Money Tutorials at Fundamental Tutorials on Personal Finance, Investments, and Economics

by William C. Spaulding

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More than 850 in-depth, continually updated tutorials on the fundamentals of personal finance, investments and economics — supplemented with full-color illustrations and charts, color-coded examples, and formatted for quick comprehension.

At first, people said that money is the root of all evil. Later, people decided to be more specific, and said that it is the love of money that is the root of all evil. But wait a minute! If money didn't exist, then the love for money wouldn't exist, so I guess money is the root of all evil, after all!wcs

Find more specific information fast by using the search engine at the top-left of every page (or near the bottom when viewing on a mobile, tablet, or other small-screen device). This page links to the table of contents to individual subjects with many more topics than are listed here.

Consumer Finance

The lack of money is the root of all evilMark Twain

Credit and Debt



Real Estate


Wills, Estates, and Trusts


If you can count your money, you don't have a billion dollars.J. Paul Getty
I can confirm this! I counted my money, and it wasn't a billion dollars!wcs

Investment Fundamentals




Investment Funds





Technical Analysis



Money can't buy happiness, but it can buy you the kind of misery you prefer.Unknown Author


Some of my Videos from my YouTube Channel

My Books

The Pauper's Money Book shows how anyone can manage their money to greatly increase their standard of living.

  • Save, Invest, and Earn More Money
  • Increase Your Credit Score
  • Learn to Negotiate Successfully
  • Manage Time Effectively
  • Invest for Maximum Results with a Minimum of Risk
  • Minimize Taxes, Earn Tax-Free Income
  • Earn More from a Career or from Running a Business
Trickle-Up Economics describes the best tax policy for any economy, based on simple economic principles that anyone can understand. I think this book is particularly pertinent for the upcoming 2020 elections, since it not only describes the best tax policy, but it also explains why the current tax policy is both inadequate for generating sufficient revenue for the government, and how it increases inequality. This book also shows the problems with the several tax proposals being presented by the Democratic candidates. So, if you want to argue intelligently about tax policy at your next party or family gathering, this is the book to get. :-)
An introductory textbook on Economics, lavishly illustrated with full-color illustrations and diagrams, and concisely written for fastest comprehension. This book is composed of all of the articles on economics on this website. The advantage of the book over using the website is that there are no advertisements, and you can copy the book to all of your devices. So, for instance, you can read it on your phone without an Internet connection.

Pedagogical Features and Sample Content of

My name is William C. Spaulding, and I write all of the articles, and do most of the illustrations for this site. The only illustrations that I have not done are graphs and photos downloaded from government websites. I present this section to illustrate the major features of the site, including types of content and other features, such as navigational aids. It also gives you a good sample of my content and my writing. But do keep in mind that these excerpts do not have the context here that they would in their original pages.

The purpose of this site is to teach the fundamental concepts of economics, personal finance, and investments. These topics were chosen because they are highly interrelated, so the concepts learned in economics, for instance, can be applied to personal finance and investments. Indeed, economics makes it much easier to learn about why things are the way they are and how they behave over time. Learning these subjects also helps to improve your life.

To facilitate learning these concepts, I use many pedagogical features that will enhance learning, which are listed below this section. There are over 850 articles on this site, grouped under the appropriate categories, which, on a desktop, you can see in the sidebar on the left, or, on a smaller screen, such as a phone, at the bottom of any article. Clicking on these links will display the list of topics in that category. I have included many of the pedagogical features on this page. Although some of them are lengthy, it does give you a good preview of what my site has to offer.

Graphs and Illustrations

As they say, a picture is worth a thousand words, so where images make concepts clearer, I use them. Most of the images also have extensive captions to clarify and expand the information conveyed by the image. Here are 2 examples:

From the Deadweight Loss of Taxation:

To see why this deadweight loss occurs, look at the supply and demand curves in the graph below. When a market transaction is taxed, the buyer pays a higher price and the seller receives a lower price. This lowers demand, which shifts the buyer's equilibrium from the market price (Pm) to a higher price (Pb) at lower quantities; likewise, because the seller receives a lower price (Ps) for his product, less of it is supplied, which moves the seller's equilibrium down the supply curve, to a lower price and quantity. The amount the government receives equals the tax, which equals the buyer's price minus the seller's price, times the quantity of the transaction, whether for goods or services.

