Explaining the magic of compound interest to teenagers

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Nosh
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Explaining the magic of compound interest to teenagers

Post by Nosh » Thu Jul 18, 2019 8:22 am

Hi everyone,
I've recently started teaching a course in a local college on a subject that has nothing to do with personal finance, but includes some basic math and critical thinking concepts. From conversations with the students, I can see why so many people complain that the lack of personal finance education is a major problem in this country. I know that 95% of the students will never use most of what I am supposed to teach, so, while creating my lesson plans, I sneak in a little personal finance education whenever the concepts are appropriately parallel. Obviously, none of this is in the textbook, so I need to provide references or write up the information myself.

My next opportunity is to talk about Compound Interest (I'll have around 15 minutes for this), and since this is such an important concept, I want to do the best job possible. So my question to the Bogleheads community is, what article / chapter in a book etc. that you have read did the best job explaining compound interest, the importance of starting to save while young and avoiding debt and lifestyle creep?

Thanks!

onourway
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Re: Explaining the magic of compound interest to teenagers

Post by onourway » Thu Jul 18, 2019 8:29 am

I can think of no simpler, more effective lesson to the power of compound interest than the 'would you rather have a million dollars today or a penny doubled every day for a month? question.

Jags4186
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Re: Explaining the magic of compound interest to teenagers

Post by Jags4186 » Thu Jul 18, 2019 8:31 am

onourway wrote:
Thu Jul 18, 2019 8:29 am
I can think of no simpler, more effective lesson to the power of compound interest than the 'would you rather have a million dollars today or a penny doubled every day for a month? question.
+1

We got this lesson in 3rd grade and I never forgot it.

Thank you, Principal Walker!

cshell2
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Re: Explaining the magic of compound interest to teenagers

Post by cshell2 » Thu Jul 18, 2019 8:34 am

I think my son was maybe 14 when I showed him the chart with the one guy that saved 2K/year for 10 years starting at 25 then quit and the other guy that started at 35 and never caught up to the first guy. That really made an impression on him.

onourway
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Re: Explaining the magic of compound interest to teenagers

Post by onourway » Thu Jul 18, 2019 8:37 am

cshell2 wrote:
Thu Jul 18, 2019 8:34 am
I think my son was maybe 14 when I showed him the chart with the one guy that saved 2K/year for 10 years starting at 25 then quit and the other guy that started at 35 and never caught up to the first guy. That really made an impression on him.
Yes, this would be a great way to make the lesson introduced in the penny question directly applicable to their lives in the near-term.

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Re: Explaining the magic of compound interest to teenagers

Post by KlangFool » Thu Jul 18, 2019 8:41 am

OP,

Rule of 72.

If the annual return rate is 8%, it takes 72/8 = 9 years for the money to double.

KlangFool

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Re: Explaining the magic of compound interest to teenagers

Post by Sandtrap » Thu Jul 18, 2019 8:42 am

My mom did this with pennies and loose change on the dinner table, the bed, the floor, the carpet in front of the TV that had tubes in it. She was a bank auditor/accountant and teaching us kids everything about finance and how money works was her priority.

Depending on how many teenagers, pass out handfuls of pennies. Some learn better when the lesson can be touched and spacially worked with on a desk.

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Re: Explaining the magic of compound interest to teenagers

Post by AAA » Thu Jul 18, 2019 8:43 am

The example of doubling a penny every day for a month is instructive but 100% daily interest is not very realistic.

How about an example of starting with $1000 and getting 5% simple interest vs. 5% compound interest every year. After 20 years, you end up with $2000 vs. $2653, respectively.

coachd50
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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 8:48 am

Nosh wrote:
Thu Jul 18, 2019 8:22 am
Hi everyone,
I've recently started teaching a course in a local college on a subject that has nothing to do with personal finance, but includes some basic math and critical thinking concepts. From conversations with the students, I can see why so many people complain that the lack of personal finance education is a major problem in this country. I know that 95% of the students will never use most of what I am supposed to teach, so, while creating my lesson plans, I sneak in a little personal finance education whenever the concepts are appropriately parallel. Obviously, none of this is in the textbook, so I need to provide references or write up the information myself.

