www.scantips.com

A Calculator for S&P 500 Index Funds
concerned with 4% Rule retirement withdrawal safety

The 4% Rule was about balanced funds (mixed with perhaps 50% bonds), so interest in the suitability of a 4% Rule for withdrawals from a 100% S&P 500 fund convinced me that a S&P calculator such as this should be of interest. This article is intended as a guide about planning a safe and sustainable investment and retirement withdrawal plan from a S&P 500 Index fund that would survive typical bad market times (which do happen, but the long term overall rewards in good times are well worth it). Withdrawals cost far more than just the dollars withdrawn. It also costs all the long term substantial future earnings those withdrawals could have earned. The best plan is of course to postpone all withdrawals until retirement, so the fund will continue growing, and will be there when actually needed at retirement. The valid concern is that continuous withdrawals during earlier years or during bear market downturns (before fund has grown to be able to survive the withdrawals too) could deplete a fund, ending it prematurely, not lasting when needed for retirement. Is 4% a right number for S&P 500 plans too?

If you already know how the market works, the S&P 500 calculator and Fund Survival Test is below, which examines 50 years of historic S&P 500 returns. Don't miss that, there is a lot there. Try the calculator options which can compare and show the effect of the past history and very importantly, show the effect of withdrawals (4% or any others). It certainly offers an interesting view about the years of market gains.

But there is a lot more here. This page is just the calculator now, but this page was too long as one page, so much of the general material describing the S&P 500 and the market and the 4% Rule was moved to a second page. Reluctantly moved, because its material there was intended to be the entry introduction, a few things of interest about the market — but the combined page was too large. If you are new to the market, my intention is that all those moved words on the second page may also be a help. It's there if you want to see it.

Thinking of stock dividends as being new income to be withdrawn is a mistake. Yes, the dividend money was moved from the companies (who's value went down by millions or billions) into your fund, but the remaining stock price (which reflects the value of the company) is equally reduced when the dividend is paid. The value sum of withdrawn dividend and the remaining stock value remains exactly the same, no gain. The value increase of that transaction on that day is zero. Withdrawing dividends would instead only be a simple direct withdrawal that reduces your current fund value (same as any other withdrawal). Regarding that loss, there's a table below showing the huge long term loss of withdrawing dividends. See more facts on a following page: Stock Dividends are valuable, but withdrawing them is withdrawal, Not income.
However reinvested dividends become additional shares which do create significant future compounded earnings. (But just not on that same first day, and Not if withdrawn.) The withdrawn dividend may seem small, but in the calculator below, click the "withdraw all dividends" option (or Example 2) to see the unimaginable compounded fund value loss in 50 years. It's good to know how it works.

Calculator for Survival Test if Starting Fund Each Year

The Survival Test feature of this calculator performs an examination for S&P 500 Index funds to show how market drops and/or withdrawals have survived in the past bad bear market history typical of the real world over the last 50 years, from any starting year, and can be started with any fund amount. It restarts the calculator at every past chart year, with any withdrawals or additions, seeking to find the effect of the bad times. We can't know future performance, however the overall S&P annual gain has always averaged about 10% a year, even more in its good years, but then with losses in the bad years. We cannot repeat those same past years, but the same kind of periodic market crashes have always happened, and are still routinely expected now and then (the bitter with the sweet, which averages out, and the sweet wins). But is a valid future concern about retirement withdrawals being more than the situation can bear. We don't know that future situation, but if we can determine a withdrawal rate that would have always been safe in any starting year in the last 50 years, it should seem safe in the future too. This past history has some very bad years, and some very good years too, more good than bad.

We can't see the future to know when a crash might occur, but the calculator below computes "how much" occurred in past "typical" crashes. You might plan for it by having more fund money in the fund, or by allowing for reducing withdrawals, especially during bad market times.

Test it yourself (next below). This Fund Survival Test performs the convenience of recomputing the fund beginning in each and every year in the 50 year chart, and looks at the survivability in any situation there due to any specified withdrawals. Various Start Years do cause different results depending on market year situations then, and especially of course, due to any withdrawals specified, and on how many years of opportunity follow. We don't know when future crashes will occur, and adding more investment money all along is always a great plan too (more money grows more). This is historical data, Not the future, so the exact dollar values of the past data are not significant today. But the past can be said to be "typical market situations", and it can show a lot in a glance. The idea is to show impact of withdrawals (how the market works), in situations that have happened and conceivably might happen again. The best earning plan is always "no withdrawals", but this topic is intended to be about necessary withdrawals during the 30 years of retirement.

