Question:
(a) (i) De ne net premium and state the equation for net premium.
(ii) Arshad, aged exactly 50, buys a 15-year endowment assurance policy with a sum assured of $ 50,000 payable on maturity or at the end of the year of earlier death. Assuming level premiums are payable monthly in advanced, calculate the monthly premium of Arshad based on AM92 Ultimate mortality and 4% pa interest.
(iii) Yan, aged x, buys a whole life assurance policy. The premiums are payable annually in advance and the sum assured is payable at the end of the year of death. Derive a formula for the variance of the insurer's pro t on Yan policy.
(b) A life, aged 45, buys 20-year temporary assurance policies. The sum assured, which is payable immediately on death, is $ 400,000 for the rst 10 years and $ 100,000 thereafter. Assume level premiums are payable in advance for 20 years or until death, and the premium basis is AM92 Ultimate mortality at an interest of 4% pa.
(i) Prove that the premium payable is approximately $ 850.25 per annum.
(ii) Using the same premium basis, calculate the net premium reserve ten years after the commencement of the policy, immediately be-fore the payment of the eleventh premium.
(iii) Provide an explanation of the net premium reserve obtained in part (b)(ii) above. Describe the disadvantages to the insurance company of issuing this policy.
(iv) How could the terms of the policy be altered, so as to cater for the described disadvantages in part (b)(iii).