My next opportunity is to talk about Compound Interest (I'll have around 15 minutes for this), and since this is such an important concept, I want to do the best job possible. So my question to the Bogleheads community is, what article / chapter in a book etc. that you have read did the best job explaining compound interest, the importance of starting to save while young and avoiding debt and lifestyle creep?

Thanks!
Good luck to you :) It will be a noble effort I am sure. The hardest part will be to find a real example that the students can relate to and yet still be alluring. As we all know, the biggest part of compound interest is TIME. The real "power" of compounding doesn't kick in for decades in most real world situations. It will be hard to get the avocado toast and premium coffee generations excited over the idea of of an extra $10.

That said, I think what @cshell2 described had the most impact on me.

Definitely worth it to teach though, you might impact one or two, and that would be a great/life changing thing for those students.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 8:52 am

At the college level students should see the functional form of different dependences on time, such as linear, geometric, power presented with real life examples such as the one mentioned just above for 5% simple and compound. The doubling every period is a good way to make an impression but I think a realistic real life interest rate is more helpful. If these students are still struggling with fifth grade math concepts than maybe the algebra would be too much and other suggestions in this thread sound good. It might be nice if you had time to show the impact of costs on compounded growth of investments. I also like cshell's example.

If there were more time and the audience is literate in algebra one can show how the "magic" of compound growth is not even magic but that the difference is the accumulation over time of growth applied to previous growth, which is the whole point. But showing that explicitly takes some work and an audience willing to pay attention. I personally prefer not so see words like "magic" applied to things that in fact are perfectly ordinary but just not intuitive. The whole point of a lot of math education is honing the intuition to get past things like that. But again, as you say, this is not the main point of what you are doing and time is limited.

Anyway, good for you.
Last edited by dbr on Thu Jul 18, 2019 8:59 am, edited 1 time in total.

jibantik
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Re: Explaining the magic of compound interest to teenagers

Post by jibantik » Thu Jul 18, 2019 8:58 am

Exponential growth is extremely hard to get an intuitive sense of. That is why advisors can charge 1-2% fees, which can end up losing you over 50% of your total retirement savings, because the 1-2% _seems_ small.

To see how unintuitive exponential growth is for our minds, one interesting thing you could mention is that if you fold a paper in half ~100 times, it will be thicker than the size of the known universe. Easy to walk through specific points too, like at X folds you are in the next town, at Y folds you are at the moon, etc.

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Re: Explaining the magic of compound interest to teenagers

Post by miamivice » Thu Jul 18, 2019 9:00 am

I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.

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Re: Explaining the magic of compound interest to teenagers

Post by livesoft » Thu Jul 18, 2019 9:01 am

Whatever you do, do not use the word "magic" because it is not magic. It is math.
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 9:03 am

jibantik wrote:
Thu Jul 18, 2019 8:58 am
Exponential growth is extremely hard to get an intuitive sense of. That is why advisors can charge 1-2% fees, which can end up losing you over 50% of your total retirement savings, because the 1-2% _seems_ small.

To see how unintuitive exponential growth is for our minds, one interesting thing you could mention is that if you fold a paper in half ~100 times, it will be thicker than the size of the known universe. Easy to walk through specific points too, like at X folds you are in the next town, at Y folds you are at the moon, etc.
That paper folding thing is really good. The pennies doubling, folding paper, and cutting toothpicks in half are great experiments for early elementary kids. Another insight about exponential "growth" is to mention radioactive decay which extends the model to negative exponents but is highly relevant in a nuclear age.

I agree 100% with trying to communicate the impact of compound fees on investment results, and that example is a real life financial truth.

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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 9:05 am

miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 9:08 am

livesoft wrote:
Thu Jul 18, 2019 9:01 am
Whatever you do, do not use the word "magic" because it is not magic. It is math.
A point I would emphasize also.

coachd50
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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 9:10 am

dbr wrote:
Thu Jul 18, 2019 9:05 am
miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.
I don't see how that is discussing compounding though. I took his post to mean that for most of an average human investor's life span, the deposits/contributions will impact the balance far greater than any compounding benefit. THAT is the hard part to get the young to embrace.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 9:20 am

coachd50 wrote:
Thu Jul 18, 2019 9:10 am
dbr wrote:
Thu Jul 18, 2019 9:05 am
miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.
I don't see how that is discussing compounding though. I took his post to mean that for most of an average human investor's life span, the deposits/contributions will impact the balance far greater than any compounding benefit. THAT is the hard part to get the young to embrace.
That is a fair point. That was what I meant by the statement "you have to do the math in a little more complicated way." What is involved is both the contributions and the compounding. Also, compounding is not a "benefit" that one somehow "gets." It is just a name for the model that describes what happens when something grows by applying a periodic growth rate to what one has at the beginning of each period. I am not even sure there is a real life example in day to day investing to which the compound model does not apply. That case would be a deposit at simple interest, which is not where most people would be invested.