Here, a fund depletion failure is indicated if the fund value falls below the specified Failure Minimum Limit, which you can choose. This limit is because the limit zero does not seem useful with percentage withdrawals, like even 30% is hard to ever reach zero (at 10 cents, even 30% reduction is still not zero.) The default $500 limit does not hurt the concept, but you can change it. Entering recovery with only $500 is not optimum for fast growth, but we are looking for a busted fund near value zero here.

The best explanation of what this Survival Test does is seen by running a Test example. I invite you to try it with a hypothetical example with calculator initial defaults (starting with $25K in 1970) except with button 2 at $200/month withdrawal. The Test All Start Years choice will show the situation (computes up to 1378 year situations if no depletion failures). This example shows the possible risk of the specified withdrawal. And if the plan should fail, of course there are smarter plans.

Show this setup in calculator below (called Example 0)

Then while there, also instead use button 1 for 11% (which is near the average fund gain), which just always continually maintains more or less about the same fund value (withdrawal dollars to be recomputed as the same percentage every year). The 11% did not fail, but it limited the fund value to about $19K, and the total growth value recoverable to about $140K (including the withdrawals) instead of the $4.7 Million if instead no withdrawals for 51 years. Withdrawals have a very high earning cost, but are of course the expected plan during retirement.

Then also try button 3 with both 11% and $200/month acting as limits on each other, smoothing the action. It is a more even and reasonable result that does not fail the Test, but the recoverable Total Value is still only about $250K (about 4.5% for 51 years).

And just to make the point about the cost of withdrawals, also try button 1, no withdrawals at all. Seeing how crashes and withdrawals work can only make any question about the withdrawal danger be better understood.

Or to make the point about a larger fund value, try button 2 and the same $200/month again that failed quickly (in each of 13 start years), but a $50,000 starting investment smooths it over and does not fail. In fact, it was enough to get past the bad years and then it still grows to $4.4 Million in 52 years. So situations differ, and the details are far from absolute. Letting the fund grow before starting withdrawals is the best plan.

But for a dramatic difference, contrast that with Example 4 below about letting the $25000 grow first (for 20 years), before starting any larger retirement withdrawals. There are no hard answers, but this is intended to be instructive. This does show past years history, and future years are unknown. It will depend on the fund value, which depends on the withdrawals you choose.

There are several more examples below. More money in the fund will always last longer, but technically, if no withdrawals, the fund does not go bust in the bad periods even if starting with only $100 in 1970 (declaring a $60 Minimum). The value does fall to near 60% about three times then, if starting at 1973, 2000, or 2008, but it still survives to grow to near $21K today if left undisturbed. Any fund failures are due to your withdrawals, which should be left until retirement. The Test result shows that this example $200/month fixed amount withdrawal works if the fund value grew a little larger, or started larger, but otherwise, it also still fails in quite a few years too. Since we don't know the future, that's a serious problem that conceivably could happen again. Starting with $25K at 1970, the early fund bad times did not yet have sufficient gains in the fund to provide the withdrawal demands. As the fund decreased, the fixed withdrawal was withdrawing more and more percentage, and could not survive that. The later bad times of the 2000s also took it down so some starting years failed. If instead withdrawing a small percentage, like 5% or even 10% (with dollars to be recomputed every year), the percentage withdraws much more when the fund value is high, but very little when the fund value is low, which helps survival considerably (fund probably never reaches zero). But it is variable, and a fixed dollar amount is constant and more suitable for retirement living expenses, but it really hits the fund hard in down years. Button 3 provides both percent and dollars as limits on each other, which can smooth it out. But all withdrawals are costly, and if no withdrawals, $25000 could have earned more than $4 Million (in 50 years, in spite of the bad years). Maybe some of those results look scary, but please also just retry it with No Withdrawals to see the really huge difference. It will not fail if no withdrawals. And of course, more fund money does last longer. There are more examples below, just some ideas to think about. Less withdrawal generates More total earned income, except it is in different time frames.

IRA RMD: A fixed dollar withdrawal starting from the current fund value might be of interest to retirees subject to the Required Minimum Distribution (RMD) of an IRA or Roth fund at that age. Put RMD withdrawal amount at button 2, and (if no previous data) put the current IRA fund value as Starting Investment. The RMD increases with your age (see RMD on next page)), and the fund should earn gains too. Note that the RMD amount is computed from the total of all your RMD funds, but here, the percentage shown is from that one fund you are withdrawing it from. Of course, an IRA RMD is Not designed to last, but is instead designed to pay the taxes.

