Introduction to S&P 500 Index Funds
and the 4% Rule

A Few Market Things You Need To Know, if you don't already

The S&P 500 calculator is on the previous page, and its calculations include past fund survivability of withdrawals. My interest was about how appropriate is the 4% Rule for a 100% stock fund like the S&P 500? (as opposed to a balanced fund with bonds?) This page is the general introductory info describing the 4% Rule, the S&P 500, the general market, bonds, dividends, gain, Bear markets, etc. This is some market stuff that you should know. You might find a few things of interest.

This was to be the introduction to that same S&P 500 calculator, but it was too large to include there. And there were additions to it, so it is a large page, but a Menu to several of its subjects below is:

The 4% Rule

What are S&P 500 Index funds?

A few important facts to know about Dividends of stocks and funds

A few important facts to know about Bonds

Computing methods of compounded gains, and Annualized Return

Four calculators about Gain, Compounded and Annualized

Rule of 72 Expanded with a Calculator

How to Earn a Million Dollars for Retirement

Bad times in the market  with a recent graph of S&P 500

The 4% Rule

The 4% Rule was originally about balanced funds, meaning stocks balanced with bonds, typically containing 60% stocks and 40% bonds (but there are also other mixes). In the past, the idea was that bonds would also provide some earnings when the market is down. A balanced fund (with bond income) should drop less than a 100% stock fund during a market crash, but it also earns less in the good times (and there are many more good times than bad). The 4% withdrawal rate has been promoted as safe, determined by testing past market history with 4% withdrawals lasting through 30 years of withdrawals in retirement from any starting date. However it did not specify any specific fund investments, nor any value of fund growth, but which seems a major factor to me. And it was from history when bonds paid more than now, but 2022 has to be the worst year for balanced funds, because both stocks and bonds were down big.

And Note: 4% withdrawal does NOT mean from Day One. It means waiting to start withdrawals until retirement, after building with many years of gain. Then it also means recomputing the 4% withdrawal every year, 4% of the then current fund value. In bad times, a continuous fixed dollar withdrawal can be devastating for a relatively small fund.

But instead of balanced funds, the point here is that I also wondered about 100% stocks (like the S&P 500 Index funds for example). Any X% percentage withdrawal rate might seem safe if the fund average earning gain was X% to support it, except years vary in gains, at an irregular rate. A 50% loss (say $100 down to $50) requires a 100% gain to recover, which might take a few years (see calculator 4 below). The bonds in balanced funds used to add income to aid that, but times change, and with interest rates increasing now, resale of bonds is also losing money now (see Bonds below). The 4% concept specifically means the withdrawal dollars are adjusted each year to not exceed withdrawing more than 4% of the then current fund. And market years do vary erratically, when a couple or three seriously bad years in a row can make a serious departure from the average. So the rule examines market history verifying survival of all starting dates enduring all known bad year periods. This sites S&P 500 calculator (link at top above) has the Test that does the same thing, with variable withdrawal rates. The future is unknown of course, but knowing the history should help know what possibilities could happen (the 2000 decade was particularly poor).

Origin of the 4% Rule: Interest rates of bonds were higher in older years, and the purpose of a balanced fund (Balanced meaning equities mixed with some degree of bonds, often 40% composed of bonds called 60/40 stocks/bonds) was market safety, because bonds are not affected by the market, and the bonds contributed to help tide it over in bad market times.

A good description of the 4% Rule was that it comes from a 1994 investigation of historical market data that tested for a reliable safe withdrawal amount, specifically for a balanced fund. Its conclusion was that a 4% withdrawal would survive 30 years of retirement withdrawals in past situations if invested anytime since 1928. However, it was done earlier than the worst times in the 2000s. Bonds are a different factor. The bonds did provide some income in those days for a degree of safety in bear markets. Here's a chart of the Federal Reserve Bank's interest rate history, and I'm thinking the 4% Rule look in 1994 could not foresee today's zero interest rate. A good recent article about the 4% withdrawal number 4 is at Morningstar.

IMO, a downside of the 4% Rule is that it does not consider the gain of the fund, nor how much money it has accumulated before withdrawal begins. These seem serious factors in predicting how long the fund can survive the withdrawals.

What are S&P 500 Index funds?

There are many S&P 500 Index funds which as a group, are widely considered to be one of the wisest market investment choices for most people (those who are not market professionals following the market closely every minute). These Index funds keep their S&P 500 holdings exactly matched with the index it is tracking, to match the same performance. The S&P 500 Index is the collection of the 500 largest US publicly-held companies (the largest large-cap stocks, including both growth and value stocks), all well established, and widely including most industry types. Might say it's where the money is, since the S&P 500 includes about 80% of the total available (public) US market capitalization. Capitalization is a companies total dollar market equity value, equal to the companies number of public stock shares × current price per share. The S&P 500 index is weighted by capitalization, including total public stock amounts, so that the largest companies count proportionally more in the index, according to their overall capitalization dollar value. The many S&P 500 Index funds try to exactly match the S&P 500 Index performance, but these funds do have different expense fees (and the lower fees leave more for you to keep each year).

There are actually 503 tickers in the S&P 500 (today, but it has varied), because three of the companies have two major classes of public common stock included (Google, Fox Corp and Discovery Communication). Google's company name is Alphabet, with two public stock classes A and C, with two tickers GOOG and GOOGL, which are added together here in the table here. The S&P rules today prohibit including more than one class of public stock, but these three are grandfathered.

S&P 500 Weighting
Top 10 as of 25 May 2023
Alphabet (Google)GOOG3.97%
Class A & CGOOGL
Berkshire Class BBRK.B1.65%
Meta (Facebook)META1.62%
United HealthUNH1.28%
Exxon MobileXOM1.25%

S&P 500 Weightings

as a percentage of the S&P 500 Index are as shown by their top 10 here. The Apple plus Microsoft stock total is approximately 14% of the S&P 500 Index value. The combined weightings of the five largest companies (1% of 500) often comprise around 22% of the S&P 500 index (because their capitalization totals about that). Whereas if it were instead equal weighting, each of the 500 companies would be 1/500 at 0.2% each. However the argument is their values are not equal, and the S&P 500 is instead weighted by capitalization (total dollar value of each company's stock). So as weighted, the smallest companies in the S&P 500 list get down to about 0.01% weighting (with little impact individually), but which are still among the 500 largest US companies.

The weighting method is that Apple's capitalization is several hundred times more dollars than the smallest member company (Apple's worth is about $2.6 Trillion, which is near 7% of the total S&P 500 capitalization), so the weighting is per each invested dollar instead of per company. Some do fault it because a few companies dominate the total, but it seems proper to me. So the weighting numbers vary with the daily prices, computed each trading day (to compute the S&P 500 Index). All of the 500 "Weights" add to 100, so these numbers are the actual percentages of the total Index value. The S&P 500 is near 80% of the total U.S. market capitalization.

See the current weighting of all of the S&P 500 companies. All the numbers change slightly every market day.

To be eligible for S&P 500 inclusion, each company's stock must be publicly held, and to be in the top 500 companies, currently each is at least $14.6 Billion capitalization. However each company must also be selected by a S&P committee with additional performance concerns. Companies can also be similarly removed from the S&P 500 (one must be removed for every company added). These S&P 500 are the Big Boys, the largest and most financially successful. Then all of the S&P 500 index funds simply plan to exactly track and match the performance of the S&P 500 index (less the fund's expense fee).

Probably about any question you might have about the S&P 500 Index would be answered here: S&P U.S. Indices Methodology.

Dow Jones189630$9.67 TrillionShare Price
S&P 5001957500$33.8 TrillionCapitalization
Nasdaq19713564$18 TrillionCapitalization

The Dow Jones Index is the major index normally reported by the news media. The Dow Jones index represents 30 US stocks (all are in the S&P 500). It is price weighted, meaning a $1 change in a $10 stock has the same effect as a $1 change in a $100 stock. The 30 stocks have relatively frequent changes replacing some stock choices (see a DJ list of stocks and changes).

The S&P 500 Index represents the 500 largest US stocks. It is capitalized weighted, meaning a $1 change in a $2 Billion company has twice the effect as a $1 change in $1 Billion company. Many consider the S&P 500 Index to be most representative of the overall market performance.

The Nasdaq Index (Nasdaq Composite) is 3564 stocks (all types, but also generally including the newer technologies). Even more so than in the S&P 500, the Nasdaq is very heavily weighted with the largest stocks also in the S&P 500: Apple (13.7%), Microsoft (10.8%), Alphabet (Google 6.3%), Amazon (5.6%), Nvidia (3.5%), Tesla (3.3%), Meta (Facebook, 2.4%), and more. The additional 2000 companies are smaller than the S&P 500, but not small, the Index requires a capitalization of at least $550 Million.

