$5.(2$ points$)$ For a special fully discrete $30-$year term insurance on $(40)$:

$($i$)$ The force of mortality is $\backslash$mu x $=0\mathrm{.}0001(1\mathrm{.}07$x $).$

$($ii$)$ i $=0\mathrm{.}04.$

$($iii$)$ The death benefit is $10,000$ in the first $15$ years and $5,000$ afterwards.

$($iv$)$ Death benefits are paid at the end of the year of death.

$($v$)$ Premiums are paid quarterly for at most $10$ years.

$($vi$)$ Annual expenses are:

Year Per premium Per policy

First year $30\%8\mathrm{.}00$

Renewal $3\%0\mathrm{.}70$

$($vii$)$ Per premium and per policy expenses are payable at the beginning of each year. Per premium ex$-$

penses are calculated based on the sum of premiums scheduled to be paid during the year.

Using a SULT spreadsheet, calculate the annual gross premium using the equivalence principle.