Pop Up Factor Formula

[Guest chrisb]

Looking for the formula for a joint & survivor factor where the benefit reverts to the single life annuity value if the contingent annuitant dies before the participant.

Thanks!

[Andy the Actuary]

Ooooooh, a pop-up formula! You can come up with a nice looking formula, say for a joint & 50%,

r x (ax + .5* (ay - axy)) + (1-r) x (ax - axy) = ax

==> r = 2 axy / (ay + axy)

Let's see

x and y both living, then payment is r x ax

x dies before y, then payment is .5 x r x ay

y dies before x, then payment is r x ax + (1-r) x ax = ax

Better check this carefully -- I passed part IV in '73.

[Guest chrisb]

Thanks Andy!