S&P 500 Index Mutual Funds and 4% Rule

The S&P 500 calculator is on the previous page, and it includes withdrawal capability. My interest in the calculator was about how appropriate is the 4% Rule for a 100% stock fund like the S&P 500? This page is general introductory info describing the 4% Rule, the S&P 500, the general market, bonds, Bear markets, taxes, etc. This is some market stuff that you should know.

A large page, but a Menu of items below:

The 4% Rule

S&P 500 Index funds

A few important things to know about bond investments

Computing Compounded gains and Annualized results, and calculators

How to make a Million dollars for retirement

Bad times in the market

U.S. Tax Summary

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

The 4% Rule concept:  This idea was originally about balanced funds, meaning stocks balanced with bonds, perhaps containing 60% stocks and 40% bonds. The idea was that adding bonds can shield some portion from market volatility, and at least in the past, could also provide some earnings when the market is down. My own notion is that a 50-50 balanced fund might indeed drop half as much during a market crash, but it also only earns half as much 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 as lasting through 30 years of withdrawals in retirement from any starting date. Any X% withdrawal rate might seem safe if the fund average earning gain was X% to support it, but years vary in gains, and the average is not linear. The bonds in balanced funds used to pay more to aid that, but times change, and bonds pay very little now. 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 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. The 4% Rule was from a 1994 investigation of historical market data that tested for a reliable safe withdrawal amount 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 another 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 is at Morningstar.

A S&P 500 Index fund is widely considered to be one of the best market investment choices for most people (those who are not market professionals following the market closely every minute). Here is one link about that. An Index fund keeps its holdings exactly matched with the index it is tracking to match the same performance. The S&P 500 is the collection of the 500 largest US publicly-held companies, (all are 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 US market capitalization. Capitalization is a companies total dollar market equity value, equal to the companies total stock shares x price per share. The S&P 500 index is weighted by capitalization, so that the largest companies count proportionally more in the index, according to their greater overall value.

Similarly, the Total Stock Market Index Fund (Vanguard VTSAX) has 4000+ companies (blend of large-cap, mid-cap, and small-cap U.S. companies), and like S&P 500, it is similarly weighted by capitalization, which boils down to be that the S&P 500 are still the top 500, and the smaller ones are weighted much less strongly. So in effect, it has similar performance as the S&P 500 (usually within a percent or two less than the S&P 500 index in individual years).
There also are various S&P Equally Weighted funds, either all of the 500 or just of specific industries, for example ticker RSP.

All of 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. There are actually 505 listed tickers in the S&P 500, because five companies have two major classes of public common stock included (Google, Discovery, Comcast, News Corp, 21st Century Fox). Google's company name is actually Alphabet, with two public stock classes A and C, with two tickers GOOGL and GOOG, which are added together in the table here.

S&P 500 Weighting
Top 10 as of 23 June 2022
Alphabet (Google)GOOG4.05%
Class A & CGOOGL
Berkshire Class BBRK.B1.51%
United HealthUNH1.47%
Meta (Facebook)FB1.14%
S&P 500 Weightings as percentage of the S&P 500 Index are as shown. The weighting of the five largest companies comprise about 22% of the S&P 500 index. Whereas if equal weighting, each of the 500 companies would be 1/500 at 0.2% each, except the S&P is instead weighted by capitalization (total dollar value of stock). As weighted, the smallest companies in the S&P 500 list get down to about 0.01% weighting, but which are still among the 500 largest US companies. Weightings vary with current prices, and weightings are computed before each trading day. To be eligible for S&P 500 inclusion, each company must be publicly held and each is currently at least $13 Billion capitalization, but all are selected by a committee with additional performance concerns. 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).

See the current weighting of all of the S&P 500 companies. Near 80% of the S&P 500 companies pay dividends in some degree. See a list of those ranked by dividend.

See the largest company stocks NOT in the S&P 500, but in some cases, there are different classes of stock. For example, this list includes Berkshire Hathaway private class A as the largest entry not in the S&P 500, however Berkshire Hathaway public class B was added to S&P 500 in 2010.

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 automatically buying the matching shares of each company (passive investing, low fee cost). Whereas actively managed funds instead have a manager trying to pick the 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.

