SOA Exam ALTAM Sample Question 50
Study guide: Exam ALTAM
An insurer issues a Type A universal life policy with a face amount of 100,000 and an annual premium of 50,000.
You are given:
| Policy Year | Percent of Premium Charge | Annual Expense Charge | COI Rate per 1 of Insurance | Annual Discount Rate for COI | Annual Credited Interest Rate | Corridor Factor |
|---|---|---|---|---|---|---|
| 1 | 20% | 75 | 0.025 | 4.5% | 6.50% | 1.5 |
| 2 | 8% | 75 | 0.030 | 4.5% | 5.75% | 1.4 |
Part a (3 points)
Show that the account value at the end of two years is 91,000 to the nearest 1000. You should calculate the account value to the nearest 1.
Part b (3 points)
The policyholder surrenders the policy at the end of the second year, when she is age 60. The policy does not have a surrender charge. She uses the surrender value as a net single premium to purchase a special last-survivor life annuity-due with her husband, who is 10 years older than the policyholder.
This annuity provides the following payments at the beginning of each quarter:
- For the first ten years, a guaranteed payment of
Q - After the first ten years, a payment of
Qif the policyholder is alive - After the first ten years, a payment of
0.6Qif the policyholder is dead, but her husband is alive.
You are given that the net single premium and reserves for this annuity are calculated based on the following information and assumptions.
- (i) The future lifetimes of the couple are independent.
- (ii) Mortality follows the Standard Ultimate Life Table.
- (iii)
i = 0.05 - (iv) The two-term Woolhouse formula
Show that Q is 1630 (as printed) to the nearest 10. You should calculate Q to the nearest 1.
Part c (1 point)
You are given that the policyholder's husband dies during the first 10 years of the annuity.
Calculate the net premium reserve immediately prior to the payment of Q at the start of the eleventh year.
Part d (1 point)
In the eleventh year, Person S (as printed) decides that they no longer needs the annuity and asks the company to pay the reserve. The insurance company refuses to pay the full reserve.
Explain why the insurance company would not agree to S's request.
(This is Question 3 from the Spring 2017 Written Answer exam.)
Answer this question and see the worked solution