Tax Revenue = Tax × Quantity

Supply-demand graph illustrating the deadweight loss of taxation on goods or services.

The area of the light purple rectangle in the graph = the tax revenue collected by the government. The area of the dark purple triangle = the economic welfare lost to taxation.

  • Pb = Price buyers pay. Demand is reduced because buyers must pay a higher price because of the tax.
  • Pm = Market price without taxes.
  • Ps = Price sellers receive.
  • Qe = The quantity supplied without the tax.
  • Qt = The reduced quantity supplied because of the tax.

From Duration and Convexity, with Illustrations and Formulas

Note that the price-yield curve is convex, and that the modified duration is the slope of the tangent line to a particular market yield, and that the discrepancy between the price-yield curve and the modified duration increases with greater changes in the interest rate. It can easily be seen that modified duration changes as the yield changes because it is obvious that the slope of the line changes with different yields. The gap between the modified duration and the convex price-yield curve is the convexity adjustment, which — as can be easily seen — is greater on the upside than on the downside.

Diagram of modified duration and convexity and the price-yield curve of a bond.

SVG Images

Many of the images use a format called scalable vector graphics, or SVG, which are defined mathematically, so they are usually much smaller than raster graphics such as PNG, GIF, or JPEG images. Since they are constructed mathematically, they can be adjusted to any size without losing any resolution, from phones to high resolution monitors. Moreover, they look a lot better than the rasterized equivalent. The 2 images above are both SVG images. However, SVG is only suitable for simple graphics and illustrations, such as diagrams. More complex images, such as photographs, uses the JPEG format.

Color-Coded Examples

For more complex examples, I use color coding to show the interrelationship of different parts, making it easier to follow and faster to comprehend.

From Child Tax Credit:

Example: Calculating the Child Tax Credit for Incomes Above the Phaseout Amount

Ava is a single parent with 2 dependent children and she earned $90,020 for the tax year. Because her income is $15,050 more than the phaseout amount of $75,000 for a head of household, she must reduce the $2,000 child tax credit that she would otherwise be entitled to by:

$90,020$75,000 = $15,020, which is rounded up to $16,000, since the $20 portion is a fraction of $1,000.

$16,000/$1,000 = 16

16 × $50 = $800

Child tax credit = 2 × $1,000 − $800 = $1,200.

Note that although she only earned $20 more than $90,000, she must round her income up to $91,000, which is why the $50 is multiplied by 16 rather than 15.

Here's another example from Bond Pricing and Accrued Interest, Illustrated with Examples, where color coding facilitates following the example and also illustrates how to use certain tools, such as Microsoft Excel, in doing some of the examples:

Examples — Using Microsoft Office Excel for Calculating Bond Prices and Discounts

The following listed variables — where they apply — will be used for each of the example calculations that follow, for a 10-year bond originally issued in 1/1/2008 with a par value of $1,000:

Price of a bond with a yield to maturity of 8%:

Bond Price =PRICE("3/31/2008","12/31/2017",0.06,0.08,100,2,1) = 86.62092 = $866.21

The discount price of a zero coupon bond with a $1,000 par value yielding 8%:

Price Discount =PRICEDISC("3/31/2008","12/31/2017",0.06,0.08,100,1) = 21.99288 = $219.93

The interest rate of a discounted zero coupon bond paying $1,000 at maturity, but that is now selling for $219.90:

Interest Rate of Bond Discount = DISC("3/31/2008","12/31/2017",21.99,100,1) = 0.080003 = 8%

PRICEMAT calculates the prices of securities that only pay interest at maturity:

What is the price of a negotiable, 90-day CD originally issued for $100,000 on 3/1/2008 with a nominal yield of 8%, a current yield of 6% and a settlement date of 4/1/2008? Using the Microsoft Excel Date function, with format DATE(year,month,day), to calculate the maturity date by adding 90 days to the issue date, and choosing the banker's year of 360 days by omitting its value from the formula, yields the following results:

Other Special Types of Content

I use real-world examples to illustrate how the concepts are applied to the real world, to increase understanding both of the material and of the real world, such as this example from Will Execution: The Common Law Elements of the Wills Act Formalities

Real Word Examples: Testamentary Intent Clauses of Famous Wills

I also include alerts about special situations that readers should be particurally aware, such as this one about credit ratings on bonds from credit rating agencies, from the Complete Introduction to Bonds:

Investor Alert! Note that credit ratings are not foolproof. Enron had an investment-grade rating right up until it declared bankruptcy, and WorldCom up to 3 months before filing for bankruptcy! It's also a good idea to check all the credit-rating agencies about a particular issuer, because different agencies have different criteria, and different strengths and weaknesses in rating bond issuers.