Again, this Test cannot predict the future. It only shows historical results, assumed possibly typical of the future too, but future dates are unknown. The previous bad years are useful to show examples of possible market action. The important thing is that surviving bad market years needs sufficient remaining fund value to recover, so minimizing withdrawals is important, certainly in early or bad years. Starting in later years also limits earnings simply because of the fewer years left to grow then.

The S&P 500 had 70 record high closes in 2021. The last record high was 3 Jan 2022 at 4796.56
See the S&P 500 market action, including the frequency of the S&P 500 record highs.

		Gain $	Dividend $	Net fund value $	Gain + Div $	Date	Div %	Year	S&P yr Close $	Price gain %
$	%	Gain $	Dividend $	Net fund value $	Gain + Div $	Date	Div %	Year	S&P yr Close $	Price gain %
						27-Jan-22	0	2022	4326.51
						31-Dec-21	1.82	2021	4766.18
						31-Dec-20	2.14	2020	3756.07
						31-Dec-19	1.83	2019	3230.78
						31-Dec-18	2.09	2018	2506.85
						31-Dec-17	1.84	2017	2673.61
						31-Dec-16	2.03	2016	2238.83
						31-Dec-15	2.11	2015	2043.94
						31-Dec-14	1.92	2014	2058.90
						31-Dec-13	1.94	2013	1848.36
						31-Dec-12	2.20	2012	1426.19
						31-Dec-11	2.13	2011	1257.60
						31-Dec-10	1.83	2010	1257.64
						31-Dec-09	2.02	2009	1115.10
						31-Dec-08	3.23	2008	903.25
						31-Dec-07	1.87	2007	1468.36
						31-Dec-06	1.76	2006	1418.30
						31-Dec-05	1.76	2005	1248.29
						31-Dec-04	1.62	2004	1211.92
						31-Dec-03	1.61	2003	1111.92
						31-Dec-02	1.79	2002	879.82
						31-Dec-01	1.37	2001	1148.08
						31-Dec-00	1.22	2000	1320.28
						31-Dec-99	1.17	1999	1469.25
						31-Dec-98	1.36	1998	1229.23
						31-Dec-97	1.61	1997	970.43
						31-Dec-96	2.00	1996	740.74
						31-Dec-95	2.24	1995	615.93
						31-Dec-94	2.89	1994	459.27
						31-Dec-93	2.70	1993	466.45
						31-Dec-92	2.84	1992	435.71
						31-Dec-91	3.14	1991	417.09
						31-Dec-90	3.68	1990	330.22
						31-Dec-89	3.17	1989	353.4
						31-Dec-88	3.53	1988	277.72
						31-Dec-87	3.66	1987	247.08
						31-Dec-86	3.33	1986	242.17
						31-Dec-85	3.81	1985	211.28
						31-Dec-84	4.58	1984	167.24
						31-Dec-83	4.31	1983	164.93
						31-Dec-82	4.93	1982	140.64
						31-Dec-81	5.36	1981	122.55
						31-Dec-80	4.61	1980	135.76
						31-Dec-79	5.24	1979	107.94
						31-Dec-78	5.28	1978	96.11
						31-Dec-77	4.98	1977	95.1
						31-Dec-76	3.87	1976	107.46
						31-Dec-75	4.15	1975	90.19
						31-Dec-74	5.37	1974	68.56
						31-Dec-73	3.57	1973	97.55
						31-Dec-72	2.68	1972	118.05
						31-Dec-71	3.10	1971	102.09
						31-Dec-70	3.49	1970	92.15
						31-Dec-69	3.47	1969	92.06
		Gain $	Dividend $	Net fund value $	Gain + Div $	Date	Div %	Year	S&P yr Close $	Price gain %
$	%	Gain $	Dividend $	Net fund value $	Gain + Div $	Date	Div %	Year	S&P yr Close $	Price gain %

Chart bottom summary row: Withdrawn sum values are shown in blue. Left side of bottom row are column Sums. On right side are column simple Averages (of individual years, no compounding), of all rows except 2022, which is an incomplete year so far. Columns 1 & 4 on bottom summary row may contain two rows itself. Sums added or dividends reinvested are on its top row (black text there). Any sums withdrawn are at its bottom row and in color blue.

Price Gain and Dividend and Withdrawal and Fund Fee cost amounts are computed from the previous year end total. S&P declares dividend dollars in mid-January, which is paid quarterly. The dividend in the data is the S&P 500 dividend, and the S&P funds will match the same dividend percentage for the funds shares, but will subtract their fund fee from it. The "Gain + Div" column is just the sum of the years gains, but Dividend is not included if it is withdrawn.

