Hypothetical case of two brothers, one who invests early and one who starts later

Question

I've seen a hypothetical case of two brothers, one of whom invested until 25 and stopped. The other invested from 25 until 65. The brother who invested earlier winds up with more money. Does anyone know where I can find this parable online? I wanted to show it to my kids.

Google 'retirement calculator' and put in some numbers yourself to see what different scenarios would look like. Better to teach yourself first, before you try to teach your kids. — Grade 'Eh' Bacon, Mar 10 '22 at 14:00
Clark Howard touches on this topic a lot: https://clark.com/personal-finance-credit/summer-job-millionaire/ — JohnFx, Mar 10 '22 at 16:43
I first ran into it in a highschool Dave Ramsey class. https://www.youtube.com/watch?v=eIOUGZcmauo — Azendale, Mar 11 '22 at 12:41
Keep in mind that this is strictly a theoretical mathematical exercise that has very little bearing on reality. As such, it has little more value than the infamous spherical cow. For instance, the calculation is completely overthrown if the second brother used the money he didn't invest to buy a home by age 25, while the other brother continues renting to age 65. Not to mention life events like marriage, children, ... — Kevin Keane, Mar 13 '22 at 06:43

Pete B. · Accepted Answer · 2022-03-10T19:58:44.060

21

Do a search for "Ben and Arthur". The problem with most versions of this chart is that it uses a high discount rate (14% IIRC), but it is still illustrative.

The reality is none of us are either Ben or Arthur. Most have crappy jobs at the start of our career so we have little money to invest. As our career progresses we get raises and jobs with better benefits like higher 401K matches. More and more money is freed to invest.

So the illustration is very unrealistic but provides an insight into the power of compounding.

edited Mar 10 '22 at 19:58

answered Mar 10 '22 at 13:26

Pete B.

76,481
16
167
236

4

Engineering interns get $20 to start. Live efficiently, live below your means, don't chase the Jones'es next door, and for fks sake, don't go into debt. – paulj Mar 10 '22 at 21:52
7

@paulj that is nothing nowadays. A buger combo at mcdonalds is 12.00$. 20$ an hour is absolutely nothing nowadays. – JonH Mar 11 '22 at 03:57
6

Wendy's has $4 and $5 combos. You'll get much more money to invest! – Ark-kun Mar 11 '22 at 07:56
4

@JonH Then cook yourself? If you have a $20 per hour job then you won't have to work 16 hour days to make a living, so you'll have time to cook. There are tons of recipes that are tasty and nutritional despite costing less than $2 per portion. Make the math for that; assume homecooked costs $2 per portion and fast food costs $10 per portion (for simplicity) and with two meals a day that means you save $240 per month if you cook all your meals. That is a pretty good monthly savings – Anju Maaka Mar 11 '22 at 08:42
@AnjuMaaka You do understand that this issue is not one purely monetary, but compounded by the issue of energy and time ? Somebody living on minimum wage, or even a bit above like 20$, often do not have the time and energy needed for cooking, which push them to easier food, like Wendy's or McDonalds. – DrakaSAN Mar 11 '22 at 12:01
4

In other words the legitimate takeaway from the parable is the magnitude of the unearned advantage you get from being in the rare position of being able to start early, not a course of action for someone who doesn't have that advantage. – R.. GitHub STOP HELPING ICE Mar 11 '22 at 13:49
2

@DrakaSAN If you read my whole comment then you'd have noticed that I did mention the part about time. I work full time, 9 hours, and spend 2 hours getting to and from my work. That's a full 11 hours. Even so, I find time to cook just about all my meals. Unless your wage is so low that you cannot live on it without working 12 hours a day you can find the time to cook. If you can find the energy to do so is another matter, but that is a personal matter; it is extremely rare to be so tired as to be litterally INCAPABLE of cooking dinner, so many CHOOSE to buy takeout – Anju Maaka Mar 11 '22 at 14:57
@AnjuMaaka the implication seems to be that by choosing not to buy takeout now you will have the ability to choose to buy some different luxury later. This is a personal choice that offers no informative insight into how this answer should approach the question. Some will prefer your choice, others will prefer the opposite. – Will Mar 11 '22 at 16:48
Anju you are including only the cost of food. Are you washing veggies, washing dishes, using condiments. Your response is ludicrous 20$ an hour is absolutely nothing nowadays in the USA. – JonH Mar 12 '22 at 01:35
1