One thing that is illustrated here is what livesoft stated in this thread is that the point is not some entity called "compounding" but rather it is just doing math as appropriate. There is no easy route to doing that quick and dirty.

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Re: Explaining the magic of compound interest to teenagers

Post by miamivice » Thu Jul 18, 2019 9:22 am

dbr wrote:
Thu Jul 18, 2019 9:05 am
miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.
To state what I said above in a different way, the net worth line on my Excel chart is a linear rather than polynomial line. This is different than I expected when I was a college student. I was sure it woudl be a poly curve fit due to the magic of compound interest. Maybe someday it will become polynomial but not today.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 9:28 am

miamivice wrote:
Thu Jul 18, 2019 9:22 am
dbr wrote:
Thu Jul 18, 2019 9:05 am
miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.
To state what I said above in a different way, the net worth line on my Excel chart is a linear rather than polynomial line. This is different than I expected when I was a college student. I was sure it woudl be a poly curve fit due to the magic of compound interest. Maybe someday it will become polynomial but not today.
Yes, I understand that exactly. That is what you would expect if you are making constant contributions and engaging in a compound growth process at the same time. If the contributions are not constant and the compound growth rates are variable it gets more involved. Whoever taught you in college didn't talk enough about what model applies to which real-life example and what the effect of the magnitude of each contribution has on what the outcome looks like. I think your example is very helpful.

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Re: Explaining the magic of compound interest to teenagers

Post by finite_difference » Thu Jul 18, 2019 9:29 am

dbr wrote:
Thu Jul 18, 2019 9:08 am
livesoft wrote:
Thu Jul 18, 2019 9:01 am
Whatever you do, do not use the word "magic" because it is not magic. It is math.
A point I would emphasize also.
Not sure I agree. Math is real magic. The wizards in Harry Potter are make believe. The real magicians are teachers, professors and researchers.
The most precious gift we can offer anyone is our attention. - Thich Nhat Hanh

coachd50
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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 9:34 am

finite_difference wrote:
Thu Jul 18, 2019 9:29 am
dbr wrote:
Thu Jul 18, 2019 9:08 am
livesoft wrote:
Thu Jul 18, 2019 9:01 am
Whatever you do, do not use the word "magic" because it is not magic. It is math.
A point I would emphasize also.
Not sure I agree. Math is real magic. The wizards in Harry Potter are make believe. The real magicians are teachers, professors and researchers.
To expound on that, if you can get someone to embrace delayed gratification, self discipline (when it comes to contributions and investing) and to live below their means... that is indeed magic.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 9:36 am

finite_difference wrote:
Thu Jul 18, 2019 9:29 am
dbr wrote:
Thu Jul 18, 2019 9:08 am
livesoft wrote:
Thu Jul 18, 2019 9:01 am
Whatever you do, do not use the word "magic" because it is not magic. It is math.
A point I would emphasize also.
Not sure I agree. Math is real magic. The wizards in Harry Potter are make believe. The real magicians are teachers, professors and researchers.
No, I disagree with you. I spend a lot of time working with kids in school and I think one of the obstacles to math learning that holds back a lot of kids is the idea that math is something magic, complicated and special that they will never be able to do. That is especially a challenge when students that struggle more see some kids that can do math more easily. The breakthrough is when someone finds out they can do something after working on it for awhile. It is important for everyone to be able to recognize that math and science are not magic but something everyone can understand at least some of, if an effort is made. I do agree that it is a good thing to recognize that Harry Potter is fiction.

finite_difference
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Re: Explaining the magic of compound interest to teenagers

