Suppose that $6-$month, $12-$month, $18-$month, $24-$month, and $30-$month zero rates are $4\%,4\mathrm{.}2\%,4\mathrm{.}4\%,4\mathrm{.}6\%,$ and $4\mathrm{.}6\%$ per annum with continuous compounding respectively. Estimate the cash price of a bond with a face value of $100$ that will mature in $30$ months and pays a coupon of $5\%$ per annum semiannually. please make sure it is correct with work