Actuarial Outpost What do N65 and D65 mean?
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#1
10-22-2019, 09:00 PM
 pony SOA Join Date: Sep 2012 Posts: 12
What do N65 and D65 mean?

Calculate the accumulated value of the benefit paid from age 60 to age 65:
(N60 - N65)/D65

What are N65 and D65?

Thanks.
#2
10-22-2019, 09:27 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,625

These are commutation functions, not used much any more in the SOA exams. Long ago (like back when I was taking the life contingencies exam) they were used a lot. Values by themselves really mean nothing, but ratios can be used for some calculations.

$D_x =v^x l_x$, not very useful. (where lx is from a standard life table, the number of people alive at age x; v is the normal interest function) Why you would want to calculate v^(number of people alive) seems incomprehensible, but the ratios actually turn out to be useful. Equally incomprehensible, why you would want v to that power times the number of people alive.

$N_x = \sum_{t=0}^\infty D_{x+t}$, not very useful.

That means (if you do the algebra / manipulation)

$N_x / D_x =\ddot{a}_x$, and that is a useful thing to be able to calculate.

You can do other similar calculations from a single table of N's and D's. For example

$N_{x+5} / D_x$ is a 5-year deferred life annuity due on (x), and that is a useful thing to be able to calculate.

Your study material may have a section on commutation functions, or you could Google them.

Last edited by Gandalf; 10-22-2019 at 09:38 PM..
#3
10-22-2019, 10:44 PM
 pony SOA Join Date: Sep 2012 Posts: 12

thank you so much Gandalf! 50 internet points for you