## Part II – Compound Interest and Wealth

Compound Interest Math Formula – The Most Powerful Math in the Universe

Please see my earlier post, Part I – Why don’t they teach this math in school?

For the sake of blowing the lid off this vast cone of silence, here’s the compound interest formula:

Future Value = Present Value * (1+Yield)N

This is the formula you use if you want to see how money grows over time, to become “Future Value.” Present Value is the amount of money you start with.  That could be \$100, such as in my examples below, or likewise a series of \$5,000 IRA investments each year.  Present Value is whatever you’re starting amount of money is today.

Yield is the interest rate, or rate of return, you get per year.  Usually expressed as something like 5.25% or 0.0525.[1]

N is the number of times you ‘compound’ the yield.  In its simplest form as written above, if you compound annually, N is the number of years your money compounds.

Example of the power of compound interest: Early investment for retirement

When do you use this formula?  You use it when you want to know how much your \$100 invested today, or this year, will grow over time.

To offer you an extreme example, using the compound interest formula:

What if you invested \$100 today, left it invested for the next 75 years, and you were able to achieve an 18% annual compound return?  How big an investment does your \$100 become?

Can I interest you in \$24 million?  Without working?

As I say that out loud, I feel like a late-night infomercial guy.  And that feeling makes me want to take a shower.  But the money and the pitch is nothing more than compound interest math.

I happen to believe there’s quite a few 20 year-olds who:

a) Could put their hands on \$100 today for the purpose of investing in a retirement account, and

b) Would like, at the end their life, to boast a net worth of \$24.6 million[2]

I know all you realists out there will say that 18% annual compound return for 75 years is a fairy tale, and of course I can’t disagree with you.

But I’m doing a magic trick here for the sake of making a point, so would you please suspend disbelief for just a moment and revel in the magic?  The point is not to argue about what reasonable assumptions may be, rather the point is to show why knowing how to do compound interest math could be a life-changing piece of information.

At the very least, its a tool that every citizen should be armed with.  Thank you.

To be slightly more realistic, but equally precise, with a series of other assumptions:

If you’re 20 years old now and you let your money grow for the next 50 years, at 12% yield, your \$100 invested today becomes \$28,900.  That’s also an amazing result.

Try it and find the Future Value for yourself, by inputting into the formula

Future Value = Present value * (1+Yield)N

PV = \$100

Yield = 12%

N = 50

Heck, having your money grow like this sure beats working for a living.

These facts are so amazing, I think, that they might induce a 20-year-old to forgo his XBox purchase this year, and invest the money instead in stocks, in a retirement account.

What about putting your money away in your IRA, \$5,000 per year from age 40 to age 65, earning 6% return on your money every year?  Would you like to know what kind of retirement you will have at age 65?  Compound interest can tell you precisely the number.[3]

You’ll have \$290,781.91[4]

And all of that becomes possible if we have some insight into the inexorable growth, the most powerful force in the universe, the one math formula to rule them all, compound interest.[5]

Part III – Compound interest and Consumer Debt

and Video Posts:

Video Post: Compound Interest Metaphor – The Rainbow Bridge

Video Post: Time Value of Money Explained

Addendum by Michael, added later: It turns out one of my high school math teachers not only does teach compound interest, but he included it in his math textbook, linked to here:

[1] I fear many of us learned how to convert a percent into a decimal in sixth grade, but not how to do anything useful with it.

[2] Yes, I hear you cynics, that this is in nominal dollars, and \$24 million won’t buy them then what it buys today.  But would you just stop being cynical for a moment, and appreciate the magic of compound interest?  Thank you.

[3] If your assumptions are correct, of course.

[4] To achieve this calculation, you’ll have to add up 25 separate amounts, in a spreadsheet.  The first amount, invested at age 40, compounds the most times and is expressed as \$5,000 * (1+.06)25.  The second amount, invested at age 41, compounds as follows: \$5,000 * (1+.06)24.  The third amount is \$5,000 * (1+.06)23, all the way until the 25th amount, which is simply \$5,000 * (1+.06).

[5] Thank goodness Sauron didn’t get his hands on the formula FV = PV*(1+Y)N, or else the hobbits would have been so screwed.  Ancient legend has it in the Silmarillion that Sauron actually did acquire the compound interest formula, but he interpreted the mysterious algebraic symbols as high Elvish, a language he could not read at the time.  Speaking of which, does anybody else want to use compound interest to become a Silmarillionaire?  Um, not so funny?  Ok, you’re right, but don’t worry, I’ll be here all night folks.  Don’t forget to tip your waitress.  And try the fish.

## Part I – The Most Powerful Math in the Universe Goes Untaught

On Teaching Compound Interest and Discounted Cash Flows

“The most powerful force in the universe is compound interest”

– Albert Einstein[1]

“Tomorrow and tomorrow and tomorrow,
Creeps in this petty pace from day to day
To the last syllable of recorded time”

This Spring I began teaching Personal Finance to a group of bright college students, and we recently wrapped up a section on compound interest and discounted cash flows.