Post by finite_difference » Thu Jul 18, 2019 9:37 am

dbr wrote:
Thu Jul 18, 2019 9:28 am
miamivice wrote:
Thu Jul 18, 2019 9:22 am
dbr wrote:
Thu Jul 18, 2019 9:05 am
miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.
To state what I said above in a different way, the net worth line on my Excel chart is a linear rather than polynomial line. This is different than I expected when I was a college student. I was sure it woudl be a poly curve fit due to the magic of compound interest. Maybe someday it will become polynomial but not today.
Yes, I understand that exactly. That is what you would expect if you are making constant contributions and engaging in a compound growth process at the same time. If the contributions are not constant and the compound growth rates are variable it gets more involved. Whoever taught you in college didn't talk enough about what model applies to which real-life example and what the effect of the magnitude of each contribution has on what the outcome looks like. I think your example is very helpful.
But if you put in $2,000 at the start of your career vs $50,000 ten years later, your yearly contributions will dwarf the compound interest. When the rates are relatively low (2-5%), compound interest takes quite a few years to magnify.
The most precious gift we can offer anyone is our attention. - Thich Nhat Hanh

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Re: Explaining the magic of compound interest to teenagers

Post by Meg77 » Thu Jul 18, 2019 9:41 am

onourway wrote:
Thu Jul 18, 2019 8:37 am
cshell2 wrote:
Thu Jul 18, 2019 8:34 am
I think my son was maybe 14 when I showed him the chart with the one guy that saved 2K/year for 10 years starting at 25 then quit and the other guy that started at 35 and never caught up to the first guy. That really made an impression on him.
Yes, this would be a great way to make the lesson introduced in the penny question directly applicable to their lives in the near-term.
I saw that classic chart in a Motley Fool book when I was thirteen and marveled at it - I longed for one that showed how rich a 15 year old would get if they started investing, given the amazing difference between the 25 and 35 year olds. My dad helped me open a "discount brokerage account" that year and have been investing ever since, graduating to a Roth IRA at Vanguard at age 18. Best thing I ever stumbled upon.

I know there is one in my Automatic Millionaire book by David Bach. I'm sure you can google around for one as well. If you only have 15 minutes, handing out that chart and explaining it briefly is the best use of time I can think of.
"An investment in knowledge pays the best interest." - Benjamin Franklin

finite_difference
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Re: Explaining the magic of compound interest to teenagers

Post by finite_difference » Thu Jul 18, 2019 9:42 am

dbr wrote:
Thu Jul 18, 2019 9:36 am
finite_difference wrote:
Thu Jul 18, 2019 9:29 am
dbr wrote:
Thu Jul 18, 2019 9:08 am
livesoft wrote:
Thu Jul 18, 2019 9:01 am
Whatever you do, do not use the word "magic" because it is not magic. It is math.
A point I would emphasize also.
Not sure I agree. Math is real magic. The wizards in Harry Potter are make believe. The real magicians are teachers, professors and researchers.
No, I disagree with you. I spend a lot of time working with kids in school and I think one of the obstacles to math learning that holds back a lot of kids is the idea that math is something magic, complicated and special that they will never be able to do. That is especially a challenge when students that struggle more see some kids that can do math more easily. The breakthrough is when someone finds out they can do something after working on it for awhile. It is important for everyone to be able to recognize that math and science are not magic but something everyone can understand at least some of, if an effort is made. I do agree that it is a good thing to recognize that Harry Potter is fiction.
I think the worst obstacle is that kids think math is simply boring. And it should be anything but. So tread carefully.
The most precious gift we can offer anyone is our attention. - Thich Nhat Hanh

miamivice
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Re: Explaining the magic of compound interest to teenagers

Post by miamivice » Thu Jul 18, 2019 9:45 am

finite_difference wrote:
Thu Jul 18, 2019 9:37 am
dbr wrote:
Thu Jul 18, 2019 9:28 am
miamivice wrote:
Thu Jul 18, 2019 9:22 am
dbr wrote:
Thu Jul 18, 2019 9:05 am
miamivice wrote:
Thu Jul 18, 2019 9:00 am
I was taught about the magic of compound interest when I was a teenager. I have yet to see the benefits in real life.

