SOA Exam ALTAM Sample Question 36
Study guide: Exam ALTAM
An insurer offers "immediate needs annuities" (INAs) to lives age 80 or older who are moving permanently into long term care facilities (LTCFs). The annuity may be purchased as a single premium annuity-due, or as a single premium deferred annuity-due, with a 2-year deferral period. The annuity payments are paid directly to the care home to cover the resident's costs.
(Part (a) and (d) are covered by the FAM-L exam.)
Part a (2 points)
You are given the following excerpt from a select and ultimate mortality table used to price the INA. The selection age is the age at which the life moves into an LTCF. The selection period is 1 year.
[x] |
l_{[x]} |
l_{x+1} |
x+1 |
|---|---|---|---|
| 94 | 1200 | 700 | 95 |
| 95 | 1000 | 550 | 96 |
| 96 | 750 | 385 | 97 |
| 97 | 450 | 195 | 98 |
| 98 | 220 | 50 | 99 |
| 99 | 75 | 0 | 100 |
(i) Calculate the 1-year mortality probability for (95) assuming that she moved into an LTCF at age 95.
(ii) Calculate the 1-year mortality probability for (95) assuming that she moved into an LTCF at age 94.
(iii) Describe how the selection effect in this model differs from that of typical select and ultimate tables used for pricing life insurance.
Part b (4 points)
You are given the following additional information for a profit test of an annuity-due contract issued to a 95-year old who is just moving into an LTCF.
- For a single premium of 110,000 the annuity payment is 50,000 at the start of each year including the first, conditional on survival.
- Pre-contract expenses are 300.
- Expenses of 100 are incurred with each annuity payment. There are no other expenses.
- Reserves for the first two years are:
{}_0V = 0;{}_1V = 105{,}000;{}_2V = 80{,}000 - The insurer earns 7% per year.
- The hurdle rate is 12% per year.
You are also given the following partially completed profit test table, which is missing the entries for the first two policy years:
t |
{}_{t-1}V |
Premium | Annuity | Expenses | Interest | Expected End-year reserve | \Pr_t |
|---|---|---|---|---|---|---|---|
| 0 | -- | -- | |||||
| 1 | -- | -- | -- | -- | -- | -- | -- |
| 2 | -- | -- | -- | -- | -- | -- | -- |
| 3 | 80,000 | 0 | 50,000 | 100 | 2,093 | 31,656 | 337 |
| 4 | 62,500 | 0 | 50,000 | 100 | 868 | 12,846 | 422 |
| 5 | 50,100 | 0 | 50,000 | 100 | 0 | 0 | 0 |
(i) Determine the missing entries for the first three rows of the table (missing entries are indicated by --).
(ii) Show that the net present value of the contract, is 6,710 to the nearest 10. You should calculate the value to the nearest 1.
(iii) Show that the profit margin is 6.1% to the nearest 1%. You should calculate the profit margin to the nearest 0.001%.
Part c (3 points)
The deferred annuity contract is identical to the annuity-due contract, but with no payment in the first two years, and with a lower single premium payable at issue. The time 1 reserve for the deferred annuity contract is {}_1V = 54{,}900. All other reserves and expenses are identical to the annuity-due contract.
Calculate the premium required under the deferred annuity contract that generates the same profit margin as the annuity-due.
Part d (1 point)
The insurer offers the deferred annuity at a single premium of 28,500. Describe one advantage and one disadvantage of the deferred annuity, compared with the annuity-due, from the perspective of the purchaser of the annuity.
(This is Question 6 from the Spring 2022 Written Answer exam.)
Answer this question and see the worked solution