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 also probably in the S&P 500, contributing their share, which is diversification). However their downside is these currently hot stocks are more volatile, their prices can swing widely, which is great when it goes up, but is costly when it comes down. And it does seem that the faster they grow, the faster they fall. The current year 2022 is not a good year yet, with the biggest usual leaders way down (for an awakening, see current results). The market is good overall, but there certainly can be big surprises. If investing in individual stocks, you will need to watch closely, and know when and why to switch stocks (preferably before it changes, but that is very difficult, it happens before we know about it). The S&P 500 can be more comfortable long term without close watching.

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, emerging markets, foreign, 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 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.

Compounding gains: 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 40 years becomes a final value of 1.1040 = 45x the initial value and 4400% overall gain. The market gains vary each year (often large, but sometimes negative), see below for computing the overall gain. In addition to the price gains, another major factor is that reinvested S&P 500 dividends add very roughly about 2% to total returns each year, and then those additions see gains too, and those gains see more gains, compounding every following year. Even if a few random years are negative, compounded earnings are a Real Big Deal, so think of a long term investment always with reinvested dividends. Start young, and then 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 math of compounding is shown below.

The fund's average annual gain is Not the precise measure of short term withdrawal safety. Because the average is just the sum of all years gain divided by the number of years, accurate "on average" over all of the total years. But the long term compounding result is about the multiplication product of the specific years of gains. The multiplication effect depends on that specific years value too. Might not always be a large difference, but it is just different numbers. The average can hide a few adjacent down years during which withdrawals could deplete the fund. The S&P 500 will recover, but if all your funds money was depleted earlier, it ends there. The first early years are the higher risk, before it has earned much, since more money in the fund will of course always last longer in a crisis. So first building more money in the fund (before withdrawals) is the insurance to last longer when down, and to make recovery easier. Reason would suggest that first allowing maybe 20 or more 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, 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, because it's a percentage thing. 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 chart of a few years of S&P 500 record highs. But when and if it is down low, 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 are not limited to a reasonable current percentage, of which an example is shown in the Test section on previous calculator page. 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 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 huge 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 a tiny 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 calculator here to more clearly define the end of Survival due to depletion. Possibly this limit should be higher for a stronger recovery, and you can change it, because the fund does need some money left to be able to earn a faster recovery. 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.

Knowing the first facts about Bonds is especially important today

Investing in bonds is a very different game than investing in stock. I am far from encouraging bonds now, just offering some facts you need to know first. This is all true both of direct bond purchases, and of bond funds too. Bonds may have paid higher dividends in 1994 (for the 4% Rule study), helping to support withdrawals, but interest rate has bottomed out near zero today, so IMO, now bonds seem an outdated investment idea. However, bonds do 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 occurring this year. Also, inflation is a serious concern, at a 40 year high at 8.6% in May 2022.

Government bonds are different yet, sold at auction to bidders. U.S. Treasury bonds of 1 to 10 year maturity are called Notes, and those of 20 or 30 years are called Bonds (why I don't know, but "bonds" here refer to both). The Treasury bonds are safely backed by the the government, and both have face values and a fixed interest based on face value, but then buyers buy by bidding at treasure auctions on new treasury notes and bonds, so the final yields vary with the selling prices (basically what buyers will pay). 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 goes higher (the yield to maturity), and of course vice versa too. But until redeemed at maturity (at face value, for expected income then), 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. 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.

Definition of very important bond "Duration":   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 they still redeem face value at maturity. Bond resell value varies with current interest rates 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.

The term Duration has a very important special meaning. It 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 their "Duration" percent. Bonds can be volatile when interest rates change. If interest rate doubles (like 1% to 2%), existing bond values can drop to half (so that then buying two existing bonds effectively pays the higher interest income of one new bond). However since bonds are still redeemed at face value, short term bonds, and bonds nearing maturity date, will have low durations. Long term bonds likely have high duration (more volatile). 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 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 face value return then will be as expected.

But if in a bond fund, or if planning resell, there's much more to know about the volatility. Resell value of 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, and you get whatever the fund is paying that day (due to interest rates). That could be a plus if interest rates fall, or costly if interest rates rise. Right now, interest rates are near zero but the Fed is planning to fight inflation with multiple interest rate increases during 2022.

