f$)$ A life insurance company issues $20-$year temporary assurance policies to lives

aged $55.$ The sum assured, which is payable immediately on death, is Ksh

$5,000,000$ for the first $10$ years, and Ksh $10,000,000$ thereafter. Level annual

premiums are payable in advance for $20$ years, or until earlier death. The

premium basis is: Mortality AM$92$ Ultimate. Interest: $4\%$ p$.$a and no

expenses.

$($i$)$ Calculate the annual premium.

$($ii$)$ Find the net premium reserve ten years after the commencement

of the policy, immediately before the payment of the eleventh

premium, assuming the reserving basis is the same as the

premium basis.

$($iii$)$ Give an explanation of your numerical answer to part $($ii$).$

Describe the disadvantages to the insurance company of issuing

this policy.

$($iv$)$ How could the terms of the policy be altered, so as to remove the

disadvantages described in part $($iii$)?$