ERE in the university

[loutfard]

I just realised that 15€ earned and invested no has fair probability of growing into 32€ (42.56€ before inflation correction) in 15 years.

I thought I had a thorough grasp of the concept of compound interest. While that was true in a mathematical sense, I had until failed to see many of the very obvious real life consequences of that. Just mucking about with a spreadsheet and FI / ERE goals made this suddenly click for me.

This enables all kinds of funny math. A FI / ERE example. I plan to start cycling to work soon. For under four hours, I'll get paid 32.16€. That's about 8.5€/hour. But if investment portfolio performance stays somewhat in line with historical averages, my one hour effort now will be worth 18.18€/hour in 15 year, or 23.43€/hour in 20 years. While cycling! Totally worth it!

[loutfard]

I tried to visualise this exponential growth a bit using the excellent Lybniz graph plotting software using fairly simple high school math. Jupyter notebooks certainly are more versatile, but this old fart has strong muscle memory. Look at these plots:

y=1.06^x
y=1.33*1.06^(x-5)
y=1.8*1.06^(x-10)
y=2*1.06^(x-12)
y=2.4*1.06^(x-15)

The math really speaks for itself, but I've only recently grasped the real world consequences. You'd need 33% more if starting in 5 years and 80% more if starting in 10 years than the person who saved at the very beginning. This might sound like elementary financial education to a lot of US citizens. I can assure you that it is not to oh so many with a firm grasp on maths outside the US.

[WFJ]

One of my former professions was attempting to teach how to use/apply the financial calculator. Out of a large sample, I know of three students who had lightbulb moments and drastically changed their spending/savings habits. Most treated the knowledge of how to use a financial calculator or TVM as nothing more than another exercise in memorization, like knowing when the war of 1812 began. Most students are exposed to TVM in basic math courses or economic courses in high school but the knowledge is internalized by few. Standard deviation is historically introduced in 7th grade life science (part of heredity lesson plan) but how many college graduates can even define it, let along calculate it? It is sadly the same thing with TVM/compound interest.

[loutfard]

I studied latin, greek and mathematics in secondary school (12-18yo). This traditionally was the intellectual elite's path over here. It was also a curriculum with zero economics. We deeply understood this stuff from a mathematical perspective, going far beyond into thoroughly understanding matrices, Bayesian probability, advanced 3d geometry, geometrical functions, derivatives, logarithmics at as advanced a level as could be expected from a 17 year old. Application to the economic world was extremely rare though.

It didn't help my parents - really great people - were financially illiterate beyond the point of "we save diligently, like squirrels.". At one point, young me, very aware of compounding, suggested them to move their savings account from a very expensive bank they had traditionally used to a newcomer on the local market with a higher credit rating. They offered three times the interest rate: 6% instead of a lowly 2%. They wouldn't hear a word of it. A few year later, their bank went under in the financial crisis. I've since slowly gained their trust in financial matters. I even got them into index investing a tiny part of their nest egg that had always been in savings accounts. Just to say that apart from the important absolute foundation, I educated my parents instead of the other way round.

Happy I have finally internalised the economic application more deeply. Even if I'm 25 years late to the party, it feels I discovered this blind spot just in time to still considerably benefit and guide my younger spouse along a much clearer financial path.

[Sclass]

I was taught this stuff at a very young age. 13 I think. It was kind of a tradition from my grandfather. Actually it was taught like a religion in our home. Generational wisdom.

At 13 dad sat me down and showed me the chessboard and wheat problem. The folded paper problem. Then the interest problem. We wrote all the payments term by term on a big sheet of computer paper. Once the pattern became clear he showed how it could be handled as a binomial expansion. Later on came some calculus and the simplest differential equation. Then how to search for that relationship in the wild.

Took me twenty more years to actually connect this to stock investing.

My grandfather and father had already connected the two. But they never explained the whole thing to us. It’s taken me to today to finally understand why they never taught the connection from the get go even though they both used it to make the overwhelming majority of their wealth.