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. And also vice versa, lower interest rates will increase the value of existing bonds that still pay more. (See Duration next below).

Also 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), perhaps planning to issue new bonds paying lower interest rate (if rates are falling).

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

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 they continue paying face value interest rate. So if you buy bonds directly yourself, and hold until redeemed at maturity, the return will be as expected. However bond funds must buy and sell bonds continually, as investors buy and sell shares. And while those bonds are still held, 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 a special calculation called Duration.

Definition of bond "Duration":  Bond resell value varies with current interest rates. This concept is Very Important. 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. Interest rates dropped the couple of prior years, so existing bond resell values increased then, and bond funds showed better results. But vice versa, existing bonds lose resell value when interest rates increase (and now last one year return is negative, and interest rates are near zero now with only one direction they can move). The U.S. Federal Bank has announced expected plans for more interest rate increases in 2022 to fight inflation.

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 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.

FWIW, note that Junk bonds exist too (called high-yield bonds), from lesser companies with lower credit rating, paying more dividend to attract buyers, but with higher possible risk of default failure. For bond funds, Morningstar.com Portfolio tab shows bond ratings too. AAA is 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, and C rating is a highly speculative bet (speculative meaning offering greater dividends if paid, but with greater risk they could fail and default and stop, and not redeem at all).

The big point here is to not be confused by Morningstar's 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 also check their current YTD (Year To Date) 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 likely changes during the year. The Federal Reserve Bank interest rate was near zero at the start of 2022, so the only way it can go now is up, and it is increasing now with inflation (and increased interest rates means resell values of existing bonds then will go down). 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. 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 increases and increasing interest rates. Bond dividend income is taxed with regular income tax rates, but the price changes are capital gains or losses if held a year or more.

So IMO, it's difficult to think that Now is the time to buy bonds. With rising inflation and interest rates, that can only be bad. If bonds are a goal, I'd wait to buy for the future peak of high interest rates, because then instead of value continuing to drop, existing bond prices (i.e., in bond funds) will turn around and will increase as interest rate falls again (as in the text above). For that to happen will require reducing inflation first, but then as interest rates fall, the increasing bond value will outperform than the bond interest paid. Bonds can be volatile.

If considering stock dividends for income, see Stock Dividends are valuable, but withdrawing them is just a withdrawal, and Not new income. There are about 65 stocks referred to as Aristocrat Stocks, which to be included, 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. The annual increases can be small, and a good half of them still pay less than 2.5% dividends, and a few of those pay less than 1%. A favorite of Warren Buffet at Berkshire Hathaway is Coca Cola (COKE) paying 3% plus decent earnings. Whereas most of the best growth stocks pay no dividends, and also can have prices varying widely.

Inflation has historically averaged about 3%. Bonds earn less than that now, but the S&P 500 total returns (plus its dividends) has averaged 11.77% for the last 50 years (including the 13 negative years).

Since very low earnings today 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. 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.

Investing for Retirement

So if interest rate (of bonds in balanced funds) is near zero today, what about a "4% rule" for 100% in a S&P 500 Index fund? The calculator and Test on the first page is about that.

My strong 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. The time to realize this is when young with still many years of great opportunity.

Computing Compounded Gains with Time, and Annualized Return

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, and continuing so on growing every year. But market gain is variably different every year, so here's a math example with six years of gains. For it to be Total Return, don't forget to add any reinvested dividends and adjusted cost basis.

The same percentage numbers are computed for any initial value, $10 or $10,000,000. But calculations with rounded significant digit precision might be slightly affected.

The Manual Calculation Method of Annualized Return

Annualized return includes the long term compounding of several years, and is a hypothetical number computed to be AS IF the same final result instead resulted from a Fixed equal gain, same every year. This Annualized gain rate purpose is for comparisons (with banks and 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. But first, you need the overall percentage gain.

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

Method A:

From the computed table method, this overall six year gain is
  ((19995.35 - 10000) / 10000) × 100 = 99.9535% gain.

Or assuming no withdrawals yet, if you already know the final and the initial values, then the same gain formula, or see the Value Gain calculator below.

Method B:

Or these yearly gains will compute as
  (1.15 × 1.235 × 1.104 × 0.948 × 1.121 × 1.20 - 1) × 100 = 99.9535% gain.

