• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

CT5- Retrospective Accumulations

Bharti Singla

Senior Member
Hi all
In ch5, section 5 talks about restrospective accumulations. The expected AV of benefits is derived here. I got the formuale derived in sec 5.1 but got stuck in sec 5.2.
As they have already considered the random variable of AV of benefit and did its expectation, then why we need to divide it by npx?
The expectation of AV of benefits is expressed as (1+i)ⁿ A¹x:-n and this is what we need. Then why npx is here?

Could anyone please explain?
Thanks
 
Here we are calculating EPV @ given time from starting time.
So we are 1st calculating PV @ time 0 and then accumulating it over given period.
For PV of payment certain, the accumulating factor is (1+I)^n
And for EPV ( (1+I) ^n * surviving probability i.e nPx
Now we need to multiply by (1+i)^n/nPx or in simple term multiply by ( Dx/Dx+n)
 
Accumulations in CT5 are always defined in terms of the amount of money accumulated per survivor. That is, we take the money that's accumulated in the bank and share it out between the survivors at time n.
Imagine in your example that we have 1000 people at the start, aged x. The accumulated amount in total would be:
1000 (1+i)ⁿ A¹x:-n
We then divide the total amount by the expected number surviving to time n, which would be 1000 nPx. So we get
(1+i)ⁿ A¹x:-n / nPx
altogether (the 1000 cancels).
Robert
 
Accumulations in CT5 are always defined in terms of the amount of money accumulated per survivor. That is, we take the money that's accumulated in the bank and share it out between the survivors at time n.
Imagine in your example that we have 1000 people at the start, aged x. The accumulated amount in total would be:
1000 (1+i)ⁿ A¹x:-n
We then divide the total amount by the expected number surviving to time n, which would be 1000 nPx. So we get
(1+i)ⁿ A¹x:-n / nPx
altogether (the 1000 cancels).
Robert


Thankyou so much sir. Got it.
 
Back
Top