CT5 April 2006

[shdh]

Hi,
In question number 13 part 1,

I'm using the following equation to get the premium:
P- annual premium

245150*A[35]:30 + 5000*(IA)[35]:30 + 250 + .5P + .03*P* {(adue)[35]:30(payable monthly) - 1/12} + 150*A(^1)[35]:30 = P payable monthly in adv for 30 yrs.

245150 is of 150 for the maturity benefit and 150 of death cost.

The additional 150 term Assurance benefit belongs to the death cost (as the death cost was 300 so I broke it into 150 which goes to the endowment part and 150 becomes term).

I am getting a different answer as opposed to the required one.

Why has the solution taken 31*(pure endowment) instead of 30?

Thanks for the help!

Regards
Shyam

 

[deepakraomore]

1) If you break the equation like the examiner report then there are less chances of errors.

2) 2nd term of your equation "5000*(IA)[35]:30"
to calculate the increased maturity benefit, i think you are using \(n * A_{\left[35\right]:{30}^1}\)
Use \(\left(n+1\right) * A_{\left[35\right]:{30}^1}\) and check, here \(n = 30\)

3) Also term ".03*P* {(adue)[35]:30(payable monthly) - 1/12}" wrong
it should be \(12 * 0.03 \left\{\ddot a_{\left[35\right]:{30}} - \left(11/ 24\right) \left( 1 - D_{x+n}/ D_x\right)\right\} - 0.03 * P \)
Check using above 2 and 3rd alternatively.

 

[Dona169]

Hello, I think I'm having the same problem. Did you figure it out eventually?

I'm confused as to why there seems to be an extra bonus at maturity even though we already accounted for it with the endowment assurance function A[35]:30] for death OR survival.

The answer on page 110 of Revision booklet 4 is:
245,000 A[35]:30] + 5000(IA)[35]:30] +5000(D65/D[35])

Why is that last bonus necessary?
Thanks!

 

[Robert Chadburn]

This is an example of how to deal with simple bonuses that vest at the END of each year.
If the person dies in the final year (for example) they will receive the sum assured plus 29 bonuses. That is, 250,000 + 29x5000.
The (IA) endowment function will provide 30 years of bonuses on death in the final year, hence we need to add a level benefit of 245,000 to give us the right death benefit in this case. That is, 245,000 + 30x5000.
Now, on survival to the end of 30 years, the person receives 250,000 + 30x5000. But if you add up the two endowment assurance functions, we find that the survival benefit valued is only 245,000 + 30x5000. That is, we are 5000 short on survival. So we need to add the extra 5000 survival benefit value (5000xD/D) to make it right.
In these questions I always recommend valuing the death benefits and survival benefits separately, which makes it less likely to miss something like this - ie use term assurances functions for the death benefit and D/D for the survival sum assured, and don't use endowment assurance functions at all.
Robert