Example

You are given the following extract from a triple-decrement table. Calculate (l_{63}).

(x)	(p_x^{01})	(p_x^{02})	(p_x^{03})	(p_x^{0bullet})	(l_x)	(q_x^{prime(1)})	(q_x^{prime(2)})	(q_x^{prime(3)})
60	0.010	0.050	0.020		10,000
61				0.076
62							0.033	0.990
63

Solution.

For the first row, we have (p_{60}^{0bullet} = 0.01+0.05+0.02 = 0.08).

For the second row, we have (l_{61} = 10000(1-0.080) = 9,200).

For the third row, we have (l_{62} = 9200(1- 0.076) = 8,501).

For the third row, we also have (p_{62}^{0bullet} = 1- (1-0.023)(1-0.033)(1-0.99) =
0.06468).

For the fourth row, we have (l_{63} = 8501(1-0.06468) = 7,951).

(x)	(p_x^{01})	(p_x^{02})	(p_x^{03})	(p_x^{0bullet})	(l_x)	(q_x^{prime(1)})	(q_x^{prime(2)})	(q_x^{prime(3)})
60	0.010	0.050	0.020	0.08	10,000
61				0.076	9,200
62				0.06468	8,501		0.033	0.990
63				0.098	7,951