For a decreasing $20-$year term insurance issued to $(40),$ you are given that

$($i$)$ The death benefit at time $t$ is $b_t=1000{}_{\frac{?}{\text{b}\text{a}\text{r}}(20-11)}$ for $0t20.$

$($ii$)$ Premiums are payable continuously at a constant rate.

$($iii$)$ Mortality follows the Illustrative life table.

$($iv$)$ Deaths are uniformly distributed over each year of age.

$($v$)i=0\mathrm{.}06$

$($a$)$ Calculate the level premium rate.

$($b$)$ Calculate the benefit reserve at the end of $15$ years for this insurance. Does the answer appear surprising?