MTH 214 Life Insurance Mathematics II 2021/22 Class Test
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MTH 214
2nd SEMESTER 2021/22 Class Test
Life Insurance Mathematics II
Questions
Q 1. A special 3-year term insurance issued to a man aged exactly 62 pays $50,000 immediately
on death within the policy term. On survival to the end of the term, or immediately on earlier surrender, half of the total premiums paid to date (without interest) will be returned to the policyholder. A level annual premium is paid at the start of each year. The insurance company uses the following basis to calculate its premiums:
Mortality: Independent probabilities as defined by the AM92 Select table Surrender: Forces of surrender (intensities) of 5%, 2.5% and 1% in policy
years 1, 2, and 3 respectively
Interest: 3% per annum
Expenses: None
(i) Assuming that forces of decrement (transition intensities) are constant over each year of age, construct a multiple decrement table that would be suitable for valuing the cash flows for this policy, using a radix of p62 = 100, 000.
[20 marks]
(ii) Using the entries in the multiple decrement table, or otherwise, calculate the annual premium for this policy. (You should assume deaths and surrenders occur on average half way through each year). [30 marks]
Hint: You may need to use the following formula between the dependent rates and indepen- dents rates in a multiple decrement model
pz(0)j = 
(1 − pz(00))
under constant transition intensities
[Total 50 marks]
Q 2. A man aged 64 and his wife aged 62 purchase an annuity by paying a lump sum premium
of $600,000. The annuity provides the following:
. A level annuity payment payable monthly in advance during the husband’s lifetime.
. A level reversionary annuity payable at a rate equal to 2/3 of the rate of payment of
the original annuity, payable monthly in advance to the wife for as long as she survives, commencing upon the death of her husband.
The following basis is used to price the annuity contract:
. Mortality: PMA92C20 for the male; PFA92C20 for the female
. Male and female lives are independent
. Rate of interest: 4% per annum
. Initial Expense: $1,200
Calculate the annual amount of annuity that will be payable while the husband survives. Specify the assumption you will use in the calculation.
[20 marks]
Q 3. A pension plan member is aged 56. One of the plan benefits is a death in service benefit
payable on death before age 60.
(i) Calculate the probability that the employee dies in service before age 60. [5 marks] (ii) Assuming that the death in service benefit is $200,000, and assuming that the death benefit is payable immediately on death, calculate the EPV at age 56 of the death in service benefit. [10 marks] (iii) Now assume that the death in service benefit is twice the annual salary rate at death. At age 56 the member’s salary rate is $75,000 per year. Assuming that deaths occur
evenly throughout the year, estimate the EPV of the death in service benefit.
[15 marks]
Basis: Service table and relative salary scale in Formuale and Tables.
[Total: 30 marks]
2022-07-30