Many articles also have Notes and History, to point out certain facts or to illustrate how things were or came to be, such as these 2 examples from Credit Scores:

Sometimes payments are not made because they are disputed. If the dispute is not resolved, then you have a right to add a statement in your credit report, limited to 100 words, explaining why you refuse to pay. Note, however, that your statement will not protect your credit score, since explanations cannot be quantified, so the credit-scoring algorithm cannot take your statement into account. It will, however, take in account that you have missed a payment.

Fannie Mae Starts to Use Trended Credit Data to Underwrite Consumers

In mid-2016, Fannie Mae started using trended credit data from all 3 credit reporting agencies — Equifax, Experian, and TransUnion — for all mortgage applications. The trended credit data focuses on credit data from the past 30 months, showing not only if payments were made on time, but whether the borrowers carried balances from month-to-month, paid off the balances in full, or at least paid more than the minimum. Studies by TransUnion have shown that consumers who carry balances or who only pay the minimum balance are a greater risk than those who pay in full. TransUnion estimates that trended credit data will put more consumers, from 12% to more than 21%, in the so-called Super Prime risk tier, who are offered the best credit terms.

Source: A Focus on Credit History for Mortgage Approvals - The New York Times

Or this one from  United States Treasury Securities: Bills, Notes, Bonds, Treasury-Inflation Protected Securities (TIPS), and STRIPS:

Quick Facts on the National Debt

The US debt is financed mostly by selling U.S. Treasury securities. The United States has carried debt since the American Revolution. Only during the presidency of Andrew Jackson has the United States been truly debt-free. As of the end of March 2016, the US debt slightly exceeded $13.4 trillion. You often see in publications that the debt exceeded $19 trillion, but more than $5 trillion of that debt is what the government owes to other government agencies, such as the Social Security trust fund.

Source: National Debt

While this site focuses on how things work, it also has many tips for using the information in real life, such as the following, from Credit Scores:

Additional Tips and Resources for Improving Your Credit Score

I also provide a little bit of humor, such as:

I'm living so far beyond my income that we may almost be said to be living apart.e.e. cummings

And I include news items:

March 9, 2015 update: The credit bureaus use automated dispute resolution processes to correct errors reported by consumers, which is why mistakes in their credit reports frequently go uncorrected. In their settlement with the New York Attorney General's office, with changes being phased in over the next 3 years, the 3 credit bureaus will provide specially trained employees to resolve disputes. Additionally, the credit bureaus will establish a 6-month waiting period before listing medical debt, and any such debt that was reported, but subsequently paid by insurance, will be removed. - TransUnion, Equifax and Experian Agree to Overhaul Credit Reporting Practices -

Believe it or not, I also have opinions, such as this one from Payment Systems:

Bitcoins and Cryptocurrencies Will Never Be Major Currencies

Another form of payment receiving media attention recently is through the use of Bitcoins or other cryptocurrencies. Some of the main advantages advanced for Bitcoin are that:

However, some of these advantages touted for Bitcoin result because it is an entirely electronic form of money. If the United States dollar or the euro was made entirely electronic, then those currencies could be subdivided indefinitely to allow for micro-payments. Most fiat currencies have a lower limit for value because they are represented by coins and paper currency, which cost money to produce. Indeed, the US penny and nickel cost more to produce than their fiat value. On the other hand, the value of electronic money can be reduced, virtually without limit, to form smaller payments.

That transaction costs for Bitcoins are usually lower than using other electronic payment systems, such as credit or debit cards, is also artificial, since transaction costs are set by banks and other payment service providers, such as MasterCard and Visa, who are reluctant to lower prices that constitute a major source of profit. The transaction costs for current methods of payment could be much lower, but the lack of competition and government control has kept these transaction costs higher. When money becomes entirely electronic and the government institutes reforms to take advantage of electronic payments — which I believe is inevitable — then all the advantages of electronic payment, such as enabling micro-payments and lowering the transaction costs, will be realized for that currency.