See the Yearly Total Return Percentages calculator below.   Morningstar.com shows ten years of these annual Total Return numbers (including 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. The initial dollar value does not affect the gain percentage. And then, the final Total Result value is (1 + gain/100) × initial invested value. For an initial $10000, then 1 + 99.9535% is 1.999535 × $10000 = $19995.35 result.

Important Details: The ±1 in these equations represents the initial investment value. That 1 becomes 100% when multiplied by 100 for percentage, and the gain is computed from that initial value. The (final value / initial value) fraction is the gain ratio, like 2x doubles the value. If the gain percentage is 12%, then (1 + the gain ratio 0.12) is the 1.12 result of the gain (as done in the six yearly terms at B above, and with current dollar value of 1.12 × initial value, whatever it was). Subtracting the initial 1 from value leaves just the gain portion. The gain computes the same numbers regardless of whatever the value of initial dollars. The 99.9535% gain in this example is 1.999535x value, which is essentially 2x total value. So the final value would be 200%, but subtracting initial value, the gain was 200% - 100% = 100% (1 x 100% less than value, for any gain). The Value Gain calculator below tries to differentiate these.

These procedures would compare with the standard compounding formula of (1 + fixed interest rate/100)years if the gain were the same every year. But market years vary, not the same, some years might even be negative, making it hard to realize the actual final gain rate. So you could instead "Annualize it", to view it as Annualized gain, which computes a fixed interest rate to be AS IF the same interest rate every year, that would still give the same total result.

Each year's gain is an individual multiplier of the initial value. Each factor is (1 + gain/100), with 15% gain becoming the 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 x 100, which is 100% of the original initial value), to see the final total value result. So this is said twice about the ±1, and just saying, the amount of "gain" does not include the initial value, but the total value result does.

Note a price Total Result is not the same as Total Return, which includes reinvested dividends and resulting cost basis. However, if there were no withdrawals, the final value resulting from the investment value is a clear total answer including everything. So $50,000 growth from $25,000 invested is a 50000/25000 = 2x gain, pure and simple. If a fixed rate that took 10 years, it is (21/10 - 1) x 100 = 7.1773% Annualized Return. Meaning, (1 + 0.071773)10 = 2x value, would be the same result if it came from a bank fixed interest. It seems a useful way to compare varying market results.

To compute the annualized gain rate for the example in the above table is:

Next is some calculators for compounded gain and Annualized Return rate.

Compute Compounded Gain and Annualized Return

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

New value from Old over years

Any units (like feet or weight). Gain need Not be money.
Years can be blank if annualized return not needed.
Any $ or , format keys are optional, and ignored.

Compute Compounded Value at Annualized Gain

Initial value and Rate % over years

This is for curiosity, a future market rate is not predictable.
But 12% has been reasonable for S&P 500 long term.
Any $ or , format keys are optional, and ignored.

Compute Compounding of Yearly Total Return Percentages
and Annualized return



This final year is the partial Year-To-Date % gain until
    days before today (back to date of prior YTD report)

Leave unused years blank. Order of the Years does not matter.

Results in 2nd calculator

Test of twice the investment for half the years
g1 is with the default initial investment for the years.
g2 is with twice the investment for half the years.
The numbers are dollars, of the method difference,
and the larger result, and that investment.

