Suppose that $6-$month, $12-$month, $18-$month, $24-$month, and $30-$month spot rates are $4\%,$

$4\mathrm{.}2\%,4\mathrm{.}4\%,4\mathrm{.}6\%,$ and $4\mathrm{.}8\%$ per annum with continuous compounding, respectively.

Estimate the 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.