That the supply of Bitcoin is limited is actually a major disadvantage, since the value of Bitcoin varies widely over short spans of time because supply cannot be increased or decreased to meet changing demand. The problem with Bitcoin and other cryptocurrencies, or for that matter, any other means of payment, such as gold, where the supply cannot be controlled, is that it cannot satisfy the primary functions of money, as a unit of exchange, as a unit of account and as a store of value.

Although cryptocurrencies can be used as a unit of exchange, it is very risky to do so. Imagine if Walmart or Amazon accepted Bitcoin for payment. What would happen to these companies — or any other company — if the value of Bitcoin suddenly dropped to half its value or more, as it has already done? In December, 2017, the price of 1 Bitcoin reached almost $20,000. Shortly afterwards, near the start of 2018, the price of Bitcoin was less than $9,000 (USD)! The pay rate for employees would have to change every single week and prices paid to suppliers, likewise. This would be a managerial nightmare!

It cannot serve as a unit of account, because the variation in its value, even within a short time, makes its exchange value for goods and services unpredictable; price comparisons would be impossible because these cryptocurrencies vary in value by the minute, so any prices you would see may be stale, reflecting the value that Bitcoin had at an earlier time. Likewise, it cannot serve as a store of value, since it can lose value very quickly, as has already occurred several times with Bitcoin and many times with gold. Additionally, using methods common in business and investments, such as calculating present value or future value of projects or investments or even calculating financial risk, becomes impossible. Calculating present value or future value is only meaningful if the value of the currency is stable. Even though most currencies decrease in value because of inflation, inflation is usually low and predictable, so it is easier to account for inflation.

Hence, in my opinion, Bitcoin or any other types of money where the supply cannot be controlled will never serve as a major currency, or even as a co-currency. Instead, Bitcoin will remain as it is, a novelty currency that can be used either as a medium of exchange for those businesses or individuals willing to assume the risk of a widely fluctuating currency or to profit from speculation, where profits are contingent on the greater fool theory. Because the intrinsic value of Bitcoin and other cryptocurrencies is 0, that is the price that I believe it will fall to, eventually, although it may take many years.

(I think another factor propping up the prices of cryptocurrencies far beyond their intrinsic value is micro-demand. Because cryptocurrencies can be subdivided into ever smaller amounts, I believe many people are getting these small amounts to experiment with these novel currencies. When the demand for these micro-amounts are totaled over the entire global population, the result is significant demand. Eventually, people will realize that cryptocurrencies really offer no added value over traditional forms of electronic payments, nor are they spendable at most places, so, it is still my prediction that the value of all cryptocurrencies will eventually drop to their intrinsic value of 0. Blockchain, of course, has great promise, but this is used only to record transactions. Although Bitcoin and other cryptocurrencies depend on blockchain, blockchain does not depend on the cryptocurrencies.)

From Employment Taxes:

How to Save Social Security and Medicare

There has been much press lately about the trust funds for Social Security and Medicare running out of funding, that they soon will both be broke. Of course, the Republicans want to decrease payments as a solution, but that would deprive much of the poor and middle-class of funds that they sorely would need in their old age. And employment taxes are already high enough to hurt the poor significantly and to lower the standard of living for the middle class. Here's a solution that can greatly increase funding without raising the employment tax rate.

For the self-employed, employment taxes are called self-employment taxes, about 14.13% of income earned from work for those who earn less than the Social Security wage cap. For employees, the employer pays ½ of employment taxes for their employees, and the employees pay the other half. Economists generally agree that employees pay a larger share of the tax through lower wages, what economists refer to as the tax incidence. In other words, employees get paid less because the employer must pay their share of the employment taxes, so the employees pay additional employment tax through lower wages.

So how can the Social Security and Medicare trust funds be saved? By increasing the minimum wage, by taxing all earned income, such as the compensation earned by high income employees through stock options, and as a clawback from people who receive more in Social Security and Medicare payments than what they paid in, by subtracting it from their estates before the unified tax credit is applied. Adjusting the minimum wage for inflation would also help to increase tax revenue to cover Social Security and Medicare payments, since both payments are adjusted for inflation annually.

