ct5 2017 april ques 10

[Sudhan Paudel]

I am confused on the part where the EPV of pension benefit is calculated. I am trying to grasp the idea that 10,000 per annum to two people is equal to 5000 per person. But what if the amount was different, say 11,000 if both lives alive and 5000 of only one person is alive. Could you please help me grasp the idea used in the answer of pastpaper, and also suggest me another alternative approach to this solution?

Thank you very much!

 

[Richie Holway]

Hi Sudhan,

For the pension benefits, the payments that would be made at any future time t are:
(1) nothing if t<10
(2) 5,000 pa if t>=10 and just one life is alive
(3) 10,000 pa if t>=10 and both lives are alive.

If we pay two single whole life annuities of 5,000 pa, one to each life separately, then:
· when both are alive the total payment will be 10,000 pa
· when just one person is alive the total payment will be 5,000 pa
· when both are dead no payment will be made.

This matches the required payments, except that we need to ensure that no payment is made before time 10 – that is, we need the annuities to be deferred annuities.

If you didn't spot this, an alternative is consider the benefits that start paying at time 10:

(1) 5,000 pa if (55) is alive and (50) is dead at time 10, paid until death of (55)
(2) 5,000 pa if (50) is alive and (55) is dead at time 10, paid until death of (50)
(3) 10,000 pa if both (55) and (50) are alive at time 10, payable while both remain alive; reducing to 5,000 pa on first death and continuing until the second death.

It is then possible to construct formula for the EPV of each of these using appropriate single life and joint life annuities.

I hope this helps,
Richie