@JonH I'm not so sure my response is "ludicrous". I understand Will saying that it's a personal choice of luxury now-vs-later, but you saying that $20 an hour is nothing really feels strange. I make $21 an hour ($15.5 after taxes in Sweden) and can cover stuff like rent, food, bus-card, gym-card, and other necessities working a 40 hour week. I cook most of my food myself (and yes, I use water, wash my dishes, and have a rather large spice/condiment collection). Even so, I am able to put away about $500 each month for long-term savings. What about my response is ludicrous? I really don't get it – Anju Maaka Mar 12 '22 at 16:45
O boy sweden does not equal the usa sorry 20$ in the usa is absolutely nothing. 500$ a month is 6k a year. Do you realize that is also not a lot of money? – JonH Mar 12 '22 at 17:09
@JonH Of course I understand that $6k a year is not that much. I'm not expecting to retire to a mansion. I just don't understand why you called my answer "ludicrous" when I feel like I got a decent (but not amazing) thing going. I can afford to buy food that I like, I can afford the games I like to spend my free time on, I don't have any housing issues, etc. I feel like I can live like this for the rest of my life, and the last thing I did to get to this state was to stop eating takeout in favor of home cooking, so I suggested that in my answer. Again, why was my answer "ludicrous" to you? – Anju Maaka Mar 12 '22 at 19:15
Because it certainly did not account for all costs from cooking at home. Trust me cooking at home is comparable to eating at mcdonalds when you include the costs of condiments, prep, napkins, washing etc. all of which you failed to mention. Dont think your two dollar burger is two dollars. – JonH Mar 12 '22 at 21:33
@JonH I see. Can't help but disagree though. Unless running the dish washer once costs at least $10 it costs me less than half as much cooking at home as it does to get takeaway. Maybe it's a difference in takeaway prices, I've heard those are low in the US. Unless you're buying some pretty luxurious condiments and such, they are not going to be a large part of the meal cost. And why even mention napkins? A roll of common household paper costs like $1 and provides like 100 squares that can be used for napkins – Anju Maaka Mar 13 '22 at 00:30
If you're a teacher in Florida, be sure to include "chart" after "Ben and Arthur" in your search. Wouldn't want to get in trouble acknowledging the existence of gay people! – Acccumulation Mar 13 '22 at 06:11
1

@AnjuMaaka Comparing solely on dollar rate conversion to euros is heavily biased, as it doesn't really translate to buying power and cost of living. I'd need somebody there to confirm, but the cost of vegetables, meat or fish (non processed food) is absolutely bonkers compared to anywhere in europe, whereas processed food or fast food is dirt cheap compared to prices in the EU. – DrakaSAN Mar 14 '22 at 08:26
@JonH Maybe I am mistaken, but I think that $20 an hour in the US is very sufficient. Just a couple years ago I was making $11-14 an hour while in college, and using that part time (~20/hrs a week) pay as a means of paying all my tuition (minus scholarships) each semester, along with rent, food (home-cooked or course), gas and I even had a decent chunk of fun money left over. Of course over the summer time I worked a lot more than when I was taking classes to save up for next year, but If I had been making $20 an hour, I might have been able to max a Roth IRA too! – Flats Mar 14 '22 at 13:38
@JonH $20/hr is more than 40k/yr. There are plenty of people living on that and much less in the US. Even in the metro areas, like where I was while in school. Regions like New York City, San Francisco, and similar aside; "surviving" on $20/hr is not a difficult task, unless you're providing for more than just your own survival, with no other help. (And there are plenty of families that figure out a way to do it regardless of how difficult I think that it might be) – Flats Mar 14 '22 at 13:42
@JonH Also, $6k a year might not seem like a lot of money, but do it for 30 years inside of your Roth IRA (and get a conservative 5% return for example) and the $6k a year turns into quite a hefty sum. Does $400k qualify as a lot of money? What about $600k (7% return)? A million (10%)? If you can manage to start when you're 20, by 65 (at the original 5%) you'd have a million bucks too. Maybe it's not a lot of money in the future with inflation, but I'm sure it would help a lot more than if you didn't save that $500 a month... – Flats Mar 14 '22 at 13:55
1

@DrakaSAN I will admit that you can't just convert currency by its exchange rate and expect it to be the same. I have no experience of food prices in the US (visited a couple of times, but as a tourist you typically don't cook). I have heard how buying "raw ingredients" is shockingly expensive in the US though. My only experience of actually LIVING in a country are from Sweden and Japan, and in both it was cheaper to cook yourself (though Japan had a lot cheaper ready-made meals at restaurants, if you went with the more plain dishes, than Sweden). Many students lived off of curry with rice XD – Anju Maaka Mar 14 '22 at 15:25
@AnjuMaaka in Michigan 3 romain lettuce is 6.99. Its not cheap. Covid and the war has made everything expensive at least in this state. Mind you this is the regular brand if you buy organic or from whole foods it’s pricier. – JonH Mar 16 '22 at 02:42
@JonH A quick google of the major grocery chains here in Sweden puts 3 romain lettuce at $5.4-5.7 (though I found one of the low-price chains having a sale, so there I could buy 3 of them for $4.5) for the normal ones. If you want the organic version it's be bumped up to $7.5 for three of them. Some other prices: tomatoes for $6-7 per kilo, onions $1/kg, apples $2.5-3/kg, potatoes $1.4/kg, rice $2-3/kg, spaghetti $2/kg, cauliflower $4/kg, cabbage $1.5/kg, zucchini $4/kg, mushrooms $5-7/kg, pork tenderloin $8/kg, chicken fillet $15/kg. How does these match up to your place? – Anju Maaka Mar 16 '22 at 14:00

