Answer the following questions

A special 25-year life insurance policy is issued to a life aged x and provides the following benefits: a lump sum of $75,000 (payable at the end of the policy year) if death occurs during the first 10 years a dependants' pension (payable in the form of an annuity certain) of $5,000 pa payable on each remaining policy anniversary during the term (including the 25th anniversary) if death occurs after 10 years but before the end of the term of the policy a pension of 17,500 pa commencing on the day after the term of the policy expires and with payments on each subsequent policy anniversary while the policyholder is still alive. Write down an expression for the present value random variable of the benefits under this policy. [3]A life office sells 100 independent 5-year term assurance policies to lives aged 60. Each policy has a sum assured of $10,000 payable at the end of the year of death. Premiums of (200 are payable annually in advance throughout the 5-year term or until earlier death. Let L denote the present value of the insurer's loss on these policies. Assuming AM92 Ultimate mortality and 51%% pa interest, calculate the expected value and standard deviation of L. [7]