Deferred Joint Benefits

Question

In question 10 attached, with regards to the pension benefit, why does it reduce to the summation of two deferred monthly annuities in advance (a_55 + a_50) ?

 My equation of value would be (the annuities's are all monthly in advance): 10000 times the joint life annuity deferred for ten years plus 5000 times the last survivor annuity deferred for ten years. Using the formula for the last survivor annuity this reduces to 5000 times a deferred whole life annuity for x plus a whole life for y minus the joint annuity for x and y. 

But this is wrong and i do not understand why the answer is only the sum of the deferred annuity for x and y (where did the joint part go?)

I hope my question makes sense :(

Please help

Thank you (in advance) <3 

Comments

Hi Faith, please could you let me know where you got this question from?

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Hi Kelly. It is from the April 2017 faculty paper :) 

Answer 1

From your EPV equation for the deferred annuity benefits you need to further subtract 5000 times the deferred joint life annuity. This is because you have added 5000 times the last survivor annuity which is an annuity which pays until the later death of the two lives so you are double counting the 5000 + 10000 while they both are alive.

Hope that helps!