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in BUS 3024S - Contingencies by (140 points)

Specifically: annuity benefit

Why is:

$$10p_{xy} v^{10} \ddot{a}_{\overline{x+10: y+10}}$$insufficient to calculate the EPV?


The memo answer, $${10}p_{xy} v^{10} \ddot{a}_{\overline{x+10: y+10}}+\ddot{a}_{x+10}10p_{x}10q_{y}v^{10} + \ddot{a}_{y+10}10p_{y}10q_{x}v^{10} $$


where x = 60 female, y = 64 male

by (140 points)

1 Answer

0 votes
by (360 points)

There are two possible scenarios here that will still result in the annuity being paid.

(i) both lives survive the deferred period

(ii) only one of the lives survive the deferred period 

$$10p_{xy} v^{10} \ddot{a}_{\overline{x+10: y+10}}$$  is insufficient because it assumes that both lives survive the deferred period i.e. \(10p_{xy}\). It does not account for point (ii)   

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