The First Million Is The Hardest

September 28, 2007 by Pinyo.

Not long ago, I participated in a conversation on NetworthIQ: “Struggling with breaking the first million mark“. The question posed was about mental focus and persistence needed to get to that magical $1 million mark. However, it got me thinking about the mathematical aspect of it.

First Million Is The Hardest

As you can see from the chart, if a person invests $15,000 per year starting at age 25 and the investment gains on average 10% a year, he can get to $1 million mark by 45. The first million took 20 years! But if you keep going down the table, it only takes…

6 more years to get to $2 million at 51
4 more years to get to $3 million at 55
3 more years to get to $4 million at 58
2 more years to get to $5 million at 60
2 more years to get to $6 million at 62
2 more years to get to $7 million at 64
1 more years to get to $8 million at 65

Not only is this mark psychologically challenging, it is also mathematically challenging.

Now back to my situation. If I can manage to save $1 million by the age of 43, I might have a shot at making the $10 million mark!

What do you think?

PS: I also saw a similar analysis by another PF Blogger not long ago. I left a comment saying it was an excellent illustration. If you are that blogger, please let me know so I can link to you.

PPS: I found him! Your First Million Is the Toughest at Accumulating Money

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34 Comments

DavidYin, 28. September 2007, 16:42

Yes, I agree with you. The first 1 million is so hard.
Xaris, 29. September 2007, 7:41

Alright, think about this:

If you can guarantee 10% a year average, then i will find funds for you to manage and you will make lots of millions much faster:D:D

You should think it over…
Chad, 29. September 2007, 13:17

Sounds great now, wait until inflation, the falling dollar, and the inevitable tax hikes cut into your spending power.

Also, along with what Xaris said, 10%-12% average is a deceiving expectation that you hear a lot. It is an arithmetic average (which tells you absolutely nothing), look at the geometric mean of returns. It takes into consideration that some years you have a loss, and how that effects your net worth.

Example: 100% gain and a 50% loss. They would say 25% gain! whoo! But actually, you had $1 it went up to $2 and then back down to $1, you made nothing.

If you could guarantee a constant 10% return, you’d be pretty close to being the next Peter Lynch and should manage -a- my mutual fund.
Pinyo, 29. September 2007, 13:46

David, Xaris, and Chad - welcome to Moolanomy and thank you for your comment.

@Xaris - Nobody can guarantee anything when it comes to investment. If I tell you I can guarantee 10%, I would be lying.

That said, based on the last 30 years, the S&P500 has CAGR of over 12%. However, this is not a guarantee of future performance either. If we assume that the S&P500 can reproduce its past performance, then we already have a fund that can perform above 10%.

@Chad - You brought up a great point. I didn’t take inflation, the falling dollar, and taxes into account and they WILL hurt.

Also your point about arithmetic average versus geometric mean of returns is very insightful. It’s a post-worthy discussion and I think I will write about it in the near future.

The 10% number I used is in fact the more conservative number based on S&P500 performance that I discussed above. Although, I don’t know if we can reproduce the 12.5% considering we only got 2.5% out of it since year 2000.
Bob Smith, 29. September 2007, 20:40

This data and the thinking behind it is almost useless. Earlier posters covered some of the problems with your thinking, but there are more.

–Typically, investors have far less to invest in the early years, and more in the later years. That’s just life.

–Investing 100% in stocks is usually a bad idea - for many reasons.

–Expecting a 10% return each and every year is nonsensical. The stock market is volatile. Your chart doesn’t take market volatility into consideration. Therefore, your argument above (that the S&P has returned 12% over the past 30 years - so 10% is somehow “conservative”) is completely bogus. It just doesn’t work that way.

–There are many reasons to expect that market returns going forward will be worse (possibly MUCH worse) than the past 30 years. Stocks can move sideways for very long periods of time.

Nice try, but you are WAY off here. Your post displays considerable enthusiasm, but a complete lack of sophistication or understanding about financial markets, investing, or personal finance. Your rebuttal of previous criticisms simply confirms your naivete about financial markets. You are clearly out of your league here. You haven’t yet grasped even the basic concepts necessary to venture into the markets, yet alone to advise others. I would strongly suggest that you educate yourself about these matters prior to posting flawed information.
Pinyo, 30. September 2007, 5:39

@Bob - welcome to Moolanomy. Aside from your somewhat harsh criticism at the end of your comment (which led me to believe that you didn’t read any other posts on this blog), I DO AGREE with your points.

