SOA Exam ALTAM Sample Question 14
Study guide: Exam ALTAM
For a fully discrete three-year term insurance of 100,000 on a person, age 40, you are given:
(i) The person's future mortality follows a double decrement model, where:
- Decrement 1 is death from Disease 1
- Decrement 2 is death from any cause except Disease 1
(ii) \mu_{40+t}^{(1)} = A + Bc^{40+t} for all t \ge 0, where A = 0.0001, B = 1.075\times 10^{-5}, c = 1.12
(iii) \mu_{40+t}^{(2)} = 3\mu_{40+t}^{(1)}, for all t \ge 0.
(iv) i = 0.05
Part a (2 points)
Show that p_{40}^{(\tau)} = 0.995 to the nearest 0.001. You should calculate the value to the nearest 0.0001.
Part b (2 points)
You are also given that {}_2p_{40}^{(\tau)} = 0.99027 and {}_3p_{40}^{(\tau)} = 0.98462.
(i) Show that the expected present value at issue of the person's death benefits is 1400 to the nearest 100. You should calculate the value to the nearest 1.
(ii) Show that the net annual premium for the person's insurance is 490 to the nearest 10. You should calculate the premium to the nearest 0.1.
Part c (4 points)
The person purchases a policy rider that pays an additional 50,000 at the end of the year of death, if death is due to Disease 1.
(i) Write down an integral expression for {}_tq_{40}^{(1)}, in terms of the dependent survival probabilities, {}_sp_{40}^{(\tau)}, and the force of mortality from Disease 1, \mu_{40+s}^{(1)}.
(ii) Using your expression from part (c) (i), prove that {}_tq_{40}^{(1)} = \frac{1}{4}\,{}_tq_{40}^{(\tau)}.
(iii) Show that the net premium for the Disease 1 rider is 60 to the nearest 10. You should calculate the premium to the nearest 0.1.
Part d (2 points)
Calculate the net premium policy value at time 1 for the policy, including the Disease 1 rider.
Answer this question and see the worked solution