I can only fathom that they wanted their kids to be indebted to them but not other bankers.

In my mind the exponential is the root of inequality, famine, disease and war.

[jacob]

Then how to search for that relationship in the wild.

I think this the lever-point of where education fails. Formal thinking is compartmentalized and mentally boxed up. It lives on a piece of paper and is only activated when that piece of paper is on a table at home or at school. It is not connected to concrete thinking outside those situations.

Even when it is, it is almost always done in a "here's the formula, now apply it on this problem", e.g. "show that X problem can be described by Y equation". Despite my physics background---the business of physics is literally describing the "wild" with math---there were very few situations where we started with blank slate theory as in "take some measurements (e.g. falling ball) and find a phenomenological description of its behavior".

I'm not entirely sure how I managed to break this compartmentalization and get to a point where I am, in my humble opinion, rather good at it. I think it was starting to look at analogies between existing theories, e.g. an electric circuit is like a hydraulic circuit because the formal thinking is the same. This is the beginning of systems thinking. For example, price volatility calculations is like the hydrodynamics of a flowing river. Interest rates are like radioactive decay in reverse-time. And so on.

[7Wannabe5]

I believe that it is entirely possible to fully comprehend the math from a young age, in both theoretical and concrete/applied context, and still flunk the marshmallow test. I offer myself as evidence

[ertyu]

it is entirely possible to fully comprehend the math from a young age, in both theoretical and concrete/applied context, and still flunk the marshmallow test.

+1

[Sclass]

Yes. It’s a lot harder to train a holistic understanding of nature. But, I’ve found it easier to use than a compartmentalized understanding as I hit the limits of my weak mind. I think it’s a more efficient way of understanding the world. More clever software for the weaker hardware.

where I am, in my humble opinion, rather good at it. I think it was starting to look at analogies between existing theories, e.g. an electri

Humble indeed. I think it’s more efficient and thus easier to understand things this way. Just getting there is tough especially the way traditional education works.

[7Wannabe5]

@ertyu:

Yeah, I can't decide if the primary problem is that I am too self-indulgent or too much of a soft touch, but it definitely isn't the lack of early education in math application to economics. My father was a CPA with a Masters in Tax Law who belonged to a stock club which doubled as a poker party. I think he gave me a government booklet on the topic of Options when I was still in elementary school. I have a degree in mathematics with focus in actuarial science, and I have also run my own business. I just do not have the boundaries that prevent a person from cashing out their "free time" chips early, and thus by necessity, often.

OTOH, a truly holistic perspective would go beyond the monetary. For instance, highly likely that my current net worth would be a good deal higher, if I had taken quant or actuary job after graduation in my early 20s rather than choosing to stay home with my babies. What's it worth to have one of your adult children tell you "Thank you for giving me a fun childhood." ?

OTOOH, what's my excuse for not revving up the earning machine in all the years I've been a member of this forum already?!?! Thus, I offer myself up as an object (or abject?) case study for FI Failure Mode 2b or 3c.

[Sclass]

OTOH, a truly holistic perspective would go beyond the monetary. For instance, highly likely that my current net worth would be a good deal higher, if I had taken quant or actuary job after graduation in my early 20s rather than choosing to stay home with my babies. What's it worth to have one of your adult children tell you "Thank you for giving me a fun childhood." ?

I think you’ve done really well at finding alternatives to the money button. This forum is interesting to me because people here live by diminishing their dependence on the button that everyone chases. There are multiple degrees of freedom. The trick is knowing them.

[WFJ]

I looked it up, powers are covered in the 8th grade, so around 13-14 years old. Most math textbooks include some kind of comparison between simple and compound interest and alternative growth rates in middle school. I've done some variation of "Sam Saver vs. Steve Spender" problem 2^20 times and few ever connect this to their daily lives.

https://www.mathed.page/middle-school/p ... er%20Notes