MTH 214
Life Insurance Mathematics II
2023 - 2024 S2
Task 1 (16% Weight)
A fully discrete 5-year term life insurance of 100,000 is issued to (50). The level annual gross premium is 2200. The reserves are 952.92, 1456.28, 1487.67 and 1015.97 in years 1,2,3, and 4 respectively. The cash value is 0%, 25%, 50% and 75% of the reserve in years 1,2,3,and 4 respectively.
You are given the following assumptions:
❼ Dependent Mortality probability: p50(0d)+k = 0.01 + 0.005k, k = 0, 1, 2, 3, 4
❼ Dependent Withdrawal probabiility: p50(0w)+k = 0.1 for all k.
❼ Initial expenses: 400 plus 30% of premium.
❼ Renewal expenses: 5% of premium
❼ Interest: 6% effective
❼ Hurdle rate: 10%
1. Calculate the profit vector. (6 marks)
2. Calculate the profit signature. (6 marks)
3. Calculate the net present value (NPV). (2 marks)
4. Calculate the internal rate of return (IRR). (2 mark)
Task 2 (14% Weight)
A life insurance company issues a 3-year unit-linked endowment assurance contract to a female aged 60 exact under which level premiums of 5,000 per annum are payable in advance. In the first year, 85% of the premium is allocated to units and 104% in the second and third years. The units are subject to a bid-offer spread of 5% and an annual management charge of 0.75% of the bid value of the units is dedected at the end of each year.
If the policyholder dies during the term of the policy, the death benefit of 20,000 or the bid value of the units after the deduction of the management charge, whichever is higher, is payable at the end of the year of death. On survival to the end of the term, the bid value of the units is payable.
The company holds unit reserves equal to the full bid value of the units but does not set up non-unit reserves. It uses the following assumptions in carrying out profit tests of the contract:
❼ Mortality basis: q60 = 0.008022, q61 = 0.009009 and q62 = 0.010112.
❼ Surrenders: None
❼ Expenses: 600 at the start of the first policy year; 100 at the start of each of the second and third policy years.
❼ Unit fund growth rate: 6% per annum
❼ Non-unit fund interest rate: 4% per annum
❼ Risk discount rate: 10% per annum
1. Find the unit fund at the end of each year. (3 marks)
2. Calculate the profit vector for the policy. (7 marks)
3. Calculate the profit margin on this policy. (4 marks)