Is compounding interest on investments a myth?
"The S&P 500 index from 1974 to present certainly looks exponential to me (1974 is the earliest data Google has).  If you read Jeremy Siegel's book there are 200 year stock graphs and the exponential nature of returns on stocks is even more evident.  This graph only shows the index value and does not include the dividends that the index has been paying all these years.  There is no doubt stocks have grown exponentially (aka have grown with compound interest) for the past several decades and compounded returns is definitely not a ""myth"".  The CAGR on the S&P 500 index from 1974 to present has been 7.54%: (1,783 / 97.27) ^ (1 / 40) - 1 Here is another way to think about compounded investment growth: when you use cash flow from investments (dividends, capital gains) to purchase more investments with a positive growth rate, the investment portfolio will grow exponentially.  If you own a $100 stock that pays 10% dividends per year and spend the dividends every year without reinvesting them, then the investment portfolio will still be worth $100 after 40 years.  If the dividends are reinvested, the investment portfolio will be worth $4,525 after 40 years from the many years of exponential growth: 100*(1 + 10%)^40" Compound growth isn't a myth, it just takes patience to experience.  A 10% annual return will double the investment not in 10 years, but just over 7.  Even though a mortgage claims to use simple interest, if your loan is 5% and there's 14 years to go, $100 extra principal will knock off $200 from the final payment. The same laws of compounding and Rule of 72 are at play. So my Question is this, in reality is investment in equities like the   stock market even remotely resemble the type of growth one would   expect if investing the same money in an account with compounding   interest? Generally no as there is a great deal of volatility when it comes to investing in stocks that isn't well represented by simply taking the compounded annual growth rate and assuming things always went up and never went down. This is adding in the swings that the market will take that at times may be a bit of a rude surprise to some people. Are all these prognosticators vastly underestimating how much savers   need to be socking away by overstating what is realistic in terms of   growth in investment markets? Possibly but not probably. Until we know definitively what the returns are from various asset classes, I'm not sure I'd want to claim that people need to save a ton more. I'll agree that the model misses how wide the swings are, not necessarily that the averages are too low or overstated. "This post may be old anyhow here's my 2 cents. Real world...no. Compounding is overstated. I have 3 mutual funds, basically index funds, you can go look them up. vwinx, spmix, spfix in 11 years i've made a little over 12,000 on 50,000 invested.  That averages 5%. That's $1,200 a year about. Not exactly getting rich on the compounding ""myth?"". You do the math. I would guess because overly optimistic compounding  gains are based on a straight line gains. Real world...that aint gonna happen."
"If it could, it seems yet to be proven.  Long Term Capital Management was founded by a bunch of math whizzes and they seem to have missed something.  I'd never suggest that something has no value, but similar to the concept that ""if time travel were possible, why hasn't anyone come back from the future to tell us"" I'd suggest that if there were a real advantage to what you suggest, someone would be making money from it already.  In my opinion, the math is simple, little more than a four function calculator is needed." It is not unheard of. Celebrity investors such as Warren Buffet and Carl Icahn gained notoriety by more than doubling investments some years, with a few very stellar trades and bets. Doubling, as in a 100% gain, is actually conservative if you want to play that game, as 500%, 1200% and greater gains are possible and were achieved by the two otherwise unrelated people I mentioned. This reality is opposite of the comparably pitiful returns that Warren Buffet teaches baby boomers about, but compounding on 2-5% gains annually is a more likely way to build wealth. It is unreasonable to say and expect that you will get the outcome of doubling an investment year over year. The net return reported to you (as a percentage) by a mutual fund is the gross return minus the expense ratio.  So, if the gross return is X% and the expense ratio is Y%, your account will show a return of (X-Y)%.  Be aware that X could be negative too. So, with Y = 1, If X = 10 (as you might get from a stock fund if you believe historical averages will continue), then the net return is 9% and you have lost (Y/X) times 100% = 10% of the gross return. If X = 8 (as you might get from a bond fund if you believe historical averages will continue), then the net return is 7% and you have lost (Y/X) times 100% = 12.5% of the gross return. and so on and so forth.  The numbers used are merely examples of the returns that have been obtained historically, though it is worth emphasizing that 10% is an average return, averaged over many decades, from investments in stocks, and to believe that one will get a 10% return year after year is to mislead oneself very badly. I think the point of the illustrations is that expense ratios are important, and should matter a lot to you, but that their impact is proportionately somewhat less if the gross return  is high, but very significant if the gross return is low, as  in money-market funds.  