There is also the Total Stock Market Index Fund (Vanguard VTSAX) with stock of 3992 companies (a blend of selected large-cap, mid-cap, and small-cap U.S. companies). To me, it seems mostly a conceptual idea, because in practice, it includes many smaller companies, weighted by capitalization like the S&P 500, which boils down to be that much of the S&P 500 value is at the top of it, with the smaller stocks weighted much less strongly, with much smaller contributions. But it still has similar performance as the S&P 500 (often around ± a percent or so from the S&P 500 index in individual years).

There also are various S&P Equally Weighted funds, either for all of the S&P 500 or just including specific industries or concerns, but equally weighted, for example ticker RSP. It seems to have a slight advantage in the current bad times (when the large growth stocks are well down), but my notion is that the largest leaders are ahead in good times.

There is my Performace Comparison of about 100 stocks to which you can easily add your own stock choices with a simple Copy/Paste from the Morningstar Total Return % statistics. Be aware that the highest performing growth stocks suffer the worst in bear market lows.

A few important facts to know about stock and fund Dividends

It is important to realize that a stock dividend payment equally reduces the stock price (dollars per share). A stock dividend payment is simply a withdrawal, a distribution of the earnings you already had, so it is NOT new gain. However reinvesting it does have a tangible benefit (free added shares).

A company's publicly held capitalized value is their number of existing stock shares multiplied by one share's price value. Apple's value this way computes to be about $2 Trillion. The idea of the dividend is to distribute some of the company profit to the stock owners. The dividend money paid out (as a few dollars per share) was removed from the company's value, as a payment to you. This reduces the company's value by millions, so the stock price (which reflects the remaining value of the company) is automatically and equally reduced by the same dollars per share when the dividend is paid. Due to that corresponding stock price drop, your value of the paid dividend and your stock's remaining value remains exactly the same sum value as before the dividend, i.e., there is no gain on that day. Yes, the stock price did drop, and the company value dropped, but you did not lose anything eitherYou already owned that stock that is subtracting the dividend. It dropped in price, but you do have that cash difference now. There is no gain and no loss, not from the dividend on that day. The distribution was just from the company's stock value that you already owned before, but now is instead transferred to your cash. Then if you withdraw that dividend, it is a withdrawal from your fund value, and its value goes down equally. But if you reinvest it, your stock or fund value stays the same as the previous value (no gain, no loss), but it does acquire more shares (free shares too, from the dividend reinvestment) for future earnings.

If a stock with price $100 distributes a dividend of $1 per share:
Dividend WithdrawnDividend Reinvested
Stock price is now $99. You do have the $1 per share dividend in your pocket, so still the same value in that way, but also a reduced stock fund for less future earning. This is a continuous withdrawal every quarter Stock price is now $99, but the price drop is offset by the added reinvested shares, so you still have the same previous value now, also with additional free shares (at no cost) each quarter for years of greater future earnings.
This compounding is a big deal.

You can replace the above word "company" with the word "fund". A funds income is the dividend received from the company's stock or bonds they hold. The fund distributes that income as fund dividend, and the fund price drops in the same way. Dividends from directly held bonds are different, but bond funds are the same as said here. See more detail about Dividends here (including reinvesting stock dividends).

The best and most optimal thing to do is to reinvest every dividend, which retains today's fund value, and adds a few more free shares each time, and makes a huge difference long term. You already owned the dividend money, so it was just a withdrawal, so it is NOT new income, but you can put it back into the fund by reinvesting it. The only advantage of dividends (but it sure is a big one) is that a stock paying 2% dividend a year is (only if reinvested) contributing 2% more shares every year, which drastically increases your long term earnings, it really adds up over the years.

Stock Dividends are valuable, but are NOT new income, so withdrawing them is just a withdrawal (which is a strong detriment to future gain). Reinvesting them is more new shares at no cost. The very strong gain of dividends is the long term compounding of the additional shares added by reinvesting dividends. Near 80% of the S&P 500 companies pay dividends in some degree. Dividends are dollars per share, percentage is annual, and is typically paid each quarter. See a list of those companies in the S&P 500 ranked by dividend. The S&P 500 dividend itself is the dividend paid by all 500 companies (but about 20% of those don't pay dividends. Many growth companies instead invest profit into creating more growth.)

Reinvesting dividends is a very major part of long term earnings. Long term, the cost of withdrawing dividends is too high to consider, much more than you might ever imagine (costing about half of the total gain potential over 40 years).

There is my computed chart on the previous page showing a typical cost of withdrawn dividends over the years. It is a S&P 500 Index fund paying dividends of perhaps about 2% a year, which varies more or less.

There are about 65 stocks referred to as Aristocrat Stocks, which to be included in their list, the companies must be in the S&P 500 (largest US companies), and must have increased their dividend every year for 25 years, a point of pride indicating a stable business. See that Aristocrat Stocks list. Their annual increases can be small, and about half of them still pay less than 2.5% dividends, and some of those pay less than 1%. A favorite of Warren Buffet at Berkshire Hathaway is Coca Cola (KO) paying about 3% plus decent earnings. Whereas most of the best growth stocks pay no dividends, and also can have prices that vary widely.

If interested in a high dividend fund, you should also know the stock's Total Return (price gains plus dividends). One way is putting its Morningstar 10 year Total Return % data into the 3rd calculator below. And the 10 year history of the 50 largest S&P 500 stocks (and several others) is shown here.

Indexed funds vs. Actively Managed funds: Index funds simply try to match performance of the fund to the actual daily index of the group of companies by using computers to maintain the index match by automatically buying the matching shares of each company (passive investing, computers instead of managers, low fee cost). Whereas actively managed funds instead have a human manager trying to pick the selected best paying investments (at larger fee cost). And managers might accomplish that now and then, but next year may be rather different, and it is commonly said that indexed S&P 500 earnings beat managers about 90% of the time (the lower fee is some part of it).

Another category is ETF funds (Exchange Traded Funds), relatively new. Standard mutual funds can only be traded after the market closes, for the close price, and then Only if ordered before the market closes. ETF funds are traded like stocks, any time the market is open, at the market price. That could be important if you trade frequently, but won't be important if you buy and hold. One example is the NASDAQ 100 ETF, ticker QQQ, which is 100 of the leading S&P 500 stocks.

Fees: Brokers typically charge commissions on buying or selling stocks, however some brokers now are free or almost so. Market exchanges have a slight difference between buy and sell prices of stocks (bid and ask), which is a fee on the buyer. Some brokers sell only funds with a "sales load" commission which has been quite high, however there are also very many no-load funds with no charge (you must look those up yourself). Those are one time charges. However, funds also have annual fees, charged every year for the management, so while maybe a fee may sound low, it can add up big every year. Some fees are near zero on Index funds. The large brokers with no commission will handle your trade, probably only online, but don't expect advice on what to buy. Those earning commission may offer more advice, but they might be more interested in their commission (they have lists of what to sell today). You'd be advised to shop around a bit to be aware about the fees and commissions. It's your choice and there are good choices, and less fee is more final profit for you. Morningstar Total Return results do include annual fund expense fees, but do not include any commissions or sales charges.

So yes, there are other funds and stocks that might sometimes earn more than the S&P 500 Index (the largest of those companies are probably in the S&P 500, contributing their share, and the S&P 500 is 500 stocks which is some degree of diversification). However their downside is these currently hot stocks are more volatile, their prices can swing widely, which is great when the market is good, but is the worst when the market crashes. And it does seem that the faster they grow, the faster they can fall. The leading stocks can fall the most. The past year 2022 was a pretty bad year, the S&P 500 bottom was -25%, but -18% to -20% was more common most of the year. The biggest usual leaders (like Apple, Microsoft, Nvidia, Amazon, Google) just saw way down, values from -30% to 40%, and a few special cases like Facebook and Netflix were down 60% (for an awakening, see Total Returns of 100+ stocks). But the market always recovers, eventually, and 2023 is starting out much better, not at recovery yet, but much better (and these growth leaders are leading it). The market is usually good overall, but there certainly can be big downside surprises. If investing in individual stocks, you may want to watch closely, and know when and why to switch stocks (preferably before it changes, but that is extremely difficult to know, it happens before we know about it). The S&P 500 can be more comfortable long term without close watching, but it does go negative with the market, like this year. It has always recovered to continues growing, but that is not very comforting while waiting in the bad times.

