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What is the relationship between a term contingent insurance and a joint life term assurance.

+1 vote
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asked Sep 1 in BUS 3024S - Contingencies by Faith (400 points)

With regards to Tutorial 4 question 5 2018, how can we equate a term contingent insurance with x=30, y=30 , n=30 to half of a joint life term assurance with x,y,n as above ?

1 Answer

+2 votes
answered Sep 1 by Michael (580 points)

As the lives are identical \(x=30\) and \(y=30\), the term contingent assurance \(A_{\overset1{30}:30:30}\) is equivalent to \(\frac12a_{\overbrace{30:30}^1:30}\). 

This is because the probability of either one dying first is equal (i.e. 1/2 each) as they are identical lives, and the joint life term assurance is the equivalent of a term contingent assurance on both lives, but with identical lives this leads to the equation as in question 5 of the tutorial.

The maths is as follows:

\(A_{\overbrace{30:30}^1:30}=A_{\overset1{30}:30:30}+A_{30:\overset1{30}:30}\)

But 

\(A_{\overset1{30}:30:30}=A_{30:\overset1{30}:30}\) 

as the lives are identical.

Hence

\(A_{\overbrace{30:30}^1:30}=2A_{\overset1{30}:30:30}\)

Hence 

\(A_{\overset1{30}:30:30}=\frac12A_{\overbrace{30:30}^1:30}\)


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