Part VI – Concluding Thoughts on Personal Finance Math

conspiracy_thinkingOr, why everyone needs to know this, beyond getting rich or avoiding poverty.

Please see my earlier posts

Part I – Why don’t they teach this in school?,

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part IV – Discounted cash flows – Pension Buyout Example

Part V – Discounted cash flows – Annuity Example


A further reason why we need to learn discounted cash flows as a society

Are the US government’s assumptions about future social security obligations reasonable? Or are they instead unrealistic, or based on a Ponzi Scheme, as Peter Schiff and Ron Paul claim?

If you could do discounted cash flow calculations you could begin to form an answer.  You can see how the federal government would calculate exactly what the present value of those obligations is.

But “discounted cash flows” sound so esoteric to the average citizen – since we never learned it in junior high – that pundits and politicians with conspiracy theories who casually throw around words like “Madoff” and “Ponzi” begin to sound reasonable in comparison.  Which is really not a helpful direction for us to go in, as a society.


It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.



I would love for Bankers Anonymous readers to explain to me[1] why the most powerful mathematical formulas in the universe, compound interest and discounted cash flows, never get taught to junior high students, then high school students, then college students.  And then again to anyone applying for a credit card, or mortgage, or car loan, or annuity, or pension, or saving for retirement.  Or arguing about the growth of federal debt – or the rise of future social safety-net obligations.

We’re blind people stabbing each other in the dark without these formulas.

All of the consumer financial protection bureaus in the world can’t help if consumers have no tools to do their own thinking.

All the fiscal cliff negotiations and partisan point-scoring amount to a tale told by an idiot, full of sound and fury, signifying nothing, if we as citizens cannot see how money grows in the future or how future obligations get valued today.


“Tomorrow and tomorrow and tomorrow,
Creeps in this petty pace from day to day
To the last syllable of recorded time,
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!
Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.”

–Macbeth, Act V, Scene 5


Part I – Why don’t they teach this in school?,

Part II – Compound Interest and Wealth

Part III – Compound Interest and Consumer Debt

Part IV – Discounted cash flows – Pension Buyout Example

Part V – Discounted cash flows – Annuity Example

and Video Posts

[1] I’m searching for some explanation better than 1. Math teachers don’t get it and 2. The Financial Infotainment Industrial Complex doesn’t want you to know about it.  And by the way, I don’t really ‘blame’ math teachers, just like I don’t necessarily think there’s a vast conspiracy of the “Financial Infotainment Industrial Complex.”  But I do like saying that phrase, as it sums up nicely the financial crap we get inundated with all day long.

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14 Replies to “Part VI – Concluding Thoughts on Personal Finance Math”

  1. I just graduated with a degree in Agricultural Engineering only two years ago, and we used these formulas all the time. These forumlas were old news for all the farmers in the classes. They would never buy a tractor without running this analysis on 5 or 6 different ones. These formulas were also on the first test towards getting an engineering license. I work as an environmental engineer now and use these formulas when comparing remediation alternatives.

    I think the problem is, even if you do know these formulas, the answers they give you aren’t sexy. I own a S-10, Cherokee, and Corolla right now, all of which I have lost very little money on when you factor in the maintenance costs and how much I can still sell them for. But these vehicles aren’t sexy. ‘Bailing on old and poor people’ as it’s painted, is also not sexy.

    If you want people to use these formulas again, you have to make them sexier. Your only other alternative is to make people think with their mind again, rather than instinct, but, again, that’s just not sexy.

    1. Ok, so for my next presentation of these formulas, we’ve got to figure out a little Justin Timberlake “Bringing Sexy Back” tie-in? This a great idea.

  2. In our lifetimes we have seen the prime rate (mother of all rates) return rates ranging from >20% to <1%. Given that kind of insane volitility, even people who understand these discounting techniques are at a real loss to find present or future values. Like you I dearly wish that the average American fully understood these simple formulas, because the power of compounding interest IS the most relevant issue facing this debt ridden society. Nevertheless I disagree with your simplistic (and somewhat insulting) assuption that the poor don't get it. They get it, but the demands of their present make future planning somewhat of a entitlement they simply almost never have.

    1. Thanks for your comments and I agree that the low-interest rate environment presents new challenges. (I’m shortly going to post thoughts on some of those challenges, as I see them.)
      I really don’t mean to be insulting or to imply that poor people don’t understand the power of compounding or discounting math. I mean to imply that everybody – rich, poor, and in the middle – needs to understand this stuff better than we do. Poor people will suffer MORE from not understanding it, because wealth provides a material cushion against the consequences of ignorance. But I’m under no impression that this knowledge is widespread in any strata of society.

  3. I Forgot one extremely relevent issue concerning present and future values. How does one truly find the RATE (say of lost value due to inflation) when the government’s CPI is so OBVIOUSLY a lie for most of us? For instance, does anyone reading this truly believe that 2012’s inflationary rate was ONLY 1.7%? That’s what our goverment’s COLA’s are telling us.

  4. Great posts. However, you missed one other HUGELY important formula that everyone should follow, but most people, companies and govts don’t… here is the formula:


    As a corollary to the above: pretending everything is ok, printing money, crying, blaming everyone else doesn’t bring the equation into balance.

    1. Or another version of that formula, as another commenter wrote previously, quoting Charles Dickens, on my post “What is Wealthy:”
      “Annual income twenty pounds, annual expenditure nineteen pounds nineteen and six, result happiness. Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.”

