A life is subject to the following 3 -year select and ultimate table:

[math][x][/math]	[math]\ell_{[x]}[/math]	[math]\ell_{[x]+1}[/math]	[math]\ell_{[x]+2}[/math]	[math]\ell_{x+3}[/math]	[math]x+3[/math]
55	10,000	9,493	8,533	7,664	58
56	8,547	8,028	6,889	5,630	59
57	7,011	6,443	5,395	3,904	60
58	5,853	4,846	3,548	2,210	61

You are also given:

(i) [math]e_{60}=1[/math]

(ii) Deaths are uniformly distributed over each year of age

Calculate [math]\stackrel{\circ}{e}_{[58]+2}[/math].

• 1.5
• 1.6
• 1.7
• 1.8
• 1.9

Answer: B

[[math]] \stackrel{\circ}{e}_{[58]+2}=e_{[58]+2}+0.5 [[/math]]

[[math]]e_{[58]+2}=p_{[58]+2}\left(1+e_{61}\right)=p_{[58]+2}\left[1+\frac{e_{60}}{p_{60}}-1\right][[/math]]

[[math]]=\frac{l_{61}}{l_{[58]+2}} \times \frac{e_{60}}{p_{60}}=\frac{2210}{3548} \times \frac{1}{(2210 / 3904)}=\frac{3904}{3549}=1.100338[[/math]]

[[math]]\stackrel{\circ}{e}_{[58]+2}=1.100338+0.5=1.6[[/math]]

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Copyright 2024. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.