Diversification — Don't put all your eggs in one basket. The S&P 500 mix of 500 companies is a diversification in the various industries (tech, energy, financial, consumer, health, industrial, materials, etc). However all of the 500 are US large cap stocks (which includes No small caps, mid caps, emerging markets, foreign markets, bonds, etc.). A S&P 500 Index fund earns more than balanced funds ("balanced" means majorly mixed with bonds for diversification), but bonds can be very volatile too, because bond value varies with interest rates, which goes up and down too (see Bond Duration in the Bond box below). But overall, the S&P 500 trend line is quite appealing. The nature of investing is that some risk is necessary to earn higher gains, a low risk investment doesn't earn much. The S&P 500 does have the normal daily market ups and downs, including the rare economy crashes, but the overall S&P 500 averaged gain has historically always been of about 10% a year, compounded long term. Which is NOT a guarantee — years vary, a few years are negative, but there are many more good years than not. However a bad crash with a few bad years in a row will have a large effect. The entire 2000 decade was down -9.4% with 2001 and 2008 crashes that were pretty bad. But the long term picture is very appealing, with only a few dips, which have always recovered of course.

Nothing ventured, nothing gained. Ben Franklin said that too, but the thought is centuries older. Some people do fear anything in the market is too much risk for them (yes, the market can crash in bad times, but then it always has recovered, after a while). At least it does if it was a good investment, and the S&P 500 are the largest and most successful Blue Chip companies in the US, which is a good strong bet.

The overall years can hide a few adjacent down years during which withdrawals could deplete the fund. The S&P 500 will recover, it always has, but if all your money was depleted earlier due to withdrawals, it ends there. The first early years are the higher risk of withdrawals, when value is small before it has earned much, since more money will of course always last longer in a crisis. So first building more money in the fund (before the retirement withdrawals) is the insurance to last longer when down, and to make recovery easier. Reason would suggest that first allowing maybe 20 or better 40 years for the fund to build and grow without any withdrawals would make all the difference of survivability, and would of course also provide much greater income during retirement. The market years do vary erratically, but continually withdrawing 10% also with average earnings near 10% might (on average) usually keep it drained down to always about the same level, more or less. It can't grow more then, but its value won't vary so greatly through a long retirement. Except there are variations outside of average, and limiting withdrawals to about half of the average fund earnings rate significantly improves odds against going the fund going bust (and would also leave something for future inheritance to your heirs).

Never withdrawing anything will not go to zero, also unlikely if withdrawal is a small percentage, but fixed withdrawals can become relatively huge when the fund is small, so recompute the withdrawal percentage every year. Fixed dollar withdrawal can become very large when the stock value drops. Even an extremely bad rare crash probably leaves at least 50%, which is certainly no fun then, but it has in fact always recovered. Here is a table of a few years of S&P 500 record highs. But when and if it is down low, but then percentage withdrawals become fewer dollars of withdrawals when the fund is low. Instead, the biggest danger is fixed dollar value withdrawals, which if blind to current situations and not limited to a reasonable current percentage, of which an example is shown in the Test section on previous calculator page. Your planning for that should have occurred decades earlier. Withdrawals are the desired and necessary goal in retirement, but are very counterproductive during the growth phase. In every case, withdrawals should be reconsidered if the fund value gets low. We don't know the future but we can look at the effect of "typical" past periods, regarding our withdrawal feasibility.

One issue of a 4% Rule is that it does not specify any specific fund or contents, nor any specific fund value. However a fund containing more money can obviously survive withdrawing in a crash longer than would the same fund with less money. Meaning, a large million dollar fund and a small $10K fund both withdrawing after a bad crash might both fall to 50%, but 50% of a $Million is much more survivable (and with greater gains in recovery) than 50% of $10K. The survivability of investing for 20 or 30 years to build before starting withdrawals is a big factor of retirement withdrawal success.

The survivability of a reasonable percentage withdrawal not hitting zero seems relatively independent of value — only meaning a fixed withdrawal percentage rate (if the withdrawal dollars are readjusted every year to hold that percentage rate), it withdraws much less when fund is low, near zero withdrawal when near zero value, and worst case still always leaves some value instead of zero. Maybe only a few cents left, but not exactly zero, so hitting zero can take a very long time. Which is the reason an adjustable $100 minimum limit was added to the S&P calculator to more clearly define the end of Survival due to depletion. Possibly this minimum to define depletion should be higher for a stronger recovery, and you can change it. Whereas a fixed amount withdrawal just keeps on coming, whether the fund is low or not. But in the real world of fixed withdrawals in dollars, hitting zero is certainly about the fund value, since a higher value fund will always last longer through any crisis. The important thing is to maintain a fund value that can recover and survive. Withdrawals make remaining Fund Value be a very major survivability factor (and many years/decades of growth with no withdrawals until retirement is the obvious way to easily increase retirement fund value). If you had $1 Million in a fund, a bad crash might drop to 50%, but half a million would still last a very long time, and then the larger value will also recover with more dramatic gains than a tiny value could.

Inflation has historically averaged about 3%, and after being 1.2% in 2020, now inflation in 2022 is high but is down some, 9.1% for June 2022, and is currently at 4.9% (for April 2023) which is still a 33 year high, so the times have become very different. But the S&P 500 Total Returns (includes reinvested dividends) has averaged 11.77% gain for the last 50 years (including the 13 negative years during that period).

Since generally low earnings from bonds is less appealing, my interest was about something like the 4% Rule, but for 100% stocks, such as the very popular S&P 500 index funds. A good stock fund earns a lot when the market is good, but market value can drop significantly when market times are bad. But which is more just a delay, since long term, even a 50% drop is not the end of the world, since the bad market crashes have always fully recovered if you can hang in there and wait it out. This is definitely NOT speaking of bad investments recovering, but is instead speaking of good investments in bad times, which have always recovered. However there is always risk that withdrawals at suffering prices can deplete a small fund. More money in the fund can survive fixed amount withdrawals longer. But if no withdrawals, it should recover and last indefinitely.

So instead of 60/40 balanced funds, what about a "4% rule" for a 100% S&P 500 Index fund? The S&P 500 calculator and Survival Test on the first page is about that.

My emphatic opinion is that all withdrawals ought to be planned to occur after retirement, not before. Repeated withdrawals drastically limit long term performance. The big issue is that retirement generally means having no job or salary, requiring living off of savings for maybe 30 years, perhaps even with major health care expenses, which will require some planning about providing income. The time to realize this is when young with still many years of great opportunity. The years are the best tool, don't waste them by waiting.

A few important facts to know about Bonds

Investing in bonds is a completely different game than investing in stock. I am offering some facts you need to know first. You should also be very aware of important information about buying bonds directly vs. bond funds. Directly held US government bonds can be purchased directly from the US treasury (no commission or fees), and possibly through your own broker. Treasury bonds pay a fixed face value interest, and the sales price varies with the current Fed interest rate (a higher price means a lower effective interest rate than the face rate). If in your own control to be able to hold to maturity, face price and rate applies. But if sold before maturity redemption, there is always price risk (or possible gain too) due to whatever current interest rate then. Be aware you are betting on future interest rate at resale. If current interest is up at resale, price then is down, and vice versa.

Bonds may have paid higher dividends in 1994 (for the 4% Rule study), helping to support withdrawals and market crashes, but interest rate has bottomed out near zero more recently, so IMO, bonds seem an outdated investment idea (however the inflation today is increasing bonds and even money market towards 5%). And bonds can protect savings from market volatility, and in a market crash, a 50/50 balanced fund may drop half as much as a 100% stock fund, and the bonds still could provide some earnings. But markets always do recover, and bonds don't earn what the 100% stock fund can, and don't earn today what bonds have historically earned, and don't even match inflation today.

Most of all, you must realize that bonds are also quite volatile too, maybe safe from the market, however bond value is very seriously affected by current interest rate changes, which are increasing this year for new bonds, but increasing interest lowers resell value of existing bonds. See Duration next below. Also, inflation is a serious concern, perhaps higher than interest rates.

However, regardless of current interest rates, bonds do pay full face value when redeemed at maturity. However, holding until maturity may be difficult to achieve unless you directly own the bonds to make it be your choice, independent of mutual funds. Bond funds value their bonds daily according to the current interest rate. I expect in 1994, the 4% Rule was evaluating history with directly held bonds, when there were no bond funds.