While my initial retirement contribution in Year 1 of my professional career ($2000 or so) certainly has increased in value, it's dwarfed by my current year's contribution (around $55,000), so I really don't see the impacts of compound interest.
That is because you have to do the math in a little more complicated way that you haven't applied yet. An example for you might be how it is possible your contribution was able to grow from $2000 to $55,000. You might also be seeing the fact that compound growth can be at variable annual rates in investing. The model of steady rate of compounding is too simple for almost any real investment.
To state what I said above in a different way, the net worth line on my Excel chart is a linear rather than polynomial line. This is different than I expected when I was a college student. I was sure it woudl be a poly curve fit due to the magic of compound interest. Maybe someday it will become polynomial but not today.
Yes, I understand that exactly. That is what you would expect if you are making constant contributions and engaging in a compound growth process at the same time. If the contributions are not constant and the compound growth rates are variable it gets more involved. Whoever taught you in college didn't talk enough about what model applies to which real-life example and what the effect of the magnitude of each contribution has on what the outcome looks like. I think your example is very helpful.
But if you put in $2,000 at the start of your career vs $50,000 ten years later, your yearly contributions will dwarf the compound interest. When the rates are relatively low (2-5%), compound interest takes quite a few years to magnify.
And that's exactly the point that I am trying to make, perhaps a bit subtly.

When I was young in my career, I hardly had any money. However, I set aside $2000 for retirement even though I could have used a different car back then. Thought that the $2,000 would make a huge difference in retirement because of the magic of compound interest.

As it turned out, my income increased handsomely and I can stash a lot ($55,000 a year) away today, so I could have spent that money back then with little impact to retirement. I didn't know what the future would hold then, but in retrospect, I was a bit too focused on compound interest.

To put it a different way, when I was little I read that the amount saved between ages 20 - 40 would be double (or triple or some number) than the amount saved between 40 - 60 due to compound interest. While true if savings rates are steady, increasing savings rate (brought to you by increasing salaries) dulls the effect a lot.

Bottom line is the magic of compound interest hasn't worked for me the way that I was taught or expected.

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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 9:58 am

finite_difference wrote:
Thu Jul 18, 2019 9:37 am


But if you put in $2,000 at the start of your career vs $50,000 ten years later, your yearly contributions will dwarf the compound interest. When the rates are relatively low (2-5%), compound interest takes quite a few years to magnify.
I think that was the point he was trying to make, particularly in regard to a discussion on presenting compound interest concepts to college age (or earlier for that matter) students.

It is fairly easy to simply present the material as a mathematical representation of the concept. But given the fact that the OP is posting this on the bogleheads website and the wording he used in the original post, I don't think his/her goal was as much learning math as it was behavioral influence. And that probably requires a deeper connection. The time issue displayed above is a distraction from that connection.

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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 10:02 am

miamivice wrote:
Thu Jul 18, 2019 9:45 am


And that's exactly the point that I am trying to make, perhaps a bit subtly.

When I was young in my career, I hardly had any money. However, I set aside $2000 for retirement even though I could have used a different car back then. Thought that the $2,000 would make a huge difference in retirement because of the magic of compound interest.

As it turned out, my income increased handsomely and I can stash a lot ($55,000 a year) away today, so I could have spent that money back then with little impact to retirement. I didn't know what the future would hold then, but in retrospect, I was a bit too focused on compound interest.

To put it a different way, when I was little I read that the amount saved between ages 20 - 40 would be double (or triple or some number) than the amount saved between 40 - 60 due to compound interest. While true if savings rates are steady, increasing savings rate (brought to you by increasing salaries) dulls the effect a lot.

Bottom line is the magic of compound interest hasn't worked for me the way that I was taught or expected.

From a behavioral aspect however, your experience could derail the future of many LOL. I would argue the KEY takeway is that you had the important financial behaviors down : 1) Delayed gratification, 2) Living below means) 3) self discipline and patience.

In the current economic climate, I would not think it would be a safe bet to assume most of the OPs class will be going into jobs where their income will increase that drastically.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 10:09 am

I fully agree that financial success is about a lot of things other than invoking the magic of compounding. It is an excellent point that time in market really means delay of gratification when it is expressed as behavior and behavior is more important than math.

