Talk:Actuarial notation

Inaccurate calculations

Statement is $\,i=0.12\!$, we have $\,i^{(12)}=0.1139\!$

In point of fact $\,0.12^{(12)}=0.000000000008916\!$ Malangthon (talk) 20:59, 14 May 2012 (UTC)

You've misunderstood the actuarial notation here. You are conflating (a superscripted number denoting exponentiation) with (a bracketed superscript number which relates to the timing of compounding). The superscripted bracketed 12 is not saying to take the interest rate to the twelfth power. It is saying that a rate of interest of 0.12 per annum compounded annually is equivalent to a rate of approximately 0.1139 per annum compounded monthly. The derivation is as per the formula on the article page. The intuitive check is that if you compound interest more often (monthly as opposed to annually) then a slightly lower interest rate can be used to achieve the same value; this is borne out noting that 11.39%pa is a little less than 12%pa. -Stelio (talk) 09:03, 18 March 2016 (UTC)

curtate expectation and birthdays?

"\,e_x\! is the curtate expectation of life for the people alive at age x. This is the expected number of complete years remaining to live (you may think of it as the number of birthdays they will celebrate)."

I believe this would only be true if x is an integer? For example, for x = 0.5, the number of birthdays celebrated is not equal to the number of complete years remaining, e.g. if the number of years remaining is 0.75. 76.20.109.233 (talk) 21:39, 7 February 2010 (UTC)

You might also want to add that one only celebrates a "birthday" if one lives strictly beyond one's integer age; i.e. if the moment of death is at precisely 5th birthday t = 5, then one has only reached one's 4th birthday, but not one's 5th. 207.62.177.227 (talk) 02:33, 9 February 2010 (UTC)

Incorrect labelling of the example notation?

Symbol 4 is explained as "life insurance" in regards to the positioning of the "1" above the age of entry "x". I believe this to be incorrect. The "A" denotes the life insurance/assurance and the positioning of the 1 dictates when payment of the benefit would occur, i.e it specifies the type of life assurance be it: term (when the 1 is above x), a pure endowment (if it is above n) or an endowment assurance if it is omitted. Opinions? Quikgoner (talk) 19:38, 23 February 2010 (UTC)

This should really have a version for annuities as well - to show the similarities and differences.

term certain symbology

Using \overline and | to create a term-certain half-box is pretty ugly. The following function definition code, inserted in a LaTeX preamble, vastly improves it, but it doesn't work with texvc.

\def \termcertain #1% {% {\setbox 0 = \hbox {$\scriptstyle #1$}% \dimen 0 = \ht 0 \advance \dimen 0 by 1,0 pt \ht 0 = \dimen 0 \dimen 0 = \dp 0 \advance \dimen 0 by 1,50 pt \dp 0 = \dimen 0 \vbox {\hrule \hbox {\box 0 \vrule }}% }% }

Usage: a_\termcertain{n}

If anyone know how to fix this in any way, it would vastly improve the look of the thing! — Preceding unsigned comment added by 91.125.102.24 (talk) 21:11, 12 June 2011 (UTC)

I've raised a Phabricator ticket to improve formatting, as per User:Stelio/Actuarial/Notation. -Stelio (talk) 03:54, 13 September 2017 (UTC)

inconsistency in life annuities section

The third example in the life annuities section describes it as an annuity that ends at death. The general example though would seem to indicate that this is term certain paying for 10 years even if the annuitant dies. Which is correct? 12.34.36.250 (talk) 21:11, 29 January 2015 (UTC)

The description is correct. The life annuity is payable until the earlier of the death of the person currently age 65, or the end of 10 years. Rgrosz78 (talk) 01:35, 1 February 2024 (UTC)

Removal of external links

I've removed most of the external links, because they had nothing whatsoever to do with actuarial notation. Instead, they were simply links to the home pages of several actuarial organizations and, in one case, a primer on actuarial science that did not address actuarial notation. NewYorkActuary (talk) 01:57, 25 December 2015 (UTC)

Removal of addition re: continuous interest

I removed the recently-added sentences concerning continuously-compounded interest. The statement about the exponential distribution merely duplicated material that appeared a few lines above it. As for mentioning the Black-Scholes model, the fact is that all of the interest measures are used in some model or another. None of the others have any applications mentioned, so it seemed out-of-place to do this just for the continuous-rate version. It also seemed a bit misleading to just mention Black-Scholes, and not any of the very many other models that use it. Finally, I agree that it was appropriate to provide a link to "continuously compounded interest", so I added it to some existing language in the same section. NewYorkActuary (talk) 16:31, 2 February 2016 (UTC)