Government bonds are different yet, sold at auction to bidders (at US Treasury) or you can also buy there at the current auction price paid). So directly held US government bonds can be purchased directly from the US treasury (no commission or fees). There are Bills, Notes, and Bonds. Bills are short term, and pay interest only at maturity. U.S. Treasury bonds of 1 to 10 year maturity are called Notes, and those of 20 or 30 years are called Bonds ("Bonds" here refer to both Notes and Bonds). The Treasury bonds are safely backed by the government (when redeemed), and a fixed interest based on face value, and are redeemed at maturity at full face value. However initially, they are bought by bidding at treasury auctions on new treasury notes and bonds, so the actual final yields vary with the selling prices are basically what buyers will bid. A higher interest rate is due to a lower price (lower than the fixed face value). The variable auction prices are why interest rates of new government notes vary every day. The bid price drops if buyers won't pay more, and then the yield effectively goes higher than the face value (the yield to maturity), and of course vice versa too. But until redeemed at maturity (at full face value then, for the expected income), the bond resell value varies every day, due to current interest rates. The bond pays a fixed initial dividend in dollars, but resell value varies, making investment gain percent vary too, if sold early. But again, if redeemed at maturity, it pays full face value. The current SEC Yield reported is the previous 30 day interest result annualized to be a hypothetical 12 month rate, which is a standard way to compare the current earning rate of varying gains.

Directly held bond dividends are simple interest, which is not compounded (not reinvested). It's dividend is computed from the face interest rate and face value, which never changes value. The bond is redeemed at full face value. However, current interest rate changes do affect the resell value if sold before redemption.

Bond funds are a different picture. The fund holds many bonds, and the bond dividends go into the fund's value, and the fund issues their own dividend. Bond fund dividends are also withdrawals which also decrease the fund value (like stock and stock fund dividends do), but you can reinvest the fund dividends to maintain the same investment value, and achieve compounding.

Definition of the very important bond "Duration":  Any bond resell value varies with current interest rates. The term Duration computes that for Each 1% change in current interest rates, the resell value of existing bonds is expected to change in the opposite direction by "Duration" percent. If Duration is 5 years, and interest rates increase 1%, the bonds decrease value by 5% if resold. Interest rates dropped to zero the few prior years, so existing bond resell values increased then, and bond funds showed better results. But vice versa, today existing bonds lose resell value when interest rates increase (and now the one year return is negative). The U.S. Federal Bank has announced plans for more interest rate increases in 2022 to fight inflation. New bond interest rates is increasing, but old bond rates are negative gain now. A bond fund buys new bonds, but they already own many old bonds. But again, if bonds are directly held (in your own control), they do redeem at maturity at full face value.

Morningstar shows the bond Duration (in balanced funds at Portfolio tab, Bond sub-tab, if any). The meaning of a Duration of say 3 means the expected bond value will decrease 3% with each 1% interest rate increase, and vice versa, existing bond values also increase when interest rates fall. But either way, when and if directly held bonds are redeemed at maturity they do still pay face value. Short term bonds will have lower duration with lower risk from interest rates, but they pay even less. That is speaking of all bonds, including commercial, municipal or treasury (but excepting federal Savings Bonds, which are not sold at auction, and can be cashed in, but cannot be resold to a third party). Bonds have a face value and pay a fixed interest rate, of dollars based on their face value. However, when bought new at treasury action, or any bonds resold later in the market may pay a different price than face value, but directly held bonds still redeem face value at maturity. Bond resell value varies with current interest rates (including bond fund bonds) and with Duration, and then the actual purchase price computes the new effective interest rate (when redeemed at face value). If interest rates increase, existing bonds earning lower effective interest can only sell at a lower price to attract any interest in them (and also vice versa, price goes higher when interest rates decrease). This fact is Extremely Important, especially with interest rates currently increasing from a rock bottom low. The bond value decreases and also inflation exceeds the bond interest.

Bond resale value becomes volatile when interest rates change. I say "resale" because if held until redeemed at maturity, bonds are still redeemed at full face value (if directly purchased and in your own control to hold until then). So short term bonds, and bonds nearing maturity date, will have low durations. Long term bonds will have higher duration (more volatile due to interest rates). Morningstar.com shows the Duration of bond funds (on the Portfolio tab, computed each quarter, I think).

However, as individual bonds approach their maturity date, their duration drops towards zero, because directly held bonds do still repay full face value when redeemed at maturity or recall. And existing bonds do continue to pay their same fixed face value dividends, but their resell value varies with current interest rate (existing bond resell value drops with higher current interest rate). But if you buy bonds directly yourself, and hold until recalled or redeemed at maturity, the full face value return then will be as expected. But if sold early, they will have current market value.

So if in a bond fund, or if planning resell, there's much more to know about the volatility. Resell value of existing bonds varies inversely with current interest rates. And bond funds must buy and sell bonds continually as investors buy and sell shares, and bond values are computed daily, not necessarily held until redeemed, but the fund values its bonds at the resell price. So if you buy or resell in the fund, you get whatever the fund value is paying that day (due to interest rate changes). That could be a plus if interest rates fall, or costly if interest rates rise. Right now, interest rates were at near zero but rate is increasing due to the Fed planning to fight inflation with multiple interest rate increases during 2022. That then means the value of lower interest existing bonds is falling, but newly purchased bonds pay more interest.

When inflation increases interest rates of new bonds, it lowers old bond resell values. That's because no one would pay full price for old 1% bonds if they can buy new 2% bonds at same face value price. So then buying two existing 1% bonds at half price is required to match earnings of one new 2% bond. So existing old bond resale value can drop to half each time interest rate doubles (because then it takes two old bonds to pay what one new bond pays). And also vice versa, lower interest rates will increase the value of existing bonds that still pay more. (But see Duration too).

Some bonds are "callable" (most municipal bonds and some corporate bonds), with a callable date when the issuer can redeem the bond early (at full face value but which terminates dividend income). If current rates have increased, the bonds are worth more than face value, and you might consider selling them yourself before the recall date at face value. Or if current interest is lower, the fund issuing new bonds paying lower interest rate would be their plus.

Note that Junk bonds exist too (politely called high-yield bonds), from companies with lower credit rating, paying more dividend to attract buyers, but with higher possible risk of default failure (meaning 100% loss of your investment). For bond funds, Morningstar.com Portfolio tab shows bond ratings too. AAA is the most secure rating, including government bonds. Bonds rated down to A are considered investment grade. Generally bonds rated B or less are considered speculative and non-investment grade (speculative meaning offering greater dividends if paid, but with greater risk they could fail and default and stop, and not redeem at all). See bond credit rating.

The significant fact to know is that Interest rates dropped in 2019 and 2020 (to near zero), significantly increasing existing bond resell values, so bond funds showed good results then. The results may look real good, but it is important to realize why you see that value increase in the history, because the interest rate situation has changed. Since then, existing bonds lose resell value when interest rates on new bonds increase, and then bond return may go negative. When interest rates are near zero, there is only one direction they can move, up, which lowers bond resale value. The U.S. Fed has done several interest rate increases in 2022 due to inflation, and more are expected.

Bond price changes when reselling are taxed as Capital Gains if held one year or more. However bond dividends are taxed like interest, at regular income tax rates (except municipal bond dividends are tax free of federal tax, and sometimes free of state tax in same state, at least in some states).

Repeating the important stuff: Bonds do still pay full face value when redeemed at maturity (or when recalled earlier). And until then, they continue paying face value interest rate. So if you buy bonds directly yourself, Not in a fund, but in your name as owner, and hold them until redeemed at maturity, the return will be as expected. That's the good news.

However bond funds currently own existing bonds, which will have dropping value as the U.S. Federal Bank interest rate increases (which the Fed is currently doing in a big way, due to record high inflation). The bond funds must buy and sell bonds continually, as investors buy and sell shares. Bond funds value their bonds at the current sale price. And bond resell value varies daily with current interest rates. Bond funds recompute bond values with every days interest rate change. However, bond value does not vary much when close to maturity, so a complication is that bond value sensitivity to interest rates depends on how close it is to maturity, in the special calculation called Duration.

Again, a big point is to not be confused by market return statistics showing bond and balanced funds had good performance history in recent past years. They in fact did, but that is history, when interest rates fell more than 2% over 2019 and 2020, causing the existing bonds to increase in resell value, but which cannot continue today. So it's very wise to also check their current "1 Year Return" results too. The current SEC 30 day yield is shown annualized to represent one total year, which is the accurate current annualized rate value today, but it of course changes all during the rest of the year. The Federal Reserve Bank interest rate was near zero at the start of 2022, so the only way it could go is up. And the high inflation continues to increase it now, and increased interest rates means resell values of existing bonds are going down. However, bonds held until redemption at maturity do retain full face value then, except bond funds might not be able to hold them to maturity when their shareholders are ordering withdrawals because the value is going down. Since interest rates are near zero now, the danger for existing bonds is that rising rates (and lower values) are the only change possible now. We are expecting inflation to cause increasing interest rates. Directly held bond dividend income is taxed with regular income tax rates, but the fund price changes are mostly Capital Gains or losses if held a year or more.

