A life insurance company sells regular premium term insurance policies with return of premiums at maturity, wherein the policy holder $($or his Estate$)$ would get the sum assured payable at the end of the year of death, or the total premiums paid would be returned to the policy holder at the time of maturity on survival. A policy holder aged $35$ years exact buys one such policy with a sum assured of Kshs $5000000$ and a term of $30$ years.

Basis:

Interest rate: $6\%$ per annum

Mortality: AM$92$ Ultimate

$($i$)$ Find the values of the following actuarial functions:

a$35$:$30$

$(3$ dp$)$

A $135$:$30$

$(5$ dp$)$

A$35$

$(5$ dp$)$

A$65$

$(5$dp$)$

$($ii$)$ Calculate the annual premium for the policy assuming that premiums are paid yearly in advance for the full term and cease on earlier death. We ignore expenses, any lapses and surrenders.

$(2$ dp$)$