henry is planning to purchase a Treasury bond with a coupon rate of $2\mathrm{.}8\%$ and face value of $$100.$ The maturity date of the bond is $15$ March $2033.$

$($a$)$ If Henry purchased this bond on $7$ March $2020,$ what is his purchase price $($rounded to four decimal places$)?$ Assume a yield rate of $3\mathrm{.}14\%$ p$.$a$.$ compounded half$-$yearly.