Understanding a few Numbers of Compounded Gain

The greater number of years of long-term investments makes the compounding of gains be a huge exponential function (with years as the exponent power), which is an astounding big deal. A fixed 10% gain in each of 30 years becomes a final value of 1.1030 = 17.45x the initial value and 1645% overall gain. But the market gains do vary up or down each year (often large variations, even sometimes negative), see below for Annualizing the actual overall gain so it can be compared with others. In addition to the price gains, another major factor is that reinvested dividends add more shares every year (usually four times a year). Many but not all stocks pay dividends in some degree. The S&P 500 index fund dividends vary, but if they are reinvested adds very roughly around 2% to total returns each year. Then those gains see more gains, compounding every following year. Compounded earnings are a Real Big Deal, so think of a long term investment always with reinvested dividends. Start young, so it will be waiting at retirement. The S&P 500 calculator on previous page shows this with 50 years of past S&P 500 history.

The stock market varies every year, up and down, a little or a lot, positive or negative. The Average of the fund's annual gains is NOT the measure of stock performance. The average is just the sum of all years gain divided by the number of years, which does not include dividends or compounding. Annualized Return is the way to compare variable stock performance, including reinvested dividends and compounding.

The long term compounding result is the multiplication product of all the years of (in the format of 1 + gains, meaning the 1.15x type of number instead of the 15% type number).

For example, a stock that earned 10%, -10%, 20%, -20%, 30% and -30% over six years. What was the overall performance? The Average is 0, but that's not what happened. Calculator #3 below says the Overall gain (the dollars you are left with) is -13.51% for those six years). And its Annualized Return is -2.39% (meaning that gets the same -13.51% final result AS IF it had been -2.39% each year for six years, so that it is then comparable with other resources like banks). The reasonable plan for comparing performance is to use Annualized Return, which is described below.

Computing Compounded Gains, and Annualized Return results

Compounding is the largest gain effect of long term market investments. One year has earnings, which (if positive) then that greater working total increases the greater total amount producing earnings the next year, continually repeating every year. But market gain is variably different every year, making it hard to judge actual performance numbers, but there is a mathematical way. Here's six years of example Total Return statistics. Price gains do Not include dividends, so for it to be Total Return, don't forget to add all reinvested dividends (Morningstar also shows Total Return %). For the tax purposes, reinvested dividends were added to the cost basis (your tax 1099 shows cost).

The same percentage numbers are computed regardless of any initial value, $10 or $10,000,000. These are just made-up example gain numbers, accurate math but NOT representing any actual real stock.

Example of Manual Method of Annualized Return

Annualized Return

includes the long term compounding of several years and reinvested dividends, and is a hypothetical number computed to be AS IF the same final value resulted instead from a Fixed equal gain, same every year. This Annualized Return rate purpose is for comparisons (with other fixed rate interest), and it computes the fixed gain rate that would match the same market compounded result. It hides any volatility during the years, computing a smooth path that would give the same result in the same time. Annualized Return math is just below, but first, we need the overall gain.

Manual Method A:

  Percentage gain =
New value - Old value
Old value
× 100

This uses the actual final accumulated dollars of value, regardless if it includes reinvested dividends or not. But if there are any withdrawals, that money received should be added back to this new total.

From this computed table, this overall example six year gain (initial to final amount) is

  ((19995.35 - 10000) / 10000) × 100 = 99.95351% gain.

If you already know the final and initial values, then you can use this gain formula, or see the 1st Gain calculator below. Stock price does Not include dividends, but the dollar result does include effect of your reinvested dividends. Any withdrawals are received value which should be added back into the final total, but withdrawals will drastically reduce long term gains.

Multiplied Method B:

This uses each years annual Total Return % including reinvested dividends, instead of final value gain. These Morningstar Total Return % results assume no withdrawals. The first year gain of 15% in the table above means the first year result was 1.15 × (includes the initial 1x amount). That then becomes the initial amount for the second year. These same six individual yearly gains (as 1 + percent/100) will also compute total compounding result as

  (1.15 × 1.235 × 1.104 × 0.948 × 1.121 × 1.20 - 1) × 100 = 99.95351% gain.

See the 3rd calculator below (Compounding of Yearly Total Return Percent). Morningstar.com shows ten past years of these annual Total Return % numbers (including reinvested dividends, which for stocks are at the Price vs Fair Value tab, and for funds are at the Performance tab).

The order of the years makes no final difference. Compounding is simply repeated multiplication of gains. These methods do use the annual gain numbers with only 3 or 4 significant digits, but it is close. The initial dollar value does not affect the gain percentage. And then, the year's final Total Result value is (1 + gain/100) × initial invested value. For an initial $10,000, then 1 + 99.95351% is 1.999535 × $10000 = $19,995.35 result value.

Important Details: The ±1 in these equations represents the initial 1x investment value. That 1 becomes 100% when multiplied by 100 for percentage. If the gain is 12% (in terms of dollars gain), the year's final value will be (1 + 0.12) = 1.12x (in terms of the 1x initial value, as done in the six yearly terms at B above, and with current dollar value of 1.12 × initial value (in this 12% example). Whatever the initial amount was, it is 1x). Subtracting the initial 1 (initial value) from final multiplied result leaves just the gain portion (in Annualized Return next below). The gain computes the same numbers regardless of whatever the value of initial dollars. The 99.95351% gain in this example is 1.9995351x value, which is essentially 2x total value. So the final value would be 200%, but subtracting 1x initial value, the gain was 2×100% - (2-1)×100 = 100% (1x less than value, for any gain). The 1st Gain calculator below tries to differentiate gain and value.

Each year's gain is an individual multiplier of the initial value. Each factor is (1 + gain/100, with 15% gain becoming a 1.15x multiplier of value. Negative gains use the same method, for example -5.2% is 1 + (-5.2/100) resulting in 0.948x value that year. The -1 is subtracting the 1x initial value, to see just the gain portion. Or the 1 is added to gain (the 1 is actually 1×100, which is 100% of the original initial value), to see the final total value result. The amount of "gain" does not include the initial value, but the total value result does.

Note that a price result does not include dividends or compounding, but a formal Total Return does, including reinvested dividends. If there were no withdrawals, the final value resulting from the investment is a clear total answer including everything that happened. So $50,000 value result from $25,000 invested is a 50000/25000 = 2x gain, pure and simple. And it is a (2x - 1x)×100 = 100% gain. However, the rate of gain depends on the time of duration. If a market result took 10 years to double, it is (21/10 - 1)×100 = 7.1773% Annualized Return. Meaning, (1 + 0.071773)10 = 2x value would be the same result if it had come from a fixed rate interest source. Annualized Return seems a useful way to compare varying market results. Annualized Return is the same result, but of a fixed gain rate.

Annualized Return

The overall amount of gain is of course important, but the number of years is also a large factor of that. Annualizing it to show the equivalent fixed annual rate of gain allows understandable comparisons. It includes reinvested dividends to compute the equivalent fixed rate of return of the investment giving same gain result. It does not account for any cash either added or withdrawn along the way (so may not match your actual results), but it is valid for the published history statistics of the ticker performance.

These Annualized Return procedures are based on the standard compounding formula of
  (1 + (fixed interest rate / 100))years   Example: 10% is (1.10)years final value.

So 10% for 3 years is 1.103 = 1.331x Total Return value, which then -1 (subtracting the original principle) leaves 33.1% gain in 3 years, which is the compounded final result.

The Annualized Return is the reverse which is
  (1 + (Total Return / 100)1/years) is
  ((1 + 0.331)1/3 - 1) is 0.10 which is 10.0% Annualized Return for 3 years,
which becomes very meaningful if each years market gain was very variable.
The average gain is 13.6%, but only 10% compounded produces the same result in 3 years.

Annualized is the same compounded value achieved from the years, starting from the SAME actual final gain, but computes the Annualized gain that is the same result if from a fixed percentage every year. That result makes gains easy to understand and to compare market performance. Market years do vary widely, some years might even be negative, making it hard to realize the rate of actual final gain long term. Annualized uses the Same Actual Overall Gain, and then is a more logical way to compare actual long term performance. It hides any volatility during the years, computing a smooth path that would give the same result in the same time.