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J G Bankerton
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Re: Explaining the magic of compound interest to teenagers

Post by J G Bankerton » Thu Jul 18, 2019 10:15 am

Do they understand there is no free lunch? That seems to be the real problem.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 10:18 am

finite_difference wrote:
Thu Jul 18, 2019 9:42 am

I think the worst obstacle is that kids think math is simply boring. And it should be anything but. So tread carefully.
You are not wrong about that. I see lots of examples of classrooms that are boring and lots of classrooms that are not boring. The feedback I get is that whatever else, no one was bored. But it is also not boring to do something that is successful as well as new and different and fascinating.

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Re: Explaining the magic of compound interest to teenagers

Post by GAAP » Thu Jul 18, 2019 10:19 am

The simplest illustration that I've seen used several generations of breeding rabbits -- the translation to dollars is pretty easy...
“Adapt what is useful, reject what is useless, and add what is specifically your own.” ― Bruce Lee

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Re: Explaining the magic of compound interest to teenagers

Post by H-Town » Thu Jul 18, 2019 10:25 am

Nosh wrote:
Thu Jul 18, 2019 8:22 am
Hi everyone,
I've recently started teaching a course in a local college on a subject that has nothing to do with personal finance, but includes some basic math and critical thinking concepts. From conversations with the students, I can see why so many people complain that the lack of personal finance education is a major problem in this country. I know that 95% of the students will never use most of what I am supposed to teach, so, while creating my lesson plans, I sneak in a little personal finance education whenever the concepts are appropriately parallel. Obviously, none of this is in the textbook, so I need to provide references or write up the information myself.

My next opportunity is to talk about Compound Interest (I'll have around 15 minutes for this), and since this is such an important concept, I want to do the best job possible. So my question to the Bogleheads community is, what article / chapter in a book etc. that you have read did the best job explaining compound interest, the importance of starting to save while young and avoiding debt and lifestyle creep?

Thanks!
Great idea. I think if you want to choose a few key takeaways for the students, I'd focus on those 2 items:

1) Rule of 72: it's a simple rule of thumb to estimate time it would take to double the original investment.

2) Run an example:
a. Using 8% rate of return, money will double every 9 years. A saver will get richer thanks to compound interest.
b. Using 20% credit card debt, 5% mortgage, or 7% car note, debt will double less than 3 years. A spender will get poorer much faster thanks to compound interest.
This is the reason why you live below your means and stay away from debt.

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Re: Explaining the magic of compound interest to teenagers

Post by Dottie57 » Thu Jul 18, 2019 10:36 am

KlangFool wrote:
Thu Jul 18, 2019 8:41 am
OP,

Rule of 72.

If the annual return rate is 8%, it takes 72/8 = 9 years for the money to double.

KlangFool
I was astounded when I learned this.

Portfolio visualizer might make a nice presentation to a teenager.

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Re: Explaining the magic of compound interest to teenagers

Post by wm631 » Thu Jul 18, 2019 10:48 am

Keep it real simple. The boredom factor for kids is quick. Start with the image of a snowball rolling down a hill (actually, UP a hill ...). Collecting snow; getting bigger and bigger. Maybe draw the image, on a chalkboard. The "rabbits breeding" analogy is good, too; easy to understand.

Also, don't forget to explain diversification, and why. Not to keep all your eggs (assets) in any one basket. If/when one of them collapses, the rest of the portfolio survives. In fact, some of the other parts of the portfolio may actually thrive.
Last edited by wm631 on Thu Jul 18, 2019 11:00 am, edited 3 times in total.

dbr
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Re: Explaining the magic of compound interest to teenagers

Post by dbr » Thu Jul 18, 2019 10:52 am

Dottie57 wrote:
Thu Jul 18, 2019 10:36 am
KlangFool wrote:
Thu Jul 18, 2019 8:41 am
OP,

Rule of 72.

If the annual return rate is 8%, it takes 72/8 = 9 years for the money to double.

KlangFool
I was astounded when I learned this.

Portfolio visualizer might make a nice presentation to a teenager.
That is a great suggestion. There is nothing better than real-life growth curves to show what happens over time, how different investments compare, and it can model the example we were discussing earlier of contributions plus growth. Another thing one can see is how noisy the result is due to variability of return. I also noticed that PV lets you use linear and logarithmic scales so you can test how well growth is or isn't fit by a linear model or an exponential model, as long as we are doing math here.

