SOA Exam ALTAM Sample Question 51
Study guide: Exam ALTAM
Person D buys a Type B universal life contract of 100,000. You are given:
(i)
Policy Year k |
Annual Premium | Annual Cost of Insurance Rate per 1000 of Insurance | Percent of Premium Charge | Annual Expense Charge | Surrender Charge |
|---|---|---|---|---|---|
| 1 | 1000 | –– | 60% | –– | –– |
| 2 | P_2 |
2 | 10% | 10 | 200 |
| 3 | P_3 |
3 | 10% | 10 | 100 |
k \ge 4 |
P_k |
k |
5% | 10 | 0 |
- (ii) The credited interest rate is
i = 0.06. - (iii) D's account value at the end of year 1 is 165.
- (iv) Except as indicated, there are no deaths or surrenders.
Part a (2 points)
Show that if P_2 were 1000, D's account value at the end of year 2 would be 920 to the nearest 10. You should calculate the account value to the nearest 1.
Part b (2 points)
D's account value at the end of year 3 can be expressed as aP_2 + bP_3 + c. Calculate a, b, and c.
Part c (4 points)
In year 2, D pays a premium of 1000 with probability 0.6, or 200 with probability 0.4.
If D paid 1000 in year 2, then in year 3 D will pay either 1000 with probability 0.6, or 200 with probability 0.4.
If D paid 200 in year 2, then in year 3 D will pay either 1000 with probability 0.2, or 200 with probability 0.8
- (i) Calculate the expected death benefit payable at the end of year 3, if D dies then.
- (ii) Calculate the expected surrender benefit payable at the end of year 3, if D surrenders the contract then.
Part d (2 points)
D's identical twin, M, buys a contract identical to D's. If M pays 1000 every year, M's account value at the end of year 10 will be 5114.
M will pay premiums of 1000 in 9 of the first 10 years. M will pay no premium in one year, with the year of no premium equally likely to be year 3 or year 10.
Calculate M's expected surrender value at the end of year 10.
(This is Question 5 from the Fall 2015 Written Answer exam.)
Answer this question and see the worked solution