CT5 Premium conversion equation

I always have doubt about the premium conversion equation for Assurance paid immediately.
Which one is correct?
i) \( \bar A_x = \left(1+i\right)^{0.5} \left(1 - d \ddot a_x\right)\)
OR
ii) \(\bar A_x = 1 - \delta \ddot a_x\)
extended to contingent benefits... Some solution used as...

AND

 

Got it.
Thanks for viewing and thinking

 

Could you tell when to use which?

Thanks!
Regards,
Shyam

 

The first one

It is easy to use because the annuity function payable in advance is tabulated

 

I believe both are correct. It is different assumption, therefore it will be slightly different.
1) assumed death occured at mid year.
2) assumed uniform distribution of death.

Q 1.19 in Q&A bank clearly explain this.

Thanks.

 

\( \bar A_x = \left(1+i\right)^{0.5} \left(1 - d \ddot a_x\right) = 1 - \delta \bar a_x\)