What is the resulting gain of the first example six years shown above as:
  15%, 23.5%, 10.4%, -5.2%, 12.1% and 20%?
The answer is shown above to be 99.95351% total gain, and 12.24186% Annualized Return, which annualized rate is more understandable and comparable as performance. Annualized Return (compounded, the same total gain viewed as the equivalent return each year if each year were equal) computes the hypothetical fixed interest rate AS IF it were that same interest rate every year. It still gives the same final total result, still an accurate result number, it just didn't actually happen that way. But it would be the same final result if it did, so that's a good way to understand the gain. Annualization can be helpful because otherwise it is very difficult to visualize the result of a string of variable years, maybe both large and small gains, some even negative. The Average of the years is NOT the correct answer. Average is a sum (not compounded), but compounded gain is a multiplied product.

To compute the Annualized Return rate for the example in the above table with the above gain formula is:

Four calculators for compounded gain and Annualized Return

Caution: Annualized Return cannot and will not be calculated correctly if including the current incomplete year data, or any partial years. Gain calculations are OK YTD, but Annualization is Whole Years Only.

1. Compute Annualized Return of Compounded Gain

Percentage gain =
New value - Old value
Old value
× 100

New value from Old over years

Years can be blank if annualized return is not needed.
Any $ % or , format keys are optional, and are ignored.

2. Future Value of Fixed or reversed Annualized rate

Old Value at Rate % over years

Any $ or , value format keys are optional, and ignored.

3. Total Return % and Annualized Return %

Enter each year of a stock's Total Return % in a span of years

A. Copy/Paste the Morningstar Total Return % line (for stocks is
    at the Price vs Fair Value tab, or for funds at the Performance tab)
B. Or just enter all year's numbers with a space separating each

Any number of years can be entered.
The last year will be assumed to be the current partial year

4. Recovery Gain needed when a stock or fund is Down

If a stock or fund price is down %

Recovery Needed if a stock or fund is Down this percent
Recovery gain11.1%25%42.5%66.7%100%150%233%400%
to 100% Value1.11x1.25x1.43x1.67x2x2.5x3.33x5x

1st calculator, Compounded Gain and Annualized Return: Hopefully it is both self-explanatory and maybe the most useful. Technically, any units work (like price or distance or weight or time). Or Dollars or Euros or Yen, but gain calculations need Not be about money.

2nd calculator, Future Value: This one is perhaps less used, but if no withdrawals or additions, it might estimate expectations of final value, however a future variable market gain rate is not predictable. To just see the gain rate compounding of the rate percent, you can use $1.
Or it can be used to reverse compute to verify an Annualized calculation is correct.

Significant digits: In that reverse computing use, the apparently exorbitant number of digits shown is because large values like $1,000,000.01 have 9 significant digits, which needs at least that many significant digits in the interest rate to accurately match the precision desired (years is an exponent of interest). For example in calculator 2, the initial values shown (trying to reverse compute the calculator 1 default) if using instead 12.2% (3 significant digits) computes $999,342.31, accurate to three digits, but is not 9 significant digits for the fully accurate number. Approximations might be an adequately useful estimate, but not the exact final result. Full precision does require the necessary number of significant digits. The precision of future market result estimates is unknown anyway, but exactly matching a reverse verification of Annualized rate needs about all the digits you can manage (compute it first, before any rounding). I've shown the Annualized Return with 10 significant digits, which may be excessive to view, but when the math has an exponent of 40 years for a result in the millions, it is more accurate to provide adequate accurate precision.

Any computed result will not have any more precision than the least significant digits in any number used to compute it. However, some numbers are Exact Numbers, and are fully precise, like 3 apples or 10 people or a $20 bill are precise numbers. Or perhaps sometimes 2x investment or 5 years if actually precise. The Morningstar annual Total Return percentage is shown with typically as few as 2 to 4 significant digits, but it is pretty close though.

3rd calculator, Total Return from yearly gains, Two methods of data entry:

  1. These data values are NOT the regular share prices, but are Total Return % of each year's result (which includes dividends and compounding). It accepts Copy and Paste of that data direct from Morningstar screens (or from other web tables too, if Total Return %). At Morningstar, this Total Return % data for stocks is at their Price vs Fair Value tab, and for funds are at their Performance tab. Any empty early years marked with a — can be copied or not, ignored either way.

    The calculator's initial data shown is the Morningstar Nvidia NVDA stock, 2013 to 2023, with the 2023 Total Return being near +166% so far (closed at its record high price $389.46 on 5/26/2023). Note that the 2022 year end close at -50.3% was Not the bottom low, which was Oct 14 at -61.8% from year end 2021. So the growth stocks have the highest gains, but are also among the greatest risks.

  2. Or you can simply enter each year's Total Return % separated by a space. Enter each yearly gain percentage (including dividends), in format like as 15% instead of 1.15x. The calculator will convert it to 1.15.

    The gain is a multiplied product, so the order of years does change the number, but the last year is assumed to be the current partial year. You likely will better understand seeing the years in a correct order.

Morningstar also shows another number called Trailing Returns for various year periods which is the same annualized method, but from the current date day instead of year end values as here. It may be just as useful, but that means the data of each year period also varies every day, to use that same day 5 or 10 years ago.

Each year's data percentage must be the years final Total Return %, which assumes reinvested dividends. Morningstar.com shows ten years plus YTD of these annual Total Return % numbers. If the current partial YTD is included (an incomplete year as of yet), then of course that last YTD value will change as the year progresses and we do not know a correct number. But if omitting that incomplete final year, this method makes getting histories compounded gain numbers be easy. The data is shown in a table as interpreted in case you tried editing the data and messed up somehow, it may help see the trouble. If any data trouble editing the Morningstar data, just start over with the simple Copy and Paste. That works.

Computing Annualized Return for an incomplete current year is Not done, because it is Not proper. It cannot be the correct current year result, because we do not know the future. But Annualized for earlier years is shown.

The Average gain is also shown, only to make the point that the average is not useful for gains that vary. Instead, the Annualized Return computes the years and compounding correctly. Average gain is the sum of all years, divided by the years. Total Return is the product of all years of (1 + (overall gain)/100 - 1), then that total product to the exponent of 1/years (1/years to reverse compute the Annualized fixed interest that would create the same gain, and then - 1 leaves the gain only). Compounding means a years 15% gain is multiplied as 1.15, to include the overall value as yet accumulated in previous years. The Total Return % number is less than Average %, but its compounding effect makes it much stronger, and corresponds to the actual gains. Compounding really "compounds" as the number of years increase.

Extra Calculator 3 Details: The Copy and Paste from Morningstar uses tabs for year separators (between each year value). And that tab works fine here, you can leave it just as copied, and directly Paste it. Actually, this tab thing should also work from any web screen HTML table showing years of Total Return percentage.

The concern was that if you edit the data, the calculator cannot type a tab into the browser's field. Tab means "next field" to the browser. So the calculator instead uses a space character between numbers to separate them, and shows it that way. The calculator will replace any tabs (from Morningstar Copy/Paste) with a space. So the calculator doesn't care which is present, either space or tab (but the separator used must be one of them). You will see the space in the displayed data, but the tab still works too (but you cannot type a tab, and any tab imported will become a space). Again, a Copy of the Morningstar data will have tabs in it, which works as is, but which will then become a space. Multiple embedded spaces in the data are OK, they will be combined into a single space. Simply Copy/Paste the Morningstar Total Return % data line, and it will work.

Calculate the Fixed Interest Rate
and actual Rule Number that will
compound into x value

An Enter key in either of these
two fields recomputes this table

Extend range to years

Rule of 72 Expanded with Calculator

Off-topic a little, but if checking that these numbers are reasonable, a simple rule of thumb check is the Rule of 72 that says an investment value about doubles if the years × fixed percentage gain = 72. So 6 years × 12% = 72 would approximately double to be 2x value (1.126 = 1.9738, almost 2x, and easy today). Or the precise rate that exactly doubles in 6 years is (21/6 - 1) × 100 = 12.2446%, which is the Annualized formula, and that first 2 is (1 + 1) to be value 1 doubled.

The Rule of 72 is an approximation dating back to at least the first known mention in Summa de arithmetica by Pacioli in year 1494 (in the time of Columbus, long before calculators, or even logarithms), when the calculating was pretty difficult. Actually, 6 years should be Rule 73.4772 for 12.24620483% doubling in 6 years (1.12246204836 = 2). The 12.24620483% Annualized Return is an impressive rate of gain when compounded over many long term years. The Rule of 72 is compounded annually.

This calculator purpose was to look at the accuracy of doubling with the Rule of 72, however you can also enter different multipliers here (other than 2 for double, like 1.5x or 3x or 10x, with corresponding approximate rules of 41, 116, or 259).

