CT 5, Chapter 7, example on page 21

[Nolasko]

Can anyone explain me why the underlined figure is 24000 and not 22500?

Bonuses are vested at the end of each policy year.. Which means that the sum insure in the first year has no bonus, second year has one bonus (1500), third year has 2 (3000) and so on. Thus leaving the 15 th year with 14 units of bonus worth (14*1500) over the sum assured.. This means total bonuses paid are technically 14, not 15.. This figure of 15 is the used to calculate the pure endowment. From this, please let me know where I'm making the mistake

 

[Bharti Singla]

Can anyone explain me why the underlined figure is 24000 and not 22500?

Bonuses are vested at the end of each policy year.. Which means that the sum insure in the first year has no bonus, second year has one bonus (1500), third year has 2 (3000) and so on. Thus leaving the 15 th year with 14 units of bonus worth (14*1500) over the sum assured.. This means total bonuses paid are technically 14, not 15.. This figure of 15 is the used to calculate the pure endowment. From this, please let me know where I'm making the mistake

Hi there
We have to be careful in this case. See, here the contract is endowment assurance, which we can take:
Term assurance + Pure endowment
We will deal with both the parts separately. I'm explaining from the first line of the equation of EPV of benefits..

Suppose the bonuses are vested on 31 dec each year. Basic sum assured is £25000 and per year bonus is £1500.
When dealing with term assurance part:
If the death occurs on 1 july, say, the benefit is £25000 because we haven't added the bonus yet. But the benefit will be paid at the end of the first year. And if death occurs during 2nd year, it will be (25000+1500) payable at the end of second year and so on. So, it is like 25000, 26500, 28000,...... series.
For this, they have used formula
(P-Q)A¹45:15 + Q(IA)¹45:15
Where P is first payment and Q is annual increment.


But now, see the Pure endowment part. Since we know that the benefit is payable only on maturity, provided that the life is alive. We will add the annual bonus in the basic sum assured from end the first year. Like- on 31st dec of 1st year, we see the life is alive, so we will add £1500 in £25000 on that date and so on for the whole term.
So, it is like 26500,28000,29500..... series.
And the formula is:
(25000+1500×15)A45:15¹

And in the second line, they have added the term and pure part of £23,500 to make it an endowment and so left with (47500-23500) = 24000 pure part.

 

[Nolasko]

Thanks! I was unable to decipher this explanation of the pure endowment from the exam material.. I thought that pure endowment amount grows exactly the same as the term amount.