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Re: Explaining the magic of compound interest to teenagers

Post by Abe » Thu Jul 18, 2019 11:04 am

When I first started saving and investing, I would occasionally calculate my net worth. I remember there was a point where I became aware that my net worth was higher than I though it should be. I finally realized that it was because of the compounding. At the time I understood the concept of compounding, but this was the first time I could actually see how it affected me directly. There is a huge difference between theory and practice.
Slow and steady wins the race.

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Re: Explaining the magic of compound interest to teenagers

Post by GCD » Thu Jul 18, 2019 11:08 am

Nosh wrote:
Thu Jul 18, 2019 8:22 am
My next opportunity is to talk about Compound Interest (I'll have around 15 minutes for this), and since this is such an important concept, I want to do the best job possible. So my question to the Bogleheads community is, what article / chapter in a book etc. that you have read did the best job explaining compound interest, the importance of starting to save while young and avoiding debt and lifestyle creep?
Well, I hate to be such a diehard BH about it, but...

Pages 14-16, subtitled "The Magic Is In The Compounding" in The Bogleheads Guide to Investing does a pretty succinct job. The entirety of Chapter 2, "Start Early and Invest Regularly" is pretty much exactly what you are looking for.

It just so happens that we discussed this yesterday with my two kids, ages 14 and 16. We have had financial discussions with them before, so this wasn't a fresh introduction to finance from scratch. But nothing really in-depth previously.

We are now reading The Bogleheads Guide to Investing at the rate of one chapter per day over summer break. We are only up to chapter 4 so far, but hope to finish before the summer ends. They seem to be understanding reasonably easily, it's not over their heads. For what you are looking for, this section seems to be right on point and I just discussed it with teenagers a few days ago..

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Re: Explaining the magic of compound interest to teenagers

Post by GCD » Thu Jul 18, 2019 11:13 am

AAA wrote:
Thu Jul 18, 2019 8:43 am
The example of doubling a penny every day for a month is instructive but 100% daily interest is not very realistic.

How about an example of starting with $1000 and getting 5% simple interest vs. 5% compound interest every year. After 20 years, you end up with $2000 vs. $2653, respectively.
Right. As it so happens, Chapter 2 (referenced above) starts with an example of a man who never earned more than $25,000 per year, but who retired with over $1,250,000 thanks to Vanguard's low fees, regular investing, LBYM and the benefits of compounding.

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Re: Explaining the magic of compound interest to teenagers

Post by vtjon02 » Thu Jul 18, 2019 11:20 am

As a way to finish the presentation, say something along the following lines.

Don't listen to me, listen to the smartest person in the history of the world. Albert Einstein called compound interest the 8th wonder of the world. Those who understand it, earn it. Those who don't, pay it.

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Re: Explaining the magic of compound interest to teenagers

Post by runner23 » Thu Jul 18, 2019 11:21 am

I have not read through all the posts but this article was fantastic. The paper folding analogy is great.

“Imagine you take a sheet of standard printer paper with a thickness of 0.1 mm.

Fold it over once and it gets twice as thick. Fold it again and you’ve doubled the thickness of the paper again; two folds make the paper four times as thick. Fold it a third time and now the paper is eight times as thick.

If you could fold that piece of paper 50 times, the paper would stretch 95 million miles or approximately the distance from Earth to the sun.

At 100 folds, it matches the radius of the universe.”

https://www.linkedin.com/pulse/most-pot ... f-cfa-cfp-

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Re: Explaining the magic of compound interest to teenagers

Post by KlangFool » Thu Jul 18, 2019 11:31 am

OP,

Or, you could use what my mother told me.

There is a limit that how much money you can earn by exchanging your time for money. You have to sleep X hours per day and there are only so many hours in a day. But, there is no limit on how much you can earn by investing your money. Your money will earn money for you without any additional effort from you.

KlangFool

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Re: Explaining the magic of compound interest to teenagers

Post by Alf 101 » Thu Jul 18, 2019 11:32 am

My dad presented the concept of compound interest to me as an adolescent -- probably 13 or 14, and I could do math. I think of this as "The Talk", for the impact it had on me. Of course there was another talk, but this may have been more in his wheelhouse.