1: g1-g2 = -9964 to 21194 from 20K for 0.5 years
2: g1-g2 = -9849 to 22460 from 20K for 1 years
3: g1-g2 = -9639 to 23801 from 20K for 1.5 years
4: g1-g2 = -9318 to 25223 from 20K for 2 years
5: g1-g2 = -8868 to 26729 from 20K for 2.5 years
6: g1-g2 = -8267 to 28325 from 20K for 3 years
7: g1-g2 = -7492 to 30016 from 20K for 3.5 years
8: g1-g2 = -6514 to 31809 from 20K for 4 years
9: g1-g2 = -5302 to 33708 from 20K for 4.5 years
10: g1-g2 = -3821 to 35721 from 20K for 5 years
11: g1-g2 = -2030 to 37855 from 20K for 5.5 years
12: g1-g2 = 115 to 40231 from 10K for 12 years
13: g1-g2 = 2668 to 45179 from 10K for 13 years
14: g1-g2 = 5687 to 50736 from 10K for 14 years
15: g1-g2 = 9237 to 56977 from 10K for 15 years
16: g1-g2 = 13394 to 63985 from 10K for 16 years
17: g1-g2 = 18243 to 71855 from 10K for 17 years
18: g1-g2 = 23880 to 80693 from 10K for 18 years
19: g1-g2 = 30412 to 90618 from 10K for 19 years
20: g1-g2 = 37963 to 101764 from 10K for 20 years
21: g1-g2 = 46670 to 114281 from 10K for 21 years
22: g1-g2 = 56689 to 128338 from 10K for 22 years
23: g1-g2 = 68196 to 144123 from 10K for 23 years
24: g1-g2 = 81389 to 161851 from 10K for 24 years
25: g1-g2 = 96492 to 181758 from 10K for 25 years
26: g1-g2 = 113756 to 204114 from 10K for 26 years
27: g1-g2 = 133467 to 229220 from 10K for 27 years
28: g1-g2 = 155943 to 257415 from 10K for 28 years
29: g1-g2 = 181545 to 289077 from 10K for 29 years
30: g1-g2 = 210680 to 324633 from 10K for 30 years
31: g1-g2 = 243805 to 364563 from 10K for 31 years
32: g1-g2 = 281435 to 409404 from 10K for 32 years
33: g1-g2 = 324149 to 459761 from 10K for 33 years
34: g1-g2 = 372602 to 516311 from 10K for 34 years
35: g1-g2 = 427526 to 579818 from 10K for 35 years
36: g1-g2 = 489749 to 651135 from 10K for 36 years
37: g1-g2 = 560202 to 731225 from 10K for 37 years
38: g1-g2 = 639929 to 821166 from 10K for 38 years
39: g1-g2 = 730110 to 922169 from 10K for 39 years
40: g1-g2 = 832067 to 1035596 from 10K for 40 years

1st calculator: Hopefully both self-explanatory and most useful.

2nd calculator: Perhaps not so useful, but maybe it can estimate expectations. The market gain is not the same every year, so this computes the default 12.3% annualized gain. My goal was just being curious about compounding, and it does show the effect of long term compounding. I used the calculator for this one test (using the initial defaults in the middle calculator, but rounding off cents to save page space). It uses arbitrary limits that showed that if 12 years or more, twice the years is more valuable than twice the starting investment. Using 4x investment in 1/4 the years raises the 12 years to about 15 before the years win. That is maybe obvious, since compounding works with years which keep continuing, while investing works with dollars, investment fixed here at double. After maybe 18 or 20 years, the years count significantly more than would doubling the investment. Of course, doing both things would be clearly more, and definitely better. The point and practicality of more gain is that retirement withdrawals of 4% of $100,000 is $4,000 a year, but 4% of $1,000,000 is $40,000 a year, so more is good. And which is possible if you start early. Sadly, those that most need to wake up are not likely reading here.

3rd calculator: Yearly Total Return Percentage — To be descriptive, the six initial defaults are the same six years of example numbers in the "manual calculation" table above. For the complete return, each real data percentage should be the years Total Return, which includes reinvested dividends and adjusted cost basis. Morningstar.com shows ten years of these annual Total Return numbers (which for stocks are at their Price vs Fair Value tab, and for funds are at their Performance tab). Then this method makes getting the compounded gain numbers be easy. If including the current partial year, don't compute it as a full year. The Annualized rate is distorted by incorrect duration. The calculator can define the correct annualized partial year duration so far this year.

Compounding is certainly a real big deal, making many long term years be the most profitable part of investments. Only a couple of years is not so dramatic, but compounding is exponential with time, becoming huge over the 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"). For example, the S&P 500 is down about 20% today (1 July 2022). Two facts though, this has happened several times over the years before, and it always recovers and continues. We can fix the current problems. And even if S&P 500 is down 20% at $3825 currently, 40 years ago it was only about $125, which is an increase of about 30x so far, not even counting the dividends with which 40 years compounding could double the gains.

