SOA Exam ALTAM Sample Question 27
Study guide: Exam ALTAM
For a special 3-year term life insurance issued to (50) with a premium refund feature, you are given:
(i) The death benefit is 100,000.
(ii) The premium refund feature refunds the last premium payment, without interest, at the end of the 3-year term if the insured is still alive.
(iii) The mortality rates are:
x |
q_x |
|---|---|
| 50 | 0.00592 |
| 51 | 0.00642 |
| 52 | 0.00697 |
(iv) Pre-contract expenses are 155.
(v) Commissions are 5% of each premium.
(vi) The hurdle rate is 14%.
(vii) The reserves of this policy have been set to:
t |
{}_tV |
|---|---|
| 0 | 0 |
| 1 | 400 |
| 2 | 800 |
(viii) The annual premium for this policy is 1100.
(ix) The earned interest rates are:
| Year 1 | Year 2 | Year 3 |
|---|---|---|
| 0.01 | 0.02 | 0.03 |
Part a (1 point)
Show that the expected profit in policy year 2 for a policy in force at the start of year 2 is 37 to the nearest 1. You should calculate your answer to the nearest 0.01.
Part b (4 points)
Calculate the profit vector of this policy.
Part c (3 points)
Calculate the profit signature and Net Present Value (NPV) of this policy.
Part d (3 points)
Rank from low to high the Internal Rate of Return (IRR) of the following products, explaining your order.
Product A: The special 3-year term life insurance described above.
Product B: A 3-year term life insurance policy with the following profit signature: [-155, 0, 0, 210]
Product C: The same special 3-year term life insurance as Product A, except that the reserves of the product have been set to:
t |
{}_tV |
|---|---|
| 0 | 0 |
| 1 | 300 |
| 2 | 800 |
(This is a modified version of Question 5 from the Fall 2014 Written Answer exam.)
Answer this question and see the worked solution