In fact, some money market funds which  found that X < Y have even foregone charging the expense ratio  fee so as to maintain a fixed $1 per share price.  Personally,  I would need a lot of persuading to invest in even a stock fund with 1% expense ratio. It is a good enough approximation. With a single event you can do it your way and get a better result, but imagine that the $300 are spread over a certain period with $10 contribution each time? Then recalculating and compounding will be a lot of work to do. The original ROI formula is averaging the ROI by definition, so why bother with precise calculations of averages that are imprecise by definition, when you can just adjust the average without losing the level of precision? 11.4 and 11.3 aren't significantly different, its immaterial. The effects of compounding inflation. Counter act by earning compounding interest on investments, aka the 8th wonder of the world. Maybe you have a family and have no money to save up? then u can't participate in compounding interest income, sorry I guess. My best advice to being rich is not being poor. (I'm a broke finance major at the moment, so I'm learning in depth of how I'm getting fucked) "The power of compounding interest and returns is an amazing thing.  Start educating yourself about investing, and do it -- there are great Q&As on this site, numerous books (I recommend ""The Intelligent Investor"", tools for small investors (like Sharebuilder.com) and other resources out there to get you started. Your portfolio doesn't need to include every dime you have either. But you do need to develop the discipline to save money -- even if that savings is $20 while you're in school. How you split between cash/deposit account savings and other investment vehicles is a decision that needs to make sense to you." "Two typical responses to articles/surveys making such claims:  **1. People use other forms of asset for emergency savings because interest rates are low - clearly false.**  **2. People use other forms of saving than a saving account therefore such surveys as the X% can't handle a $500 emergency are wrong on their face - this is false the vast majority use a savings account.**  I've chosen a topic that absolutely annoys the shit out of me every time it comes up, how people save their money. Every time this topic comes up about X% of americans can't come up with $Y dollars in an emergency or have less than $Z in savings someone inevitably chimes in with the linked response. I have *never* seen anyone attempt to source their hand waving response beyond their own anecdote, which is usually a thinly veiled brag about how financially savvy they are with their wealth. Perhaps people who have no assets, or crippling debt don't go out of their way to brag about it...  I could link multiple reddit posts making a similar response, which I address with my own stock response about once every 1-2 months. Instead I've decided to expand with data from several other sources. This is the prototypical good/bad research problem. If you're asserting something, but qualify your statement with, ""I""m sure we'd find...if we looked into..."" then you're doing it wrong. A good researcher or journalist doesn't put bullshit like that in their work because it's their job to actually look for sources of data; data which should exist with multiple government and independent groups. So let's get started (all data as recent as I could find, oldest source is for 2010):  * [Most americans don't invest in the stock market](https://www.federalreserve.gov/pubs/bulletin/2014/pdf/scf14.pdf)  About 48.8% of americans owned publicly traded stock directly or indirectly, with a much smaller percent (13.8%) owning stock directly -  pages 18 and 16 respectively. It's important to note the predominance of indirect ownership which suggests this is mostly retirement accounts. It's entirely possible people are irresponsible with their emergency savings, but I think it safe to say we should not expect people to *dip into their retirement accounts* for relatively minor emergency expenses. The reason is obvious, even if it covers the expense they now have to make up the shortfall for their retirement savings. This is further supported by the same source:  &gt;""The value of assets held within IRAs and DC plans are among the most significant compo-nents of many families’ balance sheets and are a significant determinant of their future retirement security.""  Ibid (page 20, PDF page 20 of 41)  There is also a break down of holdings by asset type on page 16, PDF page 16 of 41.  * [This data is skewed by the top 10% who keep more of their wealth in different asset types.](http://www2.ucsc.edu/whorulesamerica/power/wealth.html) For a breakdown between the 1st, 10th, and 90th percentiles see **table 3.**  So far it seems pretty hard to maintain a large percent of americans have their wealth stored outside of savings accounts, mattresses aside.  * [Here's my original reply as to the breakdown of americans assets by type and percent holding.](https://imgur.com/a/DsLxB) Note this assumes people *have* assets. [Source for images/data.](https://www.census.gov/people/wealth/data/dtables.html)  Most people use savings accounts, with runner up falling to checking accounts. This will segue into our next topic which is the problem of unbanked/underbanked households.  * [A large number of individuals have no assets; breaking down by asset types assumes people *have* assets in the first place.](https://www.fdic.gov/householdsurvey/)  To quote the FDIC:  &gt;*""Estimates from the 2015 survey indicate that 7.0 percent of households in the United States were unbanked in 2015. This proportion represents approximately 9.0 million households. An additional 19.9 percent of U.S. households (24.5 million) were underbanked, meaning that the household had a checking or savings account but also obtained financial products and services outside of the banking system.""*  That's right there are millions of households *so finance savvy* they don't even have bank accounts! Obviously it's because of low interest rates. Also, most people have a checking account as well as savings account, the percent with ""checking and savings"" was 75.8% while those with ""checking only"" were 22.2% (page 25, PDF page 31 of 88). It's possible in some surveys people keep all their money in checking, but given other data sources, and the original claim this fails to hold up. If the concern was interest rates it makes no sense to keep money in checking which seldom pays interest.  This survey also directly addresses the issue of ""emergency savings"":  &gt; *""Overall, 56.3 percent of households saved for unexpected  expenses or emergencies in the past 12 months.""* (page 37, PDF page 43 of 88)  Furthermore:  &gt;*""Figure 7.2 shows that among all households that saved for  unexpected expenses or emergencies, savings accounts  were the most used savings method followed by checking  accounts:* **more than four in five (84.9 percent) kept savings  in one of these accounts.** *About one in ten (10.5 percent)  households that saved maintained savings in the home, or  with family or friends.""*   Emphasis added.  * [Why don't people have wealth in different asset classes? Well they don't save money.](http://cdn.financialsamurai.com/wp-content/uploads/2014/06/savings-rates-by-wealth-class.png)  This is further supported by the OECD data:  * [Americans ""currency and deposits"" are 13% vs 5.8% for ""securities and other shares"" as % of total financial assets.](https://data.oecd.org/hha/household-financial-assets.htm)  Additionally:  * [Interest earning checking accounts: 44.6% of american households (second image)](https://imgur.com/a/DsLxB)  * [""Among all households that saved for unexpected expenses or emergencies, savings accounts were the most used  savings method followed by checking accounts..."" (page 7, PDF page 13 of 88)](https://www.fdic.gov/householdsurvey/2015/2015report.pdf)  * ~70% saved for an emergency with a savings account vs ~24% who used checking. *Ibid.*  In fairness the FDIC link does state *banked* americans were more likely to hold checking accounts than savings accounts (98% vs ~77% respectively) but that doesn't mean they're earning interest in their checking account. It's also worth noting median transaction account value was for 2013 (this is the federal reserve data) $4100." I read Q#4 as  Will $250 in one account earn more interest than $250 in five accounts? in which case Excel says no, assuming a constant interest rate for all accounts. I dunno if the same holds true for banks. What you're missing is the continuous compounding computation doesn't work that way.  If you compound over n periods of time and a rate of return of r, the formula is e^(r*n), as you have to multiply the returns together with a mulitplicative base of 1.  Otherwise consider what 0 does to your formula.  If I get a zero return, I have a zero result which doesn't make sense.  However, in my formula I'd still get the 1 which is what I'm starting and thus the no effect is the intended result. Continuous compounding would give e^(-.20*12) = e^(-2.4) = .0907 which is a -91% return so for each $100 invested, the person ends up with $9.07 left at the end.  It may help to picture that the function e^(-x) does asymptotically approach zero as x tends to infinity, but that is as bad as it can get, so one doesn't cross into the negative unless one wants to do returns in a Complex number system with imaginary numbers in here somehow. For those wanting the usual compounding, here would be that computation which is more brutal actually: For your case it would be (1-.20)^12=(0.8)^12=0.068719476736 which is to say that someone ends up with 6.87% in the end.  For each $100 had in the beginning they would end with $6.87 in the end. Consider someone starting with $100 and take 20% off time and time again you'd see this as it would go down to $80 after the first month and then down to $64 the second month as the amount gets lower the amount taken off gets lower too.  This can be continued for all 12 terms.  Note that the second case isn't another $20 loss but only $16 though it is the same percentage overall. Some retail stores may do discounts on discounts so this can happen in reality.  Take 50% off of something already marked down 50% and it isn't free, it is down 75% in total.  Just to give a real world example where while you think a half and a half is a whole, taking half and then half of a half is only three fourths, sorry to say.  You could do this with an apple or a pizza if you want a food example to consider. Alternatively, consider the classic up and down case where an investment goes up 10% and down 10%.  On the surface, these should cancel and negate each other, right?  