SOA Exam ALTAM Sample Question 13
Study guide: Exam ALTAM
An insurer issues a whole life insurance of 50,000 to (55), with a waiver of premium on disability. You are evaluating this policy using the following model:
You are given:
(i) The gross premium G is paid at the start of each year if the insured is Active.
(ii) The death benefit is payable at the end of the month of death.
(iii) Commissions are 5% of each premium paid. There are no other expenses.
(iv) i = 0.05
(v)
x |
A_x^{(12)\,02} |
A_x^{(12)\,12} |
\ddot{a}_x^{00} |
|---|---|---|---|
| 55 | 0.480 | 0.531 | 8.832 |
| 65 | 0.634 | 0.681 | 5.416 |
(vi) {}_0L^g denotes the present value of the gross loss-at-issue random variable.
(vii) {}_tV^{(j)} denotes the gross premium policy value at time t, for a life then in State j.
Part a (2 points)
The gross premium is determined such that \mathrm{E}[{}_0L^g] = -0.1G. Show that G = 2{,}900 to the nearest 100. You should calculate G to the nearest 1.
Part b (2 points)
Show that {}_{10}V^{(0)} is 16,800 to the nearest 100. You should calculate the policy value to the nearest 1.
Part c (3 points)
You are also given:
(i) {}_{10\frac{1}{12}}V^{(1)} = 34{,}110
(ii) {}_{10\frac{2}{12}}V^{(1)} = 34{,}170
(iii) The following probabilities:
x |
{}_{\frac{1}{12}}p_x^{01} |
{}_{\frac{1}{12}}p_x^{02} |
{}_{\frac{1}{12}}p_x^{12} |
|---|---|---|---|
| 65 | 0.00461 | 0.00293 | 0.00493 |
65\frac{1}{12} |
0.00467 | 0.00295 | 0.00497 |
(i) Show that {}_{10\frac{1}{12}}V^{(0)} = 19{,}500 to the nearest 100. You should calculate the value to the nearest 1.
(ii) Calculate {}_{10\frac{2}{12}}V^{(0)}.
Part d (2 points)
To increase sales, the insurance company raises its commission rate to 15% of the first premium and 8% of each renewal premium paid. The gross premium is not changed.
(i) Without further calculation, state with reasons whether the value of {}_{10\frac{2}{12}}V^{(0)} will increase, decrease or stay the same as a result of these changes.
(ii) Without further calculation, state with reasons whether the value of {}_{10\frac{2}{12}}V^{(1)} will increase, decrease or stay the same as a result of these changes.
(LTAM, Fall 2019, Question 2)
Answer this question and see the worked solution