  5. I think I can provide part of the answer to why these concepts are not taught to students in junior high, high school, or college. When I was junior high and early high school (it would be relevant to add that I attended school in the Dallas area as I suspect that some of the problems may differ from state to state) the main focus of every math class I was in centered on getting people to pass the state testing at the end of the year. Concepts that were not on the test were simply not taught. The schools were ranked and given funding based on what their student’s scores were. I should note that the state exam covered nothing that would help someone manage their money. Later in high school I started taking AP (or Pre-AP, Advanced …) classes in most subjects including math. However even here this was totally ignored, but for a different reason. In the AP classes there was an implicit assumption that you were strongly considering a career in a science or engineering, so the focus was to get the students ready to take calculus at the end of high school. I learned a lot of trig, algebra, calculus, logarithms, but not compound interest or anything about managing money. I don’t mean to imply that these reasons apply to every public school across the nation, but I know that many other schools in the state have those problems and with 30+ million people Texas is not a small part of the nation.
    College is a harder subject to address because every school has its own set of requirements that differ from major to major. The school only requires that students take either calculus or linear algebra. I think the school does offer a class in personal finance but it will not count toward any of the degree requirements. There is an attitude that college math classes should about pre-science skills and many math professors I’ve met are more interested in proving extremely abstract theorems about strange things then to apply math to anything.
    Also, I can’t help but notice that while you point out credit cards, mortgages, and car loans as places people should know these concepts, I would add that colleges and universities take advantage of people not understanding these concepts. A few weeks ago I got a notice from the university that I have come to expect every year at around this time: “Tuition to Rise 3.7 Percent”. Every single year the increase has been close to 4% and yet not a single person around me seems to think much about this at all. My girlfriend is going to be leaving school with close to $90,000 in student loans and were still not sure how we are going to address that. I cannot help but fear the fact that countless students leave college with horrifying levels of debt and most of them don’t understand this concept. The cost of college just keeps increasing at an astounding rate and this is a time where not having a college degree is not an option. The increasing cost of school will make the problem of wealth inequality even worse than it already is. I’ve talked to many other students about the increasing cost and their lack of awareness of compound interest and cash flow is extremely clear. They cannot see past the one time increase of the cost or how at 8% their loans will cost far more then they think they will. In the case on one particular person I asked them how much they though they needed to pay off student loans…they were wrong by more than $50,000. Students entering school do things like take their cost for the year and multiply by 4 thinking that they now know how much money they need. I’m watching my generation take on stunning levels of debt without understanding the true cost of school and before they even have their first job.

    1. Robert –
      Thanks so much for your thoughtful comments. I really think the nexus of higher-education and finance deserves more careful thought. I plan to do some writing and thinking about this in the coming weeks…I look forward to your dialogue.

  6. I found your site as I am going to teach a personal finance class at a local college.

    My guess is that in reality very few people have ever really accumulated money primarily through compounding.

    You used the example of saving 5,000 from the age of 40 till 65. Most Americans don’t earn enough money to do that. And the result of doing so is almost laughable. 265,000 at retirement won’t last but a year or two.

    As a general rule poor people are poor not because they don’t know about compounding, but because they don’t earn more money.

    And well-off people aren’t well off because they know about compounding, but because they earn (inherit) more money.

    Indeed it is one of the reasons that education ‘pays’ for itself. If higher compounding were the secret sauce, rather than higher salaries (of college graduates) then everyone would simply take their tuition payments and let them compound rather than invest in their education. (of course for anyone who has money compounding is wonderful)

    As a bond salesman you know the most important thing about money is the vig. What people think of as ‘Wall Street’ isn’t compounding anything, they are just taking a really small fee on a really big number.

    1. Hmmm. There are many truths, and we might agree on a number of them. But I would only teach some truths to college students in personal finance, and they wouldn’t be the ones you’ve highlighted here.

    2. “In reality very few people have ever really accumulated money primarily through compounding.” – is the real problem, not the fact that poor people don’t make enough money.

      The reason why most poor people stay poor is because they do not know how to properly budget their money so that they CAN invest.

      Addtionally, the belief that you need to earn a college graduate salary to become wealthy is completely ludicrous…

      If you simply save your money and invest it well the interest you are making on your investments can easily surpass what you could have ever dreamed of making working in a highly paid “White-Collard” job.

  7. This is a great series of post to help people understand the basics of compounding interest…BUT…as the 12,503rd reader of this post (or whatever number of previous posts…the numbers go down which is interesting), I’m wondering if the other tens of thousands of readers are as frustrated as I am? The problem with understanding compound interest is that it makes it clear that most, if not all, retail investment products which are offered to the average person are based on taking advantage of average ignorance – just like your annuity example or the pension buyout example or credit card examples, etc., etc.

    As a mere commoner, as opposed to landed gentry or Mitt Romney, where can I find a worthwhile investment? Where can someone like me find an investment vehicle, or preferably compare multiple investments using these formulas, that would make it worth my time? Should I go to EdwardJones (or their competitors) and let one of their salespersons get me into a product that MIGHT average 5%+ growth OVER 30 years (or be the same as a checking account over the past 3 years; or lose all my money in the next recession…2020?), or should I just keep my money in a savings account, bonds, and CDs? How can I use my knowledge of compound interest to benefit me, rather than simply understand how I’m being taken advantage of?

    1. Hi – I left a longer answer to your question on the other blogpost you queried. But, in brief, the answers you seek are in books. I’ve reviewed a bunch of them here. Read the classics. Also, the answer to how understanding compound interest is key to making good investments is in my book. It’s the central point of my book. If you don’t want to buy it, ask your library to order it for you.
      Good Luck!

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Public Speaking


I founded Bankers Anonymous because, as a recovering banker, I believe that the gap between the financial world as I know it and the public discourse about finance is more than just a problem for a family trying to balance their checkbook, or politicians trying to score points over next year’s budget – it is a weakness of our civil society. For reals. It’s also really fun for me.

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