In exploring the Rule of 72 (in this table), it became clear it is only a simple rough approximation. Speaking only of doubling, the worst accuracy with 72 is if 5 or less years. The most accurate case for Rule 72 doubling is for 8 to 10 years. But a Rule of 70 works better for doubling long term 20 or more years.

So I suggest that in specific situations, the first Gain calculator above will be more useful and versatile and certainly more precise than the Rule of 72. In that 1st calculator above, New = 2, Old = 1 over 6 years is 2.0x Value, 100% gain at 12.24620483% Annualized Return, but the Rule is 73.48. The calculated percentage rate numbers are about the gain ratio, independent of the actual amount of money.

How to Earn a Million Dollars for Retirement

Retirement is an income issue of course, since salary typically stops then, but we may live longer, possibly even 30 years more. So we need a plan for income then, which needs planning many years early.

Based on past S&P 500 performance history, earning a million dollars has been relatively easy, if given the sufficient span of years to let it grow. The bottom line is about Long Term. See the 2nd Future Value calculator above.

Maybe a million does take either a lot of years or a lot of investment, but the years are automatically doable if starting early enough (meaning if you will just do it now). One million dollars is roughly 40 years in the S&P 500 from $10K, or 30 years from $35K, or 25 years from $60K, or 20 years from $100K. The long range of years is a magic opportunity. The S&P 500 calculator on previous calculator page can also show that only $10,000 invested in 1980 for 40 years (which sounds like an extremely long time, but it is like age 25 to 65) and left untouched until today would have been worth about $1 Million now. That result assumes 12.2% Annualized Return which has been a valid S&P 500 average (NOT meaning an average annual gain, but instead an average Annualized annual gain), with dividends reinvested and compounded for 40 years, despite including the few very bad market years (the 2000s decade did not help, but it still got there). And much of it remains to continue growing 20 or 30 years after retirement too. Results of starting in any year, and/or with any other starting value, is shown in the Survival Test Mode chart on the previous S&P 500 calculator page. The $10,000 doesn't earn so much initially in the beginning, but after it's grown to more digits in the last several years, the growth seems amazing. And that growth keeps earning more too, which is the concept of compounding.

Here is Kiplinger's ideas to make a million.

12.25% Annualized Return for 40 years is 1.122540 = 101.73x gain from $10K is $1,017,311.58 result. Or say it was less gain, call it 8% Annualized. Then an initial $50K would be needed to make it to $1,000,000. And of course, you can start with less, and continue adding more as you go along. It is very doable if you do it. Calculator 2 will compute these cases. Or the S&P 500 calculator will show results of starting in any past year with any amount, and adding to it each year in any amount, to show the result today according to the past performance.

Compounding is easy, all you have to do is start early and then just wait long term. And think what adding even more investment to that now and then could have done. Starting or adding when the market is down (certainly including today, 2022) is a really good time (to buy low for maximum growth opportunity). A drop in the market is Not the end of the world, and recovery provides opportunity for much additional gain. The young probably think other things are more important now, but I promise that your priorities will change near retirement time, after it is too late (trying to get your attention if you need it). That growth will become quite important at retirement time, and the best tool is an early start. It also continues earning and compounding after retirement, during 20 or 30 years of retirement withdrawals. If looking for magic, this comes pretty close, and seems a mighty big deal.

$10,000 might have seemed impossible for me at age 25, but starting with $1200, and adding $1200 a year ($100/month) to it for 40 years all along (without fail, adding $51.6K overall) also creates $1 Million. Think of it as supporting yourself in your old age.
Or one approach is you can create a self-directed IRA that invests in a S&P 500 fund. A S&P 500 Roth or IRA that adds the $6000 maximum every year could reach $1 Million in just 25 years (example 5 on previous calculator page). A 401K plan has a much higher maximum contribution, and a possible company addition. And of course, if possible, a Roth instead of IRA or 401K would eliminate the taxes on the million, which would be a real big deal then.

Age 65 will come for all of us, when salary stops and we will need replacement income, which will become extremely important then. It is too late then, but planning makes that possible if you start early. Then thereafter, 4% withdrawals from $1,000,000 is $40,000 a year to add to Social Security. The fund would continue making its gains then, but if $1 Million, then withdrawing $40K a year would last 25 years even if zero additional gain. However taxes will be due on it, making any large lump sum withdrawal seem unwise. But spread out into smaller withdrawals over more years, taxes on high income will be the best problem you could have.

The easy and best solution is simply to start a good investment early, without fail, as early as possible, today. The 4% Rule was concerned with market bad times surviving 30 years of retirement withdrawals, after building substantial value with years of investment without withdrawals. From my own experience, my notion is that it takes many young people many years to realize that the many years of opportunity available to them would have been their very best and easiest and greatest tool BY FAR, but then there is no going back for a redo. Wasting that most valuable opportunity would be a tragic shame.

Again, these results are computed from the past years in history, and future results are not known. The standard obligatory investing advice is that past success does not guarantee future performance. There have been bad times (including today, 2022), but it always has recovered. Past success of long term investing in the S&P 500 seems clear enough (the 500 largest and most successful companies in the USA).

Compounding is certainly a real big deal in investments, making many long term years be the most profitable part. Only a year or two is not so dramatic, but compounding is exponential with time, becoming huge over many years. Long term can be exceptionably good. The S&P 500 (gain and reinvested dividends) has averaged an annual return around 12% for the last 50 years. The future is not known, but it sure seems a good bet if you consider "long term"). It is true that the S&P 500 is down now. Two facts though, this or worse has happened several times over the years before, and it always recovers and continues. The S&P 500 was down 25% at $3585.62 on Oct 3 2022, but 40 years ago it started with only about $122, which is an increase of about 30x so far, not even counting the dividends.

Plug in your own numbers, but if your age is 40 years or less, then you still have at least 25 years before retirement at 65 (when you will certainly be needing a source of income). Today is the latest time to be considering that. And the investment can continue earning during 30 years of retirement withdrawals too. The years will be your largest growth multiplier, so wake up, and get with it, now (the term Buy Low means, the market is currently very low to making buying right now be the very best and most profitable time, very wise). I've just shown how $10K now can grow to $1 million in 40 years, so don't foolishly waste the years. (25 years will need about $60K.) The market always recovers, but lost years cannot be recovered.

Market Bad Times

The market goes up and down a little every day. It can make you crazy to watch it every day. But don't sweat the small stuff, it will be different tomorrow. Do understand that it is very normal to go up and down every day. Another page shows four years of this daily S&P 500 activity highlighting the peaks and valleys.

There are some bad times, and some people are scared off and will cash in and get out of the bad market, but that simply locks in their losses and makes it permanent, not recovered. Others grit their teeth and bear it, and hang on and wait for the correction, and then continue on recovering and happily earning more money. I recommend this latter course. It happens now and then, and waiting it out is no fun, but it pays off. The alternative is accepting the loss as real. But the world continues on, it does not end, and the market always recovers.

What to do when the market goes down.

A Brief History of U.S. Bear Markets provides a very clear and informative view and details of our bear market history, that you ought to see (the chart titled Bear Markets and Recoveries). That one does not show the good times, but for that, also see its second green graph just below it (click it to enlarge it slightly). Certainly you should realize that crashes do happen now and then, but also, that they do recover. A Bear Market is defined by at least a 20% decline, which can seem mighty uncomfortable at the time. The worst ones have hit -50%. Many investors panic and sell and end their fund then, which just makes their loss permanent and very real. But instead hang in there, and it will eventually recover into happy times again with continued gains. Most years are good, and the long term gains are hard to ignore. Politics and taxes do need watching, and bad times do happen every once in a while, but then recovery also happens too.

The market is usually good, with many more good years than not, and long term does win. But starting the calculator data at 1970 was deliberately chosen here to include actual real data for some seriously bad times. The crashes of 1974 and 1982 and 2001 and 2008 were exceptionally bad economic and market times.

In contrast, the 2020 pandemic crash, -34% was tough on the economy and market, but its cause was not economic or political, and the market recovered in 5 months to another all time record high. And 2021 ended up 28.9%. There were other smaller dips, but the 1970s were poor and the 2000s were worse (two crashes), all near 50%. The recovery from 2008 took the longest in modern history (until 2012), and the entire 2000s decade was down 9.4% (a "lost decade"). So 2000 was the worst year to start the fund in the last 50 years of history. The price of the actual S&P 500 was under 1000 in 1997, again in 2002, and again in 2008, but even so, reached 4700 in 2021. That is just the index price (less dividends), but the compounded gains have been exponential in the many years of gains. Investing for long term is the way to bet.

