Suppose that $6-$month, $12-$month, $18-$month, and $24-$month zero rates are $3\%,3\mathrm{.}2\%,3\mathrm{.}5\%,$ and $3\mathrm{.}8\%$ per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of $100$ that will mature in $24$ months and pays a coupon of $4\%$ per annu semiannually.