1 - less to invest in early years — mostly true, but I am not trying to illustrate the saving behavior of average American. In my own situation, I actually saved more in the early years because I didn’t have to deal with mortgage, medical expenses, ate out less, etc. The $15,000 number was picked for the virtue of being 401k limit THIS year.

2 - 100% in stock is usually bad idea — agreed. In my main portfolio, I have 20% large-cap, 20% mid-cap, 20% small-cap, 30% international, 5% REIT, and 5% individual stocks investment. Outside that I have savings, money market, CDs, funds, ETFs, etc. Also, my house is an asset; but I don’t really count it since we are living in it.

3 - Expecting 10% every year is non-nonsensical — agreed. Please read my introduction to CAGR post which discussed this in more detail. I made the same point you are making there. I also indicated that CAGR depends on when you look at it. If I just look at the past 7 years, for example, the CAGR is only about 2.4%.

4 - Market cannot reproduce the return from past 30 years. I cannot predict the future, but I generally agree that we have some tough time ahead.

Please remember that this is an illustration of a concept, not a sophisticated modeling that take everything into account. If I had taken everything into account, the point will be lost.

I realize that I am not an investment professional / guru and I NEVER EVER give anyone that impression — please read my about page and the disclaimer on the footer.

This blog is one of my learning tool to improve my money management investment skill. I learn a lot from research to write a post, or when I enter into a discussion with people who knows more - e.g., someone like you.
shadox, 30. September 2007, 10:28

Yes, you are right on some levels, but it’s important to note that to go from 100K to 1M you need to increase your money ten fold, while to go from $5M to $6M you only need to add 20% to your net worth. So while in absolute numbers your argument is absilutely correct, naturally things get easier when your percentage gain gets smaller and smaller.
CHESSNOID, 30. September 2007, 20:11

This is a great post to show how time and compounding works. Of course, the longer you’re in it, the greater the effect.
MossySF, 1. October 2007, 2:08

Ã¢â‚¬â€œExpecting a 10% return each and every year is nonsensical.

And how is this relevant at all? If over some specific timeframe, your return ends up being 10% annualized, not hitting the 10% mark every year is irrelevant. A 40% gain followed by a 13.6% loss (or vice versa) ends up being 10% a year anyways. But I didn’get at 10% a year! That means my ending balance of +21% is not really +21%?
DR, 1. October 2007, 3:55

I’m really surprised by these comments. The point of the post, I thought, was the snowball effect of investments. Investments start off slow, but over time, really pick up speed. I know mine have to the point that in an “average” year my investment returns now far exceed my annual contributions. The assumed interest rate (10% or 12% or 8%) is not the point. The snowball effect remains the same regardless of the interest rate (i.e., the time it takes to reach $2M will be a lot less than the time it took to reach $1M).

The distinction between the arithmetic mean and geometric mean is an important one, but the expression of a return percentage in the financial world is always the average annual return (i.e., geometric mean). That’s what I assume was meant here.

Inflation is always a critical consideration, but again, it doesn’t change the point of the article. I’d rather have $8M at 65 than less, regardless of the inflation rate.

One comment noted that it’s harder to save and invest when you’re young. That’s absolutely true. I wish I had started in high school! Maybe this article will encourage the younger generation to save early and save often.
glblguy, 1. October 2007, 9:13

@Bob Smith and Mossy SF - I’d be very interested in reading more about your perspectives on your blogs. Maybe you could write something up that would provide your perspective on this topic. Let us know once you have something up.

@DR - Thanks for clarifying the intent of this article. Sometimes it’s difficult for people to see the forest for the trees.
Kyle, 1. October 2007, 10:54

Interesting post. If I had 15K to add every year I would be happy camper!
Robert, 3. October 2007, 8:24

amen Kyle, I am lucky if I can pay the rent, lol !
Keith Johnson, 3. October 2007, 13:20

If only everybody could save $15,000 a year!! Indeed that would be nice…but nice effort and overall presentation. Regards, Keith
Pinyo, 3. October 2007, 15:34

@Kyle, Robert, and Keith - welcome to Moolanomy. Saving $15k is very difficult and is not practical for everyone. However, I think everyone should attempt to save at least 10% of their income and invest that money.
Jake, 5. October 2007, 6:56

Forget all the naysayers - this is actually a GREAT post. It highlights the power of compound interest and given that I am 25, I’ll honestly try to make this happen!
Matt Wolfe, 5. October 2007, 10:12

This is a great chart. It’s really interesting. I think the hardest part for me would be coming up with $15,000 to set aside each year. The first million is much harder if you can only manage to set aside $5,000 or so per year (which is probably the case with most people). I really enjoyed this post.
Pinyo, 5. October 2007, 11:51

@Jake and Matt - thank you!

