SOA Exam ALTAM Fall 2024, Question 4
Study guide: Exam ALTAM
An insurance company sells fully discrete 2-year term life insurance policies to lives age 60. The death benefit is 1,000,000. The gross premium is 4,300.
You are given the following profit testing assumptions:
(i) Mortality follows the Standard Ultimate Mortality Model.
(ii) The precontract expense is 1000.
(iii) Commissions are 5% of the gross premium, paid at the beginning of each year.
(iv) Annual maintenance expenses are 100, paid at the beginning of each year including the first.
(v) The lapse rate is 8% of the policies in-force at the end of the first year. There is no benefit payable on lapse.
(vi) The earned interest rate is 6% per year.
(vii) The hurdle rate is 10% per year.
(viii) The insurer holds a reserve of 100 at the start of each year, including the first.
Part a (1 point)
Describe two uses of profit testing in insurance practice.
Part b (4 points)
(i) (3 points) Calculate the profit vector, \left(\mathrm{Pr}_0, \mathrm{Pr}_1, \mathrm{Pr}_2\right).
(ii) (1 point) Calculate the profit signature, \left(\Pi_0, \Pi_1, \Pi_2\right).
Part c (3 points)
(i) Show that the net present value of the contract is 70 to the nearest 10. You should calculate the value to the nearest 0.1.
(ii) Without further calculation, state with reasons whether the internal rate of return is greater than or less than the hurdle rate.
(iii) Calculate the profit margin.
Part d (3 points)
Your manager wants to change the gross premium to achieve a profit margin of 5%. Calculate the revised gross premium that will meet this objective.
Answer this question and see the worked solution