SOA Exam ALTAM Spring 2025, Question 3
Study guide: Exam ALTAM
A fully discrete 20-year last survivor endowment insurance policy is issued to Kim (60) and Alex (70). You are given:
- A death benefit of 10,000 is paid at the end of the year of the second death if it occurs within 20 years of the issue date.
- A survival benefit of 10,000 is paid at time 20 if at least one of Kim or Alex is alive at that time.
- Level annual premiums are payable while the policy is in force.
- Mortality follows the Standard Ultimate Mortality Model.
i = 5\%- The future lifetimes of Kim and Alex are independent.
Part a (1 point)
Calculate the probability that the survival benefit will be paid.
Part b (3 points)
(i) Show that the expected present value of the benefits under this policy is 3,865 to the nearest 5. You should calculate the value to the nearest 0.1.
(ii) Show that the net premium for this policy is 300 to the nearest 10. You should calculate the value to the nearest 0.1.
Part c (3 points)
You are given that \ddot{a}_{\overline{70:80}:\overline{10}|} = 7.9879.
(i) Calculate the net premium policy value at the end of 10 years if both Kim and Alex are alive.
(ii) Calculate the net premium policy value at the end of 10 years if only Kim is alive.
Part d (3 points)
At the issue date, policyholders may select a waiver of premium rider. In this case, the policyholders would pay a higher premium while both lives survive but would pay no premiums after the first death.
(i) Calculate the additional net premium for the rider.
(ii) Describe two factors that Kim and Alex might take into consideration when deciding whether to purchase the rider.
Answer this question and see the worked solution