What I’m trying to get across to these undergraduates is that all of the key financial choices they will make in their lives – all of their future decisions about consumer debt, retirement, insurance, purchasing a home, tax preparation, and investing – will be much, much better decisions if they deeply understand compound interest and discounted cash flows.

What are these concepts for?

The compound interest formula tells these students, and any of us who use it, exactly how quickly, and to what ultimate size, money grows in the future.[2]

Discounted cash flows reverses the process, and tells us what the present value would be of any given cash flow or series of cash flows that occurs in the future.[3]

I’ve realized over the course of the last few weeks, however, that I’m trying to convince these students of the absolute centrality of an idea that 95% of them have never heard of before walking into my class.

Not only this, but also 95% of the people my students will meet in their life never have heard of compound interest and discounted cash flows, and therefore will not have the slightest idea how profoundly it affects their lives and their personal financial choices.

Picture me in front of the class jumping up and down and waving my arms wildly (metaphorically of course), trying to get them to believe me.

And yet, why should they believe me when I appear to be the first (and possibly insane) person to ever argue this case?

I’m afraid that after they leave my class, the Financial Infotainment Industrial Complex will never again reveal the importance of compound interest and discounted cash flows to personal finance decision-making.

Why isn’t this taught as a requirement of Junior High School Math?

I was a strong math student in junior high and high school.[4]  I received a solid foundation in algebra, geometry, trigonometry, and calculus.  Of these, algebra has frequently proved useful, but none of the others apply to my life or career.

Compound interest and discounted cash flows, however, dominated my professional life as a bond salesman and hedge fund investor, and I make use of insights from them in my personal financial life all the time.

And yet, nobody taught me compound interest or discounted cash flows in school.  I’d be willing to bet that almost all of you reading this didn’t get taught these concepts in school.  That knowledge had to wait until I started as a bond guy at Goldman.  This, despite the fact that you only need junior high school level math – basically algebra and the concept of ‘X raised to the power of Y’ – to understand and use compound interest and discounted cash flows.

The fact that school taught, and I spent years learning, complex but ultimately very niche mathematical skills, combined with the fact that nobody taught the essential mathematical skills of personal finance (and Wall Street finance for that matter) really gets up my nose when I think about it.

More than gets up my nose, it puts me in a suspicious frame of mind.

Why would these essential skills not be taught to every junior high school student, and then re-taught to every high school student, and then elaborated on for every college student?  Because that’s how important this stuff is.  And how relatively unimportant trigonometry, geometry and calculus skills are for most citizens.

I’ve only come up with a couple of possible explanations, as I explain below, but please chime in with your own theories.

1. Math teachers, as a group, do not understand the role of compound interest and discounted cash flows in personal finance.

I fear this is true.  I’ve become friends with a few of my high school math teachers as an adult and with one I’ve discussed the power of compound interest as a math concept and as a personal finance concept.  Later in his career, long after I took his class, he taught compound interest as part of his lessons on mathematics skills known as ‘sequences and series.’

In these later days he emphasized to his students that if he had really understood compound interest – as a young man – as well as he does now, his working and his retirement years would look totally different.  Could somebody please tell the Professional Math Teachers Association (or whoever is responsible for this stuff) that this is really the key concept, and I mean, for everything?

2. The Financial Infotainment Industrial Complex wants to keep us down.  I’m afraid I’m coming around more and more to this explanation.  Nothing else makes sense.

I mean, seriously folks, calculus: Not relevant (for most people.)  Compound interest: relevant (for everyone.)

Coming up next: Part II –  Compound interest and Wealth

Part III – Compound interest and Consumer Debt

Part IV – Discounted Cash Flows Formula

——Addendum by Michael to this post:

One of my high school math teachers (and my high school advisor!) responded to my post by pointing out that not only does he teach compound interest, but that its part of the math textbook he wrote.  How about that?  I can’t resist linking to his textbook on Amazon, as my way of atoning for casting aspersions on math teachers.

[1] Albert Einstein frequently gets credited with this wise statement.  A quick interwebs search suggests Einstein didn’t necessarily say this, as the first mention in print is found circa 1983.  But Einstein could have, and should have, because it’s true.

[2] To get started on your own learning journey on compound interest, I recommend beginning by watching a video here, with my favorite, Salman Khan.  If you enjoy that, continue the process with videos on present value #1, present value #2, and present value #3

[3] A nice place to start on discounted cash flows is Salman Khan’s video on present value #4 (and discounted cash flow).  Khan doesn’t go far enough on discounted cash flows, or as far as I’m going to go in this series of blog posts to follow, but he at least gets us started, which is more than I can say for almost anyone else available for free out there.

[4] I didn’t pursue math in college, beyond one statistics class required for my concentration, which was Social Studies.  Shout out to the 0.0005% of readers (I chose an arbitrary but statistically insignificant number) who will recognize my major and salute me for it, rather than assume I spent my college years doing what the rest of you did in Social Studies in middle school – memorizing state mascots.