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Test%202%20Sol%20S1%2010

# Test%202%20Sol%20S1%2010 - THE UNIVERSITY OF NEW SOUTH...

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THE UNIVERSITY OF NEW SOUTH WALES Semester 1, 2010 Test 2 solution ACTL3002/5105 LIFE INSURANCE AND SUPERANNUATION MODELS 1. A special endowment assurance issued to a man aged 35 exact has a term of 25 years. A sum assured of \$100,000 is payable immediately on death, and a sum assured of \$200,000 is payable on survival to the end of the term. The policy is secured by annual premiums of P during the first five years, 2P during the second five years, 3P during the third five years and 4P during the remainder of the term. Premiums are payable annually in advance for 25 years or until death, if earlier. (a) Find the initial net annual premium for this policy. (b) Determine the prospective net premium policy value (reserves) at the end of the twenty-third (23 rd ) policy year, immediately before the payment of premium. Basis: AM92 Ultimate Mortality Table. 4% per annum interest. (c) Describe if the design of this policy is reasonable or not. Sol) (a) The APV of future benefits, from issue, can be expressed as 1 1 35:25 35:25 100,000 200,000 APV Benefits A A where we can evaluate from the AM92 Ultimate Mortality Table as following: 25 1 25 25 60 25 35 35:25 35 1 1 1 35:25 35:25 35:25 35:25 1 9287.2164 0.352096 1.04 9894.4299 0.04 ln(1.04) 0.04 0.38359 0.3520962 0.032120 ln(1.04) l A v p v l i A A A A Therefore, we have 100,000(0.032120) + 200,000(0.352096) = 73,631.2. Now, for the APV of future premiums, we have

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5 10 15 35:25 35:20 35:15 35:10 5 10 15 5 35 10 35 15 35 35:25 40:20 45:15 50:10 Pr 39.62582 APV emiums Pa P a P a P a Pa P v p a P v p a P v p a P 
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Test%202%20Sol%20S1%2010 - THE UNIVERSITY OF NEW SOUTH...

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