Actuarial notation

Actuary here. There's a subject called mathematical interest theory that explores time value of money beyond simple and compund interest that you learn in grade school. It makes use of this notation and is part of the US curriculum for actuaries.

For example, there's a concept of continually compounding interest as the limit of compounding frequency approaches infinity. Other growth patterns such as polynomial growth are theoretically possible. Anyone with basic calculus and algebra can learn it and it's a good subject for enhancing one's financial literacy. I'm surprised it's not taught in general finance.

Once you get the hang of it, AN reads beautifully. The concept of Life Tables and the ways the math can be abstracted away using these mystical symbols is incredibly elegant.

Side comment, when you get into the weeds with actuarial exams you quickly learn to respect older actuaries who had to solve these complex problems using clever heuristics instead of computing power. Once those heuristics are internalized they are able to give incredibly accurate off-the-cuff answers using their intuition. I remember my boss and I spending a week valuing a new product and presenting it to the wise old chief actuary who immediately felt something was off in the numbers and could point out where we likely made an error. It took me all afternoon to find the error, but of course he was right.

I really want to say that I hate this, but I'm sure it was invented for a reason.

And as someone who used to write half a dozen indices on tensors in general relativity problems, I should probably not be so quick to judge.

One of the points that I don’t think is fully clear from Wikipedia is that this is not just about notation - it’s about creating a limited set of tables that combine mortality and compound interest and which can then be used to calculate the desired discounted cashflow value by hand.

As such I think the use of the tables and notation have reduced significantly since PCs first appeared on the scene.

Today almost all life actuarial computations are done using either spreadsheets or dedicated (proprietary) software packages from actuarial consultancies which can do much more sophisticated cashflow projections - for example using stochastic investment return assumptions.

Might be too far to say this is a historical curiosity by now but not by much.

I used to do programming for a company that did loan calculation software. We would get specs from insurance company actuaries for how to calculate consumer loans that were made with credit life insurance attached. The ##### actuaries would always send us formulas that looked like the annuity formulas in the article: annuity due = (1 - v^n) / d, annuity immediate = (1 - v^n) / i. Except, they did not notice that the formula fails for zero interest loans ( zero divided by zero), which were a popular sales gimmick. There are probably a million or more of those loans out there still getting paid off with payments calculated using some arbitrarily small interest rate selected by the programmer to eliminate the zerodivide error when the actual interest rate is zero. Some of the actuaries calculated the insurance charges using really fancy formulas that were not zero divided by zero when the interest rate was zero, but zero divided by zero divided by zero. Limited-precision calculations of these functions were very badly behaved in quite a large neighborhood of interest rate zero, so, despite all the professional refinement of the actuaries, there is no telling how erroneous the payment number on your loan documents came out.

This makes me weirdly happy to see on hacker news. :)

Actual notation was the reason I got deep into LaTeX during my undergrad degree (actuarial science). I don't recall the library I used at the time, but if I were to re-do it today, I'd use this one: https://vigou3.gitlab.io/actuarialsymbol/. Vincent Goulet (from Laval University in Quebec) has done a lot to bring actuaries into open source and free software.

Once you internalize the notation (you have to for actuarial exams), it's actually quite powerful. Even though I have not practised in half a decade, I still am able to read 90% of the symbols and get the underlying mathematical formula.

It also makes a tremendous amount of sense when you use it in the context of a mortality table (see https://upload.wikimedia.org/wikipedia/commons/4/47/Excerpt_... as an example).

Interesting. Couldn't help but be reminded of station models in meteorology: https://en.m.wikipedia.org/wiki/Station_model#/media/File%3A...

Reluctant actuary here. It’s not as bad as Wikipedia makes it look, you guys. Not that much harder than some advanced algebra courses.