SOA Exam FAM Sample Question 4.4

Study guide: Exam FAM

For a special increasing whole life insurance on (40), payable at the moment of death, you are given:

(i) The death benefit at time $t$ is $b_{t} = 1 + 0.2t, \quad t \ge 0$

(ii) The interest discount factor at time $t$ is $v(t) = (1 + 0.2t)^{-2}, \quad t \ge 0$

(iii) $_{t}p_{40}\,\mu_{40+t} = \begin{cases} 0.025, & 0 \le t < 40 \\ 0, & \text{otherwise} \end{cases}$

(iv) $Z$ is the present value random variable for this insurance

Calculate Var( $Z$ ).

[Question 8 on the Spring 2013 exam]

Concepts tested