SOA Exam ALTAM Spring 2023, Question 3
Study guide: Exam ALTAM
You are conducting a profit test of a Type A universal life insurance policy with a face amount of 150,000 issued to (40).
You are given the following information used to project the policy account values, assuming the policy remains in force.
Policy year k |
Annual premium | Percent of premium charge | Annual expense charge | COI rate per 1000 of insurance | Annual interest rate for discounting the COI | Annual credited interest rate | Corridor factor |
|---|---|---|---|---|---|---|---|
| ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ | ⁝ |
| 9 | 7,000 | 6% | 55 | 2.0 | 5% | 6% | 1.97 |
| 10 | 7,000 | 6% | 55 | 2.2 | 5% | 6% | 1.91 |
You are also given that the projected account value at the end of year 8 is 62,000.
Part a (4 points)
(i) Show that the projected account value at the end of year 9 is 72,480 to the nearest 10. You should calculate the value to the nearest 1.
(ii) Show that the projected account value at the end of year 10 is 83,580 to the nearest 10. You should calculate the value to the nearest 1.
Part b (1 point)
You are given the following profit test assumptions.
(i) The interest earned on all insurer's funds is 7.5% per year.
(ii) At the end of each of the first 9 policy years, 2% of the in-force policyholders surrender.
(iii) At the end of policy year 10, 15% of the in-force policyholders surrender.
(iv) The surrender charge for policy year 10 is 1,500.
(v) Mortality experience follows the Standard Ultimate Life Table.
(vi) Commission expenses are 5% of premiums.
(vii) Other incurred expenses are 45 at the start of each year, 100 on surrender, and 250 at the end of the year of death.
(viii) There are no reserves held other than the account value.
Show that the expected cost of death benefit plus associated expenses payable at the end of year 10, given that the policy is in force at the start of the year, is 176 to the nearest 1. You should calculate the value to the nearest 0.1.
Part c (3 points)
Show that the expected surplus emerging at the end of year 10, given that the policy is in force at the start of the year, is 1,570 to the nearest 10. You should calculate the value to the nearest 1.
Part d (1 point)
Calculate the expected surplus emerging at the end of year 10, per policy issued, \Pi_{10}.
Part e (1 point)
Describe two reasons why the insurer might hold reserves higher than the account value.
Answer this question and see the worked solution