There may be some unavoidable precision loss. Dividends and gains are calculated here to be from the actual previous year end result values. However investments and withdrawals and start dates are on unknown individual days during the years. The calculator does appear to be pretty close to actual final past fund results.

All chart values are year end values except for 2022 being a partial year. Events within the year can be exciting, but some of the history and larger changes might be hidden, since only the year end is shown. For example, the 2020 pandemic dropped 34% in March, but recovered before year end. There was also a sudden 18% drop 12/24/2018, but it recovered in a week to only to a 6% drop at year end, and its rapid total recovery of course continued to new record highs.

Don't assume index fund expense fees are tiny and negligible. Enter your actual fund fee as zero to see the difference it makes after accumulating many years. S&P 500 funds with a small fund fee are available and advantageous. I like Vanguard VFIAX.

Fund Survival Test Results

The Test Mode computes starting the fund in every year, and watches for the fund going bust due to specified withdrawals and past market crashes. The Lowest Year Value is hopefully the starting year, but withdrawals or a later crash can lower it even more later. Every start year from 1970 is shown. Which is also useful to show overall fund gain results when starting any year (including any withdrawals or investments specified above). We of course cannot plan on repeating these same year situations, but we can plan to take precaution against any such situation. The Test shows all start year results, but you can also run the calculator manually from any Start Year of interest to see the intermediate details of that years results.

The Total End Value is the Final Fund Value plus all specified withdrawals (it is the return that is available).
Those withdrawals and the starting investment are as currently specified in the calculator above.

Here's a quick history summary of past S&P market action, in five and ten year periods (the top row is only 2+ years).

S&P 500 gains from $25,000 in 1970, invested dividends, with no withdrawals

Percentage gain =

New value - Old value
Old value

× 100

All this is history, Not the future, but it has all happened. The worst of the negative dips reached about 50% in 1974, 2001, and 2008, but had recovered somewhat by the end of the five year interval shown in this table. Perhaps better financial rules are in place now to help the market now, but all five year periods are Not alike, and some can include bad market times (it is called "risk"). Still, if it is a worthy investment, hang in there, it does routinely recover, always has, with good gains long term. Even with a few seriously bad years, if without withdrawals, the cumulative long term compounding effect should be evident and mighty impressive. All those years are the very best tool for retirement planning. The Message: Start Very Early, years before you will need withdrawals.

Maybe 20 or 50 years seems a long time away, but consider it's perhaps very important if that is when your retirement occurs. Typically retirement means no more job or salary, so you will need planned savings to live on. Maybe for travel and cruises too. The many years of Time can be your best tool now, or your worst enemy if you wait. That will certainly become extremely important, so take it seriously now, and start planning now while you have time. It will be too late then. If just $10K were put into Vanguard VFIAX in 1980 (40 years ago) and left untouched, it would be $1 Million now, in spite of a few seriously bad times. The best plan is to leave it alone and withdraw nothing until retirement needs make it necessary. Except of course, adding a little to it all along is a very good thing too.

Withdrawals are a huge cost in "What could have been"

Appreciable withdrawals from funds, including dividend withdrawals, can cost much more loss than you might imagine, and might be fatal in bad market times. All of the future years provide a very serious compounding benefit, but every dollar withdrawn loses all of the future gains it could have earned, a repeated loss every succeeding year. If the fund has grown a little, a modest percentage withdrawal rate (like 5%, with the dollars recomputed every year) should be sustainable, because the percentage means the dollar amount is low when the fund value is low. Whereas fixed dollar withdrawals are pretty much the opposite effect, percentage-wise. The sustainability of a fixed dollar withdrawal rate seriously depends on the amount of money remaining in the fund. Withdrawing the dividends might be only about 2+% a year, but the withdrawal of those "future shares" will make a huge difference preventing compounding over many years. Any way you do it, withdrawals are costly, and long term, will drastically reduce the funds total value that it could have earned. The calculator provides a visual way to realize this if you try some things in it (again, based on actual past results instead of knowing the future).

Withdrawing dividends is extremely costly to the future fund income over the many years

S&P 500		No withdrawals		Withdrawing all dividends
$25K Start	Years	Fund Value No WD	Dividends reinvested	Fund Value after WD	Dividends Withdrawn	End Value incl WD	Cost	Loss of Income

The cost of withdrawals is the money "that could have been" minus the money remaining available.