Looks like I missed a few…

@Shadox - your analysis is precise

@Chessnoid - thank you. That’s the main point of the post.

@MossySF - I got the first part of your comment and agree with it. But you lost me on the second part:

“A 40% gain followed by a 13.6% loss (or vice versa) ends up being 10% a year anyways. But I didnÃ¢â‚¬â„¢t get at 10% a year! That means my ending balance of +21% is not really +21%?”

@DR - very good comment, thank you for your contribution.

@glblguy - thank you for your comment.
Debbie M, 5. October 2007, 14:15

That’s funny, when I learned this lesson, it was worded that the first $100,000 was the hardest. And it felt just as true to me as this post.

Back when I was 25, I was not even grossing $15,000 per year. I feel like one of those old people: “In my day, …” On the other hand, I will never come anywhere near the $1 million mark because I am retiring long before then (I don’t live in New York!).
Pinyo, 5. October 2007, 15:25

@Debbie - welcome to Moolanomy. That’s funny. By the time I get to 65, $8 million might not be so impressive anymore — who knows.
Alex H, 6. October 2007, 21:31

I agree with your basic premise about how quickly compounding picks up over time and I think even your model would more or less work as is. I’ve tracked my investments closely for twenty years and my net worth has pretty much escalated on pace with it.

I’ve saved about $15k per year (on a librarian’s salary), have always kept a high percentage in stocks - because stocks have categorically performed better than any other investment over time; kept my investments diversified in index funds ranked 5 stars by Morningstar; I set savings goals and always paid myself first; I buy used cars and make a hobby out of spending my money efficiently; and now at the age of 48 am in sight of $1 million (I’m currently worth in the neighborhood of $800k but expect to crack $1M in my fiftieth year).

I have a spreadsheet that calculates what my current net worth would grow to if it gained anywhere between 3% and 12% annually and honestly it hasn’t been very hard to average above 10% per year over the past twenty years - just by picking and sticking with well-known low-overhead no-load index mutual funds. Dollar-cost-averaging is also a critical component of my approach.
Accumulating Money, 7. October 2007, 8:52

A bit late, but I believe I am the other PF blogger that you are talking about.
Pinyo, 7. October 2007, 10:51

That’s it! Here’s the post Your First Million Is the Toughest. Thank you for the inspiration!
kev, 7. October 2007, 15:25

Like DR mentioned, a few of these comments surprise me. What I took from the post was this: compound interest is awesome.

The other issues (whether or not 10% annual returns are realistic, whether or not investing completely in stocks is wise, or whether or not you can invest when you’re young) do not make the main point (compound interest being awesome) untrue.
Pinyo, 7. October 2007, 15:48

@kev - welcome to Moolanomy and thank you for your comment — that’s really nice. I also checked out your blog. I loved it!
Telemill, 7. October 2007, 22:23

Both articles are excellent! I loved reading both . . . though it’s kind of depressing to see what a mountain we must climb to gain the momentum we seek. Sigh.
kev, 8. October 2007, 15:27

@Pinyo: Thanks! Glad you liked it.
Pinyo, 8. October 2007, 15:53

@Telemill - thank you and welcome to Moolanomy. I read your goal: “Gain $2,000,000 in 3 years and chronicle my progress.”

I should be reading your blog.
Amanda, 10. November 2007, 5:58

I am so incredibly inspired by this post! Not only could I be a millionaire one day… but a multi-millionaire… and all I have to do is diligently save each year? What a wonderful post. Thank you.
Pinyo, 13. November 2007, 7:13

@Amanda - welcome to Moolanomy and you’re welcome
fiscal musings, 22. December 2007, 0:50

I think it’s interesting that everyone is so caught up in the unpredictability of the stock market and the associated gains. There hasn’t been any mention of other forms of investing.

I understand that real estate is getting a bad rap right now, but the gains there can be quite good and oftentimes predictable. My point is that there are other options and it’s not all that difficult to imagine 10% yearly returns.
Pinyo, 23. December 2007, 8:35

@Fiscal Musings - Great point.

Please take a look at Building, Diversifying, and Shifting Your Income Streams to see more ideas about income building.
Make Friends, Earn Money, 30. January 2008, 7:22

Totally agree Pinyo the first million is the hardest. What you have shown is how easy it is to accumulate more money once you already have a lot, ah the joys of compound interest!
Dividend growth investor, 3. April 2008, 13:08

To me the first million would be easy to achieve. I would start with a billion i would have to lose 99.99% which would be super tough. If I could certainly lose 99.99% with a strategy, then playing against the opposite strategy would yield a huge gain..