He started by talking about compound interest positively -- an example of if I contributed a modest set amount (e.g., $2000 or $5000) each year, with 5% annual growth, starting at ages 20, 30, 40 and 50 to an age 65 retirement. The rule of 72 made an appearance, and this made a strong point -- start early. Even if you don't have a great deal of money, anything you can put away in your early 20s will make an impact.

His second example was a credit card -- if you had carried a balance of $2000, at 15% what you would end up paying over time, and this was clearly how these companies made their profits. In short, the convenience of plastic is no free lunch. It's a good thing he didn't use the example of a mortgage, which might have inspired me to live in a cardboard box by the river.

Why this worked, I think, is that the two examples are tangible and actionable -- the value of investing early, and the trap of credit card debt.

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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 11:35 am

KlangFool wrote:
Thu Jul 18, 2019 11:31 am
OP,

Or, you could use what my mother told me.

There is a limit that how much money you can earn by exchanging your time for money. You have to sleep X hours per day and there are only so many hours in a day. But, there is no limit on how much you can earn by investing your money. Your money will earn money for you without any additional effort from you.

KlangFool
BAM! I think this is an EXCELLENT verbal representation of the concept that I am assuming the OP wants to convey. This combined with some of the math, and some real world example or two would do nicely I believe.

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Re: Explaining the magic of compound interest to teenagers

Post by Dandy » Thu Jul 18, 2019 11:36 am

Awhile back when IRA contributions were 2k I saw an article that compared two people. Person A put 2k in an IRA from age 22? to age 31? and then stopped contributing. Person B started at 31? and contributed 2k each year until 65. Person A had more money at 65. The reason for the question marks is I don't remember the specifics but it was that level of amazing.

I prepared an excel spreadsheet based on the actual numbers used in the article and showed it to some of my call center staff. It made a real impression on them.

It not only showed the power of compounding but the power of saving/investing early --even relatively small amounts. If you add a modest company match to a 401k it would make even a greater impression.

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J G Bankerton
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Re: Explaining the magic of compound interest to teenagers

Post by J G Bankerton » Thu Jul 18, 2019 11:41 am

wm631 wrote:
Thu Jul 18, 2019 10:48 am
Also, don't forget to explain diversification, and why. Not to keep all your eggs (assets) in any one basket. If/when one of them collapses, the rest of the portfolio survives. In fact, some of the other parts of the portfolio may actually thrive.
The OP only has 15 minutes.

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Re: Explaining the magic of compound interest to teenagers

Post by coachd50 » Thu Jul 18, 2019 11:49 am

J G Bankerton wrote:
Thu Jul 18, 2019 11:41 am
wm631 wrote:
Thu Jul 18, 2019 10:48 am
Also, don't forget to explain diversification, and why. Not to keep all your eggs (assets) in any one basket. If/when one of them collapses, the rest of the portfolio survives. In fact, some of the other parts of the portfolio may actually thrive.
The OP only has 15 minutes.
Not only that, but it isn't a personal finance class, and he isn't teaching investments. He is just hoping to slip a little " A-ha" moment into his class.

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Re: Explaining the magic of compound interest to teenagers

Post by investingdad » Thu Jul 18, 2019 12:24 pm

onourway wrote:
Thu Jul 18, 2019 8:29 am
I can think of no simpler, more effective lesson to the power of compound interest than the 'would you rather have a million dollars today or a penny doubled every day for a month? question.
When I was in 3rd grade, my friend's dad asked me this question. He was a psychologist.

I immediately answered, the penny doubled.

When he asked me why, I said it was because it sounded like such an obvious trick question, I figured the right answer was the one that sounded wrong.

Pretty sure that ended the conversion. :)

Also, the question speaks more to straight exponential growth.

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Re: Explaining the magic of compound interest to teenagers

Post by Chadnudj » Thu Jul 18, 2019 12:31 pm

cshell2 wrote:
Thu Jul 18, 2019 8:34 am
I think my son was maybe 14 when I showed him the chart with the one guy that saved 2K/year for 10 years starting at 25 then quit and the other guy that started at 35 and never caught up to the first guy. That really made an impression on him.
That's a good one. I'd also do the "How Did Warren Buffet Get So Rich?" chart found here: https://www.marketwatch.com/story/from- ... 2015-08-17

It really shows that the reason the richest man in the world got that way is, in no small part, due to compound interest.

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