Splitting Endowment Assurances

[jensen]

Hi

Can we split endowment assurances like how we split term assurances?

Example for term n assurances;

Ax (term n) = Ax (term t) + v^t . t_P_x . Ax+t (term n-t)


Can we do the same for endowment / pure endowments? Or is the best way is to use annuity functions, then convert back using premium conversion formula?

Thanks!!

 

[bystander]

Yes you can split them... But don't make life difficult unless there'sa specific reason like you have different assumptions over time.

 

[jensen]

Yes you can split them... But don't make life difficult unless there'sa specific reason like you have different assumptions over time.

Yes, I have different assumptions thats why.

Back to the question, so when we split the endowment assurance, is the first part also an endowment assurance, or is it just a term insurance since the maturity benefit pertains only to the end of the period?

 

[didster]

Yes the first bit is a term. Think of an endowment as a term plus a pure endowment, then split each of these as necessary, to get the concept and try to find the easiest way to get there.

 

[jensen]

Thanks didster.

If you don't mind looking, here is what's bothering me.

There is two set of assumption for interest rates; 4% for age up to 55 and 5% thereafter.

I'm trying to split the endowment assurance using what I understand but I can't match the final answer to the solution. The solution used the annuity functions instead.

The difference is 5%, so it can't be mere rounding error.

 

[didster]

Without looking at any of the numbers, I'd say the last line of the "However" solution is incorrect as it uses d = 0.04/1.04, where you have different interest rates (ie not 4%) applying.
Want to quote source of solution?

 

[jensen]

Thanks didster.

It made sense to me though, coz it's 4% up to age 55, and 5% thereafter.

It's actually assignment question X2.5 on my 2009 notes, and I am not sure if there is any correction. So embarrassed if there was.