score 6 · Answer 2 · answered Mar 11 '22 at 09:54

6

This page from a UK pension provider provides similar information. It compares the result at age 65 for the same monthly investment from age 0 to 18, versus from age 25 to 65. The 'tax relief' is UK specific, but the effect of compounding isn't:

answered Mar 11 '22 at 09:54

AakashM

3,983
1
21
24

0-18? Makes the case for parents setting money aside, but tough to do it tax-differed until the kid has earned income. 1%/yr cost over 65 years? The fund manager winds up with more money than the investor. Broken system. – JTP - Apologise to Monica Mar 19 '22 at 12:12

score 2 · Answer 3 · answered Mar 12 '22 at 16:08

Nothing magic about this. Whatever the annual investment return, when you have enough that you observe "my average return is more than my deposit", your friend just starting, with the same deposit, will never catch up to you, even if you stop. You can enter numbers in a spreadsheet to tinker with return/deposits, etc.

To Pete's point - Such articles may convince a young person to start investing early, or for parents to help their children (as the Clark article showed) get an early start. I mean not out of the house young. The teen with summer jobs can more easily choose between frivolous spending and saving than someone starting a job and having all the expenses that go with being in the real world.

base64 · Answer 4 · 2022-03-13T14:14:01.417

0

The meaning of life is not to achieve a high ranking in a scoreboard upon death, where the scoreboard says "Who has more money left".

Investment and Debt are tools for achieving consistent "spending" aka enjoyment throughout entire lifetime.

In typical economics theory, a person who is young would spend money by borrowing (from parents and student loan providers). A person who is old would spend money by using money saved from the past. If you borrow too much aka spend too much, your spending when you are old will not be consistent. If you save too much aka spend too less, your spending when you are young will not be consistent.

Mathematically, whoever spends the most in a lifetime (discounted by inflation) and consistently over every period is the winner. This implies that extreme case of living frugally when extremely young as suggested by the fund managers is not optimal.

The formal theory on this is Life-Cycle Hypothesis.

https://research.stlouisfed.org/publications/page1-econ/2014/11/01/smoothing-the-path-balancing-debt-income-and-saving-for-the-future/

https://www.investopedia.com/terms/l/life-cycle-hypothesis.asp

edited Mar 13 '22 at 14:14

answered Mar 11 '22 at 10:22

base64

10,440
2
26
39

1

"Mathematically, whoever spends the most in a lifetime (discounted by inflation) is the winner." - assuming you have no children or other dependents or no interest in looking after them. – abligh Mar 11 '22 at 17:03
3

Idea that spending = enjoyment is fallacy promoted by those who profit from such consumerist propaganda. In vast majority of the cases, it is exactly the opposite: chances are much higher that extra spending will make you extra miserable in the long term. (it is much like taking heavy drugs - it might make you feel "happy" for a short while, but you'll only require more and more to "not be unhappy" until it destroys any chance happiness ever) – Matija Nalis Mar 12 '22 at 15:40
This answer makes a very good point. Lets flip it in an equally extreme way. Arthur pays for the trip with his friends instead of saving the money, when he gets a job he lives in an apartment that's a bit expensive but is near his work and in an area with a vibrant social scene, he eats out in a nice restaurant now and again. When he retires he has to cut back on his lifestyle a little. Ben invests every penny he can, he never goes on trips or eats out. When he retires he is a multimillionaire and can finally start having fun. Who made the right choices here? – Eric Nolan Mar 14 '22 at 11:36

score -1 · Answer 5 · answered Mar 13 '22 at 20:53

Sorry to have overlooked the actual Question "Where can I find it…" as blatantly as most, and this is about dates, not maths.

How old is anyone here? That's not meant to be patronising, but to highlight that until roughly the Millenium, investment was almost incomparably more worthwhile that it is now.

Back then 5% was easy to find, 10% not uncommon and greater returns not rare, though risky.

Today 0.1% seems common and 1% magnetic so, broadly, the "traditional" expectation of return on investment might have been 100 times what we see today.

Back then, investing early was critical.

Today investing, as opposed to speculating, is worth the arithmetic it's written on…

The ten years ending 12/31/21 the S&P returned 16.58% per year CAGR. Far too high to count on continuing, of course, but an outstanding decade. Are you talking about CDs, Bank deposits? That's part of the big picture, but not what is meant by "investing." — JTP - Apologise to Monica, Mar 14 '22 at 12:05

Hypothetical case of two brothers, one who invests early and one who starts later

5 Answers5