2022 was bad too. The last record high was 4796.59 on 3 January 2022, then the S&P 500 low on October 12 was -25.4% at 3577.03. 2023 is showing better signs, but it's still a way to go to recovery.

The current version of this Google chart is here.

The 2001 and 2008 dips had bottoms at -50%, and made the entire 2000-2009 decade lose 9.4%. It was bad, but fully recovered in 2013. The 2020 pandemic dip was deep (-34%) but relatively short duration. The current inflation (2022 is still the highest in 40+ years). See a current status of Total Returns of 90+ stocks (including largest 50 in the S&P 500).

Corrections: Market drops of more than 10% are called Corrections. These are fairly routine, and happen more often then you might think, but they typically don't last long before the correction recovers. Again, we learn to take it in stride, and in fact, the low times are often welcomed as great times to buy more at the lower price. That is the meaning of "Buy low, sell high".

Bear Markets: Drops of more than 20% are called Bear Markets, occurring less often but much more severe. These might reach 50% down in truly bad economic times, but they have always finally recovered (could take a year or two then, or even more). The worst action would be to cash in by selling during the low times, which simply locks in your loss permanently with no opportunity for recovery. Buying more then is the better choice, the recovery will be profitable, but timing the exact bottom of the market is impossible (the bottom likely will not be in the first few weeks though).

One accounting of this says "Most declines are quickly erased but the deeper the stock market decline, the longer the recovery." They make this report about history (I am unsure how precise the numbers could be in the future):

And the few worst past ones have reached 50% down. But it happens, and then it recovers, always has. The 2020 pandemic dropped the market 34% in March, quite bad but short. It recovered quickly 100% by August, and the year ended up at a new record high with 18% annual gain despite the lost months. In the following March the S&P had achieved a 76% gain (a year after the low). Recovery of bad economic situations can take a couple of years though, until the economy is corrected. 1974, 2001 and 2008 crashes were spectacularly bad, and each took a few years to recover. But they do recover.

Most companies were down and negative for the year 2022. The leading growth stocks (Apple, Microsoft, Amazon, Google, Nvidia. Tesla, etc) were down big time, -25 to -45%. It's just market fears due to all the current problems. There is nothing wrong with the companies, their earnings were doing great. The Russian invasion of Ukraine is of course a big worry, but the painful self-inflicted inflation is another of the current big concerns about the US economy. The government's massive spending of Trillions is a large factor, and their own self-imposed policies last year put limits on our own U.S. oil production, which has had very strong effect increasing inflation. The U.S. oil production was self-sufficient before, but now we must import oil again, and pay the price. Oil affects the price of about everything (transportation, plastics, etc), and the doubled oil price has increased U.S. inflation, which is up from 1.2% in 2020 to 6.5% in Dec 2022 (still the worst inflation in 41 years). But the cavalry will come and the market has always recovered. And 2023 already looks more promising for the growth stocks, but there is still a way to go.

Recessions: The definition of a recession is about the decline of national GDP growth and the rise of unemployment. Recessions are NOT about the stock market. Some imagine a recession is just when there is two consecutive declining GDP quarters, and we do have that now, but a recession is also additionally about unemployment statistics, which are still rather low now, so there has been no recession called. Technically, the National Bureau of Economic Research (NBER) decides if and when it is actually a recession. The unemployment rate is still quite low right now, so it is not yet a recession. It's bad though anyway.

Predictions about the market future are only guesses, and at any given time, many "expert" guesses heard will always be rosy and bright, and many others are always gloom and doom. It doesn't take long to understand that no one actually knows the future. I am certainly no expert, and I don't know either, but it is easy to see that the long term S&P 500 graph (meaning a few decades) sure always looks great, but with some dips. The market goes up and down every day of course, with many more good years than bad years (but yes, expect a few bad years as a matter of course). Withdrawing everything when it is down in bad years is the worst plan, which simply guarantees the loss is real and permanent, with no recovery possible. It is scary, and it takes some patience, but it will recover if no withdrawals. Market crashes do happen every few years, and they are survivable. The S&P 500 does recover.

But there is no one safe magic percentage withdrawal such as 4%. Because how long a fund can survive retirement withdrawals in bad times actually depends on how much money it makes available. This 4% number does assume it is recalculated every year (same 4% percentage, which calculates different withdrawal dollars each year, depending on the different current investment total).

We don't know those things about the future, but we can see such instances in the past, to suspect what we might expect sometime in the future. We can see that it has always recovered. If the fund value drops 50%, then from there, it must recover 100% to reach the same original value again. Our own withdrawals also during the low times are dangerous to the survival of our fund. Even innocent looking fixed amount withdrawals can become drastic in bad times (see the $200/month fixed withdrawal in the 50 year S&P 500 calculator which fails soon, but a 10% withdrawal finishes 50 years, without growth, but no failure). The advantage of a percentage withdrawal is that (if the withdrawal rate is then adjusted every year to the same percentage of the funds then current value), the withdrawal becomes very low when the fund value is low. Except actual withdrawals are usually set up as fixed dollar amounts every month. But a percentage withdrawal definitely implies the withdrawal is recomputed every year from current fund value, which becomes less withdrawal when the fund value is lower.

Withdrawals of course depend on money still remaining available in the fund. If no withdrawals, the fund will survive and continue growing, but withdrawals will drop the fund value fast, especially when low in bad times. The S&P calculator program cannot predict future gains, but its purpose is to see the result of some typical actual bad times from recent history, and also to see the results of withdrawals, to help know the best future plan.

Again, this is definitely NOT speaking of bad investments recovering, but is instead speaking of good investments in bad times.

25 years ago, the original 4% Rule data looked at the market back to include the Great Crash of 1929, but times and laws and market rules have since changed so much, and IMO the last 50 years seem typical enough of today's world. The calculator Test on the previous page is ONLY about actual S&P 500 Index history. It has no historical data for any other funds except S&P 500 Index funds (which are a very popular class). All of those will show the same S&P result, except they do vary in the fee they charge (the fund fee is withdrawn every year, and a fund with a low fee is a big plus).

How much withdrawal can survive bad crashes is a vague question though. Situations vary. A market crash just when you need the withdrawals is the fear. Another danger is an early crash before the fund has grown to be able to survive it. Do realize if a fund loses 50%, the low price then has to regain 100% to recover.

The market goes up and down every day, but fund survival depends on how much value is in the fund, and specifically, how much value is also being withdrawn from the fund.

The commonly seen market advice about risk is "Past success does not guarantee future performance." Meaning, we don't know the future, and unexpected bad times do happen. But IMO, that is speaking of short term events (up to a few years). I get my encouragement by looking at a graph of the S&P 500 history. Market gains certainly offset inflation, however do unclick the Inflation-Adjusted box there to show the actual S&P data. The world might someday end, but the graph long term trend does look very promising. 😊  The notches in the rising curve are the bad times, and there's been many of them, but they get forgotten as the curve goes up. It does show that the 1970s and the 2000s decades were serious bad times (a mouse-over there shows the dates). The bad times will seem drastically bad at the time, but they always recover (might take a year or two, but retirement is a long term goal, right?)

The actual risk is that if the fund is saving for a specific time, like for retirement or a child's college expense, the market might be down. That's not comfortable, and a 100% recovery might not still be fully available at the time needed. But college is a four year duration, not all needed at once on the first day, so it has more time after it starts. And retirement is possibly a 30 year duration, and growth continues all during that time. We don't know about the future, but the calculator can show the effects of some past bad time drops.

Fund values seriously suffer from any withdrawal, both by reducing the remaining balance, which also limits the future gains. IRA RMD (Required Minimum Distribution) is required after age 72, but otherwise withdrawals are a choice, but if the withdrawn money had remained invested, that money would have earned more money itself, repeated every year, compounded. It is certainly wise to cut back on withdrawals in really bad times, to avoid depleting the fund. And it is always best to reinvest the dividends, and you can see the tremendous difference that makes here (of compounded growth in time). Bad times are the worst possible time to sell out and close the fund since that absolutely locks in and guarantees maximum loss, with no recovery possible. The market will drop in value now and then, maybe to around 50% in the very worst times, which will seem catastrophic and unbearable at the time. But if you can hang in there, it will recover and will then be forgotten (eventually, which could be fast, or could take one or more years). It no withdrawals, the S&P 500 has always recovered to hit new highs, and will resume and continue earning more. Currently, the last ten years have had good results, but the market behavior before 2010 might be considered expected now and then, however it always recovers.

Also see these pages:
Previous page with the S&P calculator.

Next page: Withdrawing dividends is a poor investment plan.

Copyright © 2021-2023 by Wayne Fulton - All rights are reserved.

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