SOA Exam ALTAM Sample Question 2

You are given the following excerpt from a triple decrement table:

$x$	$l_x^{(\tau)}$	$d_x^{(1)}$	$d_x^{(2)}$	$d_x^{(3)}$
60	1000	$d_{60}^{(1)}$	60	45
$\vdots$	$\vdots$	$\vdots$	$\vdots$	$\vdots$

You are also given the following information about the decrements:

Part a (2 points)

Calculate $q_{60}^{\prime(2)}$ .

Calculate $d_{60}^{(1)}$ .

Now suppose instead that Decrement 2 occurs at the start of the year, and that each $q_{60}^{\prime(i)}$ remains unchanged.

State with reasons the effect (increase, decrease, no change, cannot be determined) that this change would have on the following probabilities:

(i) $q_{60}^{(1)}$

(ii) $q_{60}^{(2)}$

(iii) $q_{60}^{(3)}$

(MLC, Spring 2015, Question 2.)