Tameka purchased a Treasury bond with a coupon rate of $3\mathrm{.}85\%$ p$.$a$.,$ payable half$-$yearly, and face value of $$100.$ The maturity date of the bond is $15$ April $2029.$

$($a$)$ Kyah plans to purchase Tameka's Treasury bond on $10$ April $2018.$ What price will Kyah pay $($rounded to four decimal places$)?$ Assume a yield of $4\mathrm{.}23\%$ p$.$a$.,$ compounded half$-$yearly. The correct answer is: $96\mathrm{.}6295$