SOA Exam ALTAM Sample Question 54
Study guide: Exam ALTAM
For Type B universal life insurances with additional death benefit 100,000 on lives age 60, you are given the following policy details:
Policy Year k |
Annual Premium | Credited Interest Rate | Percent of Premium Expense Charge | Annual Expense Charge | Annual Cost of Insurance Rate per 1000 | Surrender Charge |
|---|---|---|---|---|---|---|
| 1 | 5000 | 5% | 60% | 200 | 6.00 | 600 |
| 2 | 1000 | 5% | 10% | 50 | 7.47 | 200 |
| 3 | – | – | – | – | – | 0 |
You are also given the following profit testing assumptions:
Policy Year k |
Dependent Probabilities q_{60+k-1}^{(d)} |
Dependent Probabilities q_{60+k-1}^{(w)} |
Earned Interest Rate | Commissions as Percent of Premium | Other Expenses |
|---|---|---|---|---|---|
| 1 | 0.004 | 0.100 | 6% | 90% | 100 |
| 2-10 | 0.003 + 0.001k |
0.050 | 6% | 5% | 10 |
Expenses are incurred at the start of each policy year. Your company uses account values as reserves. The account value at the end of year 2, for a policy in force, is 1500.
Part a (2 points)
Show that the account value at the end of year 1, for a policy in force, is 1300 to the nearest 100. You should calculate the account value to the nearest 1.
Part b (3 points)
Your company discounts expected profits at 12%. The expected profits for the first three years are:
Policy Year k |
Expected profits at the end of the year for a policy in force at the start of the year |
|---|---|
| 1 | -1206 |
| 2 | 374 |
| 3 | 400 |
Calculate the partial Net Present Value up, to time 3, NPV(3).
Part c (5 points)
Your company's pricing actuary asks you to redo the profit test using the end of year cash values as reserves, with no other changes.
- (i) (3 points) Calculate the revised expected profit for policy year 2, per policy in force at the start of year 2.
- (ii) (1 point) Explain why the expected profit in policy year 2 decreases due to this change.
- (iii) (1 point) State with reasons whether the total present value of profits in all years will increase, decrease, or stay the same due to this change.
(This is Question 6 from the Spring 2014 Written Answer exam.)
Answer this question and see the worked solution