Suppose that $6-$month, $12-$month, $18-$month, $24-$month, and

$30-$month zero rates are $2\%,2\mathrm{.}2\%,2\mathrm{.}4\%,2\mathrm{.}6\%,$ and $2\mathrm{.}8\%$

per annum with continuous compounding respectively.

Estimate the cash price of a bond with a face value of $100$

that will mature in $30$ months and pays a coupon of $4\%$ per

annum semiannually.