The number of years as an exponent is a really huge investment factor. Long term compounding is the largest effect of investment. And the reinvested dividends really adds to that too. All of the earning keep earning more again, every year. Suppose for 40 years the S&P 500 returned an annualized price gain of 10%, and a dividend of 2% (and it has done that), then:
  1.1040 = 45x value (withdrawing dividends has a high cost)
  1.1240 = 93x value (reinvested dividend doubles the 40 year result)

Hoping this is realized, here is a chart of that repeated from the previous S&P 500 calculator page:

S&P 500No withdrawalsWithdrawing all dividends
YearsFund Value
Fund Value
after WD
End Value
incl WD
CostLoss of

Long term, reinvesting dividends is a very major part of S&P earnings.
The cost of Withdrawals is the money "that could have been" minus the money actually remaining available.
Long term, dividends have the exact same result as any fund addition or withdrawal. Reinvesting them adds shares, withdrawing them does not.

If some other example were simple fixed interest at 12% every year, each year is 12% gain, but the 30 year value would be 1.1230 = 29.96 x initial value, or 2896% gain, which is ((1 + 28.96)1/30 - 1) × 100 = 12% annualized gain (same 12% this time of course, because this was the fixed interest rate). The annualized rate can allow more insight into variable years of market results.

In history, most by far of the S&P 500 years are positive gain, but market years vary, and the future is always unknown. However the preceding 50 years of the S&P 500 have actually averaged about 12% simple average return (speaking of individual years Total Return, but which includes reinvested dividends). Your retirement might be a long time away, but the wise are already planning for it today, because a longer time is by far the best investing tool (assuming a good investment worth keeping). You run out of options if you wait. The loss of wasting that most valuable opportunity would be a real shame. Lost time is not recoverable.

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

Extend year range to years

An Enter key in an above field will
recompute the table

Rule of 72: Looking at the reasonableness of these numbers, a simple rule of thumb check is said that the Rule of 72 says that an investment value approximately doubles if the years × fixed percentage gain = 72. So 12% × 6 years = 72 would double to be approximately 2x value (1.126 = 1.9738, almost 2x, but it technically would be Rule 73.477 for doubling in 6 years). And the example 99.9535% gain is certainly very near double, so that matches too. The 12.24185% annualized is an impressive rate of gain when compounded, especially over many long term years.

The initial default case for this Rule table was to look at doubling with the Rule of 72, but you can enter different multipliers (other than 2, like 2.5 or 3 or 10). The "Rule" can also be determined by the first compounding calculator just above (by specifying two values that will double, like 2 and 1, or two values that will triple, like 3 and 1). Then multiply corresponding interest rate and years to get its "Rule" number.

But in exploring the Rule of 72 (see this table), it became clear it is Not very precise, but is only a simple rough approximation. Speaking only of doubling, the worst accuracy with 72 is if less than 6 years. The best case for Rule 72 doubling is from 8 to 10 years. But a Rule of 70 works better for doubling long term 20 to 50 years, but that long to double would not seem a great investment, but you could specify 10x or 20x growth.

So I suggest the Compounded Gain calculator (above) will likely be more useful and versatile and certainly more precise than the Rule of 72. If you want to compute the Annualized Rule to compute double value (which is a value gain of 2x), then ( (2)1/years - 1) * 100 = the annualized percent of gain to do that. If looking at tripling (to 3x value gain), change that 2 to 3, etc. Seems simple, and that is the Annualized formula above, and it is what is used in this current Rule Number table.

How to make a Million dollars for retirement

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. See the middle of the three calculators below.

The long range of years is a great opportunity. The calculator on previous calculator page can show that only $10,000 invested in 1980 for 40 years (which sounds like an extremely long time, but it could be age 25 to 65) and untouched until today would have been worth about $1 Million now. That's about 12.2% gain annually, with dividends reinvested and compounded for 40 years, despite including a few very bad market years (the 2000s decade did not help, but it still got there). And it continues growing after retirement too. Starting in any year, and/or with any other starting value, can be shown in the Survival Test Mode chart with calculator on previous 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, which is the concept of compounding.

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. Adding when the market is down is a good time. The young surely think other things are more important then, 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 important and best tool is an early start. It also continues earning and compounding after retirement, during the maybe 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.
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 save the taxes on the million.