WD Cost % =

(Final value w/No WD) - (WD + Final value after WD)
Final value w/No WD

× 100

Long term, reinvesting dividends is a major part of S&P earnings. THE major part depending on definitions. That ought to get your attention. Do you really need to withdraw that (about 2+%) dividend each year, or would it (and its compounded future earnings) be better used at retirement? You might not be aware how very expensive that gets long term, but it certainly does, and there are choices. Reinvesting the dividend would add its additional shares every year for considerably more growth every year, greatly affecting final income for retirement. The exact gain values depend on market performance in the past decades, but that's true withdrawn or not, so the degree of cost of Withdrawal Loss depends on the years of duration of the compounding gains.

So don't imagine that withdrawing dividends is withdrawing income. Withdrawing dividends only lowers the fund value, same as does any equal withdrawal. But withdrawals are too expensive except in retirement when that is the whole intended need and planned purpose. The reported year gains can only compute the same numbers the same way. Every single digit in this table is the same for any withdrawal of the same amount. The compounding of the fund gains does work well if having the dollars to work with.

Reinvesting dividends does add shares, but without changing fund value on that day, however the new shares can add additional compounded future earnings every future year, which is the big benefit. For more, see Stock Dividends are valuable, but are not actual immediate income on next page.

Dividends in the table below are reinvested, but that table then assumes you might intend to withdraw a little all along from the start... just because it's there I suppose, except it is not there after you withdraw it. The numbers here come from the calculator above. The Cost of the Withdrawals is the possible fund value without withdrawals, minus the amount available to you (after the withdrawals and the remaining value still there). The cost is the loss that you did not get (losing the compounded gains it could have earned). Greater withdrawal is less overall gain.

Cost of Continuous Withdrawals for 52 years
after S&P 500 Investment of $25000 in 1970

Annual Withdraw	Final fund remaining	Total Withdraw	Overall Gain	Cost of withdrawal	Cost as percent

Fund Fees: The fees are also a continuous withdrawal. Try entering your fund fee as zero to see the difference that compounding of lost earnings cost there. Be sure you are entering the correct fee for your specific S&P fund (fees do vary significantly). The cost of the fee every year is much more than just the fee. It also continues to cost the lost earnings on it every year, compounded over the years. You definitely want to find a low fund fee.

When losing the compounding over many years, the long term expense of regular withdrawals becomes extremely high, compared to "what could have been". As the withdrawal percent increases, the fund value decreases so then it earns less, and so the dollar amount of any percentage withdrawal total also drops. The 2% case is comparable to just withdrawing all the S&P 500 dividends, the effect is the same. It should be a sobering thought. I don't mean to be preachy, but awareness is my goal. At least evaluate the actual need first. Just because it is there seems the worst reason to withdraw it. The best reason for withdrawals to wait is that your need is likely greater at retirement time. A common purpose of mutual funds is of course for the withdrawals to support retirement, but that idea is to first invest for 20 or 30 years without withdrawals to build up the fund, so you can have something to withdraw in retirement. You can take action on that NOW. Do realize that you are not simply subtracting the withdrawals. The big deal is that you are also subtracting all the years of compounded gains those withdrawals could have earned (which is a hugely larger number). The better idea is to let the fund accumulate something first. See Example 8 below.

The magic of the gains is that the growth is compounded, with the gains earning more gains, year after year, increasing dramatically after a couple of decades. But continuous withdrawals are a real big thing affecting a fund, reducing the gains and the compounding, again over many years. If you withdraw more, you get much less. You can see the result yourself in the calculator above. Imagine investing $25,000 one initial time in a S&P 500 fund for 50 years (historic S&P 500 data from 1970). That span could be at your age 25 to 75. If you're young, you need to realize those many available years are the huge magic opportunity, which diminishes if you wait. Just ten years might be impressive, but 50 years is simply awesome.

Just to be clear, withdrawals during retirement are certainly an expected main purpose of the market funds, but earlier withdrawals are detrimental to that possible "what could have been" retirement income. This is especially true during long term, when the compounding can make so much difference.

These are just some examples from past history, but it is suggestive of the way things work, and the things that possibly (or typically) can happen in the future. There are noticeably more good years than bad, and the S&P 500 has always averaged about 10% annual gains, but there are a few down years. The bad times might last a year or two, and might drop 50%, but they have always fully recovered (2009 was special and took several years though). Withdrawing the money when it is down in bad times is the worst thing to do, because it absolutely guarantees that the loss becomes real and permanent. Instead adding more investment money when the market is low is a great opportunity offering large gains when the price recovers (buy low, sell high). Hang in there, stay the course. It can seem dark and gloomy and fearful at the time, but withdrawing all money then ends it all (and makes the loss very real). But it has always recovered to continue the gains.

Also see next pages:
General Info describing S&P 500, the market, and the 4% Rule, etc.
Stock Dividends are valuable, but withdrawing them is Not income