No, in fact the total return is down 1% as the computation would be (1.1)(.9)=.99 which is slightly less than 1. Continuous compounding may be a bit exotic from a Mathematical concept but the idea of handling geometric means and how compounding returns comes together is something that is rather practical for people to consider. This is certainly possible. There are lots of strategies that involve taking out loans to invest. However, they are all high risk strategies. There's a school district for a major US city that was able to get incredibly favorable loan terms because their repayment was assured by law. They borrowed a bunch of money and put it into a variety of sure things insured by reliable companies like Lehman Brothers. You can figure out the rest. "In addition to the choice that saving for retirement affords - itself a great comfort - the miracle of compounding is so great that even if you chose to work in old age, having set aside sums of money that grow will itself help your future.  The are so many versions of the ""saving money in your 20s"" that equals millions of dollars that the numbers aren't worth showing here. Still, any time value of money example will illustrate the truth.  That said, time value of money does start with the assumption that a dollar today is worth more than a dollar tomorrow. Inflation, after all, eats away at the value of a dollar. It's just that compounding so outshines inflation that any mature person who is willing to wait, should be convinced. Until you work the examples, however, it's not at all obvious.  It took my daughter years to figure out that saving her allowance let her get way better stuff. The same is true of everyone." Consider inflation. If you invest $10,000 today, you need to make a few hundred dollars interest just to make up for inflation - if there is 3% inflation then a change from $10,000 to $10,300 means you didn't actually make any money. "1) When it says ""an investment or mutual fund"", is a mutual fund not   an investment? If no, what is the definition of an investment? A mutual fund is indeed an investment. The article probably mentions  mutual funds separately from other investments because it is not uncommon for mutual funds to give you the option to automatically reinvest dividends and capital gains.    2) When it says ""In terms of stocks"", why does it only mention   distribution of dividends but not distribution of capital gains? Since distributions are received as cash deposits they can be used to buy more of the stock. Capital gains, on the other hand, occur when an asset increases in value. These gains are realized when the asset is sold. In the case of stocks, reinvestment of capital gains doesn't make much sense since buying more stock after selling it to realize capital gains results in you owning as much stock as you had before you realized the gains. 3) When it says ""In terms of mutual funds"", it says about ""the   reinvestment of distributions and dividends"". Does ""distributions"" not   include distributions of ""dividends""? why does it mention   ""distributions"" parallel to ""dividends""? Used in this setting, dividend and distribution are synonymous, which is highlighted by the way they are used in parallel. 4) Does reinvestment only apply to interest or dividends, but not to   capital gain? Reinvestment only applies to dividends in the case of stocks. Mutual funds must distribute capital gains to shareholders, making these distributions essentially cash dividends, usually as a special end of year distribution. If you've requested automatic reinvestment, the fund will buy more shares with these capital gain distributions as well." Depends on the fund. If it's a Target Date fund, which is inherently diversified, this comes down to how much you trust the investment house to not go belly-up. If it's another kind of fund, you need to manage your own duversification and occasional rebalancing.  Most of my money is in index funds (details elsewhere), but that's five or six very different indexes to cover the investment space with the mix of investment types I've selected. And most of it is in a single family of funds, which might be argued to be higher risk than desirable but which has been convenient. The price of a bond goes up when yields go down.  For example, you purchase a 5% bond today for $100 and the very next day the same bond is being offered with a rate of 10%.  Will you be able to sell you bond for the $100 you paid?  No, you must compete with the 10% bonds being sold so you will have to sell your bond for less than the $100 you paid to compete with the new bonds being sold.  Thus, bond prices are inversely related to bond yields. The 20-year index you cited tracks bond prices and bond prices have gone up over the last 10 years which means bond yields have gone down.  Why have bond prices gone up?  Demand.  More investors are moving their savings into bonds.  Why?  I believe there a couple of reasons.  One, US Treasuries are thought to be one of the safest investments.  With the financial crisis and increased stock market volatility (see chart below) more investors are allocating more of their portfolios to safer investments.  Two, a large portion of the US population is approaching retirement (see chart below).  These folks are not interested in watching their retirement portfolios potentially shrink in the stock market so they move into bonds.