Age 65 will come for all of us, when salary stops and we will need replacement income, which will become extremely important then. Planning makes that possible if you start early. Then thereafter, 4% withdrawals from $1,000,000 is $40,000 a year to help live on 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 (but taxes will be due on IRA or 401K).

The easy and best solution is simply to start a good investment early, without fail, as early as possible. 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 is a tragic shame.

Again, these results are computed from the past years in history, and future results are not known. Past success does not guarantee future performance.

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.

some people are scared off by the bad times, and will cash in and get out of the bad market, which simply locks in their losses and makes it permanent, not recovered. Others grit their teeth and bear it, 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 world continues on, it does not end.

Corrections: Market drops of more then 10% (from some past recent price) 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 very much 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). The worst choice would be to cash in by selling during the low times, which simply locks in your loss with no opportunity for recovery. Buying more then is the better choice, 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 (I am unsure how precise the numbers could be in the future):

And the few worst past ones have reached 50% down. But 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 year or two 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.

Currently, the S&P 500 was down about 23% on June 16, 2022 (from year end). Most companies are down and negative for the year, but the leading growth stocks (Apple, Microsoft, Amazon, Google, Nvidia. Tesla, etc) are 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 are doing great. The Russian invasion of Ukraine is of course a big worry, but the painful 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 limits our own U.S. oil production, which has had strong effect increasing inflation. The U.S. oil production was self-sufficient before, but now we must import oil again. Oil affects the price of everything (transportation, plastics, etc), and the doubled oil price has increased U.S. inflation, up from 1.4% in 2020 to 8.6% in May 2022 (2022 is by far the worst in 41 years). But the market has always recovered.

Recessions: The definition of a recession is more vague, and it is related more to decline of national GDP growth (two consecutive declining quarters) and unemployment statistics instead of the stock market. It's bad though, and recessions certainly have a major impact on the market.

A Brief History of U.S. Bear Markets provides a very clear and informative view and details of our bear market history. That one does not show the good times, but for that, also see the second green graph just below it (click it to enlarge it a bit). 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 wins. 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 quickly to current all time record highs. And there were other smaller dips, but the 1970s were poor (one crash to 50%) and the 2000s were worse (two crashes to 50%). The recovery from 2008 took the longest in modern history (until 2012), and the entire 2000s decade was down 9.4% (called the "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, has reached $4700 in 2021. That is just the price, but the compounded gains have been exponential in the many years of gains. Investing for long term is the way to bet.

This graph (1 July 2022) is Google.

The 2001 and 2008 dips made the entire 2000 decade lose 9.4%. It recovered in 2013. The 2020 pandemic dip was deep (-34%) but short. Currently the S&P 500 reached -23% from year end on 16 June 2022.

The S&P calculator on previous page shows these annual chart values too, but it shows year end values instead of the actual dips.

Predictions about the market future are largely 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 figure out 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, with many more good years than bad years (but yes, expect a few bad years as a matter of course). Withdrawing everything is the worst plan in the bad years, that simply guarantees the loss is real and permanent. It will recover if no withdrawals. But there is no one safe magic percentage withdrawal such as 4%. Because how long a fund can survive withdrawals in bad times depends on:

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. The one advantage of a percentage withdrawal is that (if the withdrawal rate is then adjusted), the withdrawal becomes very low when the fund value is low. Except actual withdrawals are set up as fixed dollar amounts every month. So a percentage withdrawal 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. This 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. This calculator Test 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, a 100% recovery might not 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. And retirement is possibly a 30 year duration, and growth continues all during that time. We don't know about the future, but the program 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.

USA Income Tax Summary

Investment tax is a pretty serious consideration. When cashing in (selling or withdrawing), taxes on gains are expected. U.S. IRS tax law extracts a penalty unless income tax is prepaid before the April 15th due date, with at least 90% of tax due, or 100% of last years tax amount. IRS RMD withdrawals can specify a withholding amount, or Estimated Tax returns can be paid quarterly.

There are different classes of market investments. This info this tries to cover the basics about tax expectations (but tax laws can change)

Also see these pages:
Previous page with the S&P calculator.
Next page, Stock Dividends are valuable, but withdrawing them is Not income.

Copyright © 2021-2022 by Wayne Fulton - All rights are reserved.

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