The federal minimum wage in 2018 is $7.25 per hour. The last time it was raised was July 2009. Inflation since then has eroded the purchasing power of that minimum wage, but even back then, it was inadequate to earn a decent living. Increasing the minimum wage to $15 or $20 per hour would greatly increase employment tax revenue, and it will have other desirable effects as well. Increasing the minimum wage will stimulate the economy, because giving more income to low-income employees will stimulate their spending, which, in turn, stimulates the economy. Moreover, the increased cost to employers will become less and less of a factor in the final price of the product or service, as automation makes each worker more productive. Although the microeconomic effect of a higher minimum wage would reduce the demand for labor, the stimulatory effect of allowing poor people to earn more money will more than compensate, with the macroeconomic effect of greater spending exceeding the negative effect of higher prices of labor on employment. Not only would this increase employment tax revenue for the government, but it would also increase tax revenue in general, since working income, what the tax code refers to as earned income, is also subject to marginal taxes.

Some highly compensated employees are paid through stock options, and if the employer follows the tax rules, the compensation earned through the employee stock options, even though such income is earned from work, is not subject to employment tax, and is only subject to the lower marginal tax rate applied to investment income. Another way highly compensated employees can avoid Social Security and Medicare taxes is by forming an S corporation and declaring part of their income as dividends, which are not subject to self-employment tax. Likewise, for carried interest, which is income earned by some fund managers, some of whom make hundreds of millions of dollars annually. These fund managers earn carried interest by working for it, since they are not investing their own money, but, nonetheless, the tax code has a special provision, allowing them to designate a substantial portion of the compensation as carried interest. Carried interest is subject only to long-term capital gains rate and is not subject to employment taxes. So why allow highly compensated employees to pay less tax on their earned income than low-income employees?

Another possibility is that employment taxes can be applied to all income rather than just employment income. After all, why should employment taxes only be applied to employment income? That they do is why they are called employment taxes, but there is no reason why these taxes cannot be applied to all income, including gratuitous transfers. Applying employment taxes only to work just increases the taxes on people who earn most of their money from work, because the tax revenue must be earned from a smaller base. If the tax rate was applied to all income, then the tax rate could be lower, since it would apply to a much larger tax base. Additionally, more people would qualify for Medicare and Social Security.

Or how about this, from Quantitative Easing:

The Best Monetary Policy to Stimulate the Economy is a Fiscal Policy: Lower or Eliminate Taxes on the Poor

To stimulate the economy, money must have velocity: people must spend it repeatedly. If money is just hoarded, then it will have no impact on the economy, regardless of its quantity. The best way to increase the velocity of money is to use it to offset taxes on the poor, who are hurt most by recessions and depressions, and who will quickly spend the money. As it is done now, QE merely makes the rich richer, who are far less apt to spend it. Lowering interest rates, even if it worked, would merely serve to increase the debt load of the public, which would eventually result in less spending, since the debt must be repaid. This is why QE is not effective either in the United States or in Europe. On the other hand, lowering taxes on the poor will increase their spending, which will increase business, which will increase money flowing to the middle class, who, in turn, will increase their own spending, and eventually, even the wealthy will benefit. Lowering taxes on the poor will benefit everyone! That is the way the economy works! Additional benefits to lowering or eliminating taxes on the poor include:

Of course, central banks use quantitative easing because that is a monetary policy tool that they can implement. Because lowering taxes on the poor is a fiscal policy, only Congress can change it, and since Congress is beholden to special interests, especially the rich, that is unlikely to happen soon. Working income, what the tax code refers to as earned income, has always been the most highly taxed form of income — at least in recent decades — and is an effective means of keeping a higher tax burden on working people rather than on the wealthy, who receive much of their income from investments and inheritance. Nonetheless, as already argued, lower taxes on the poor and the middle class will benefit everyone, including the wealthy, and is the best method of stimulating the economy.

Helicopter Money for the Poor

Helicopter money, a term coined by Milton Friedman in his 1969 book, The Optimal Quantity of Money, is a distribution of money by throwing it out of a helicopter, where the people below will grab it and spend it. Friedman envisioned that helicopter money would increase inflation, but would not increase real economic output. Ben Bernanke, a former Federal Reserve Chairman, argued that helicopter money might be a better solution than lowering interest rates to stimulate the economy in a deflationary environment, especially when there is a large economic output gap. The resulting increased spending will simply narrow or close the output gap rather than causing inflation.

