Consider a $5-$year term insurance of $(30)$ with the death benefit of $1,000$ payable at the end of the year of death. The level premiums are made at the beginning of each year until the death of the person maximum up to $5$ years. The mortality follows the illustrative life table with $6\mathrm{.}00\%.$

a$)$ Calculate the benefit premium.

b$)$ Calculate the benefit reserve at the end of $2$ years by prospective method and retrospective method.

c$)$ Calculate the benefit reserves at the end of $4$ years by prospective method.