Actuarial Notes

SOA Exam ALTAM Sample Question 33

Study guide: Exam ALTAM

A whole life insurance policy on (50) has an initial sum insured of 200,000 payable at the end of the year of death. At the beginning of each policy year after the first, the sum insured will increase by 5,000. The insured will pay level annual premiums payable for at most 20 years.

You are given:

(i) Mortality follows the Standard Ultimate Life Table

(ii) i = 0.05

(Part (a), (b) and (c) are covered by the FAM-L exam.)

Part a (2 points)

(i) Show that (IA)_x = A_x + v\,p_x\,(IA)_{x+1}

(ii) Use this relationship to show that if (IA)_{50} = 5.8255, then (IA)_{51} = 5.9 rounded to the nearest 0.1. You should calculate the value to the nearest 0.001.

Part b (2 points)

Annual gross premiums are calculated using the equivalence principle based on expenses of:

  • 1000 on the payment of the death benefit.
  • 15% of the first premium.
  • 5% of all other premiums.

Show that the annual gross premium is 5,500 to the nearest 100. You should calculate the value to the nearest 1.

Part c (2 points)

Show that the gross premium policy value at the end of the second policy year is 10,080 to the nearest 10. You should calculate the value to the nearest 1.

Part d (4 points)

You are given:

  • The gross premium policy values at times 10 and 11 are {}_{10}V^g = 63{,}208 and {}_{11}V^g = 71{,}217.
  • At the start of the 11th policy year, at time t = 10, there were 1000 identical, independent policies in force.
  • During the 11th year, the experience was as follows:
    • The interest rate earned was 6%.
    • There were six deaths.
    • Expenses of 6% of premiums, plus 1100 for each death benefit, were incurred.

(i) Show that the surplus earned on the portfolio in the 11th policy year, per policy in force at the start of the year, was 160 to the nearest 10. You should calculate the value to the nearest 1.

(ii) Calculate the gain by source, in the order: (1) Interest; (2) Mortality; (3) Expenses.

(This is Question 1 from the Fall 2021 Form B Written Answer exam.)

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Concepts tested

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