Formula for joint survivor benefit

[tope]

I am trying to price a benefit in excel but wanted to create a formula for benefit as follows:

Benefit pays 100% to member (x) and spouse (y), if spouse dies, benefit reverts to an single annuity, if member dies first benefit is paid at 75% continuous to the spouse

I see this as an ax(bar) computation but how do I seperate out the benefits

I have this formula

100% * axy

+  75% * vt tpx qx+t * ay

 

OR

 

75%* ax –  25%*(ay-axy)

 

Please let me know if Im on the right trach

 

 

 

 

 

 

 

[tope]

Thanks

[Author]

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