Assignment

a$)$ A life office issues a $20-$year term assurance to a male aged $40,$ with a sum

assured of Ksh $5,000,000,$ assuming AM$92$ Ultimate mortality and interest of

$4\%$ pa$.$ Assume that the death benefit is paid at the end of the year of death.

Calculate the annual premium.

b$)$ A life office issues a policy to a life aged exactly $50.$ The contract is a $15-$year

endowment assurance policy with a sum assured of Ksh $4,500,000$ payable on

maturity or at the end of the year of earlier death. Level premiums are payable

monthly in advance. Calculate the monthly premium assuming AM$92$

Ultimate mortality and $4\%$ pa interest. Ignore expenses.

c$)$ A life aged exactly $33$ purchases a whole life assurance policy with a sum

assured of Ksh $6,000,000$ payable at the end of the year of death. Premiums

are payable annually in advance. Calculate the variance of the insurer's profit

on this contract, assuming AM$92$ select mortality and $4\%$ pa interest.

Comment on your answer.

d$)$ You are hired as a consultant in a fund of Ksh $5,000,000$ which has $10,000$

members aged $60.$ The fund accumulates at an interest rate of $4\%$ per annum

and will be divided by all members who survive to age $65.$ Based on AM$92$

Ultimate mortality, what is the expected payout for each survivor?

e$)$ A life office issues a $20-$year term assurance with a sum assured of Ksh

$7,000,000$ payable at the end of the year of death. This is issued to a male aged

$35$ for a level annual premium payable in advance. Calculate the prospective

and retrospective reserves at the end of the $4^{th},5^{th},6^{th},7^{th},{10}^{th},{13}^{th},{15}^{th}$ year,

Assuming AM$92$ Ultimate mortality and $4\%$ pa interest. Ignore expenses.

Repeat with $6\%$ pa

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$)?$