In my opinion, helicopter money would be much more effective as an economic stimulus in a deflationary environment if it were distributed only over slums, because as I have argued above, giving more money to the poor would directly stimulate the economy. Indeed, there is no need to print any more money: taxing the rich more and the poor less would stimulate the economy, without causing hyperinflation. The rich would still benefit, because the money would eventually return to them, through their businesses and investments, and the government would collect more tax revenue from the growing economy and the higher velocity of money. Hence, everyone benefits! I should even call this the Utilitarian Tax Policy, since it is the best tax policy that I think will maximize the happiness of everyone, the primary goal of Utilitarianism.

And since the Republicans have recently enacted a generous tax package for the wealthy, I thought I would illustrate 1 of my opinion pieces with this item from my article on the Child Tax Credit:

A Tale of 2 Government Handouts

Some people consider the child tax credit to be a government handout, as evinced by the fact that the Additional Child Tax Credit has an explicit work requirement. I do not know if the Republicans have a unified view of the child tax credit, but since they oppose abortion, they should, at least, help people to afford those children. However, governments — federal, state, and local — put most of the tax burden on working people. Indeed, the Republicans do not want to tax investment income or gratuitous transfers at all! So that leaves taxing only work. They want working people to pay all the income taxes, so it is natural that they should espouse hard work, since somebody must pay for government. The Republicans just don't want it to be the rich. The tax burden on work is one reason why inequality is increasing, and why it is so difficult to move up in society by simply working for it.

In this light, it is interesting to compare the child tax credit with another very generous tax credit that benefits the wealthy: the unified tax credit, used to eliminate the estate tax on more than $5 million of gratuitous transfers, i.e., gifts and bequests.

The child tax credit:

By contrast, the unified tax credit:

The unified tax credit is very generous, indeed. For instance, the 2016 unified tax credit is worth more than most people will ever earn (adjusting for inflation) in their entire lives. A person who works for 40 years, averaging $50,000 a year, will only earn $2 million over his working lifetime, and would pay an enormous amount of taxes on that income over those years. On the other hand, a child receiving $10.9 million from his parents does not have to pay any federal tax at all on that income — and no! — he doesn't have to work for it.

Remember, too, that it seems that the tax code for the child tax credit has been carefully crafted to minimize any actual refund to low-income taxpayers, by only allowing the credit to offset payroll taxes, so that the government's net credit to the taxpayer does not exceed what it has collected through payroll taxes. The Additional Child Tax Credit increases by 15% for each dollar over the $3000 minimum, which closely tracks the total payroll liability for an individual taxpayer. Of course, if the taxpayer also qualifies for the earned income credit or the premium tax credit or even the American Opportunity Credit, then the taxpayer's refund from these truly refundable credits will be increased by the child tax credit. Although this is a rather complicated explanation, it does explain why the calculation for the child tax credit is so complicated, and why the child tax credit is not simply a $1000 refundable credit per child. Moreover, not everyone can work! And if they had children? Too bad, I guess! This is just 1 illustration showing how the tax code strives to limit payments to the poor, while being very generous to the wealthy, as demonstrated by the inflation-adjusted unified tax credit of over $2 million!

If the government truly wants to promote work, it would be more successful by taxing it less, instead of taxing it the most, as it is now, especially considering the fact that the deadweight loss of taxation on employment is greatest while the deadweight loss on taxing gratuitous transfers is 0. States and municipalities also tax work more than other forms of income.

Under the tax code, as in other things in life, the rich really do have it better!

Note: As noted in the news item above, the new tax package doubled the maximum child tax credit to $2000, with $1400 of it being refundable. However, the only reason why this was added to a tax package immensely beneficial to the wealthy is because Marco Rubio insisted on it, and without his vote, the rich would not have gotten their big tax breaks. As for the wealthy, among the many other goodies that they have received, the unified tax credit has been doubled, so now the wealthy can pass $22 million to their heirs without any tax liability. But since the government costs so much money, if the wealthy don't pay their fair share in taxes, then they must increase taxes on everybody else! While the new tax package did lower taxes for many lower income Americans, it achieved this by greatly increasing the deficit, exactly at the time when taxes should be raised rather than lowered, since the economy is peaking right now. After all, what will the government do when the next recession arrives, as it always does, since the economy continually moves in cycles. Without government spending, the economy will sink lower than it would otherwise.

Eventually, these taxes must be paid back. For years, the Republicans have been screaming about the deficit, and now that they are in complete control of the government, they have greatly increased the deficit to benefit their political donors. What this means is that the Republicans were not really concerned about the deficit, only that not enough wealth was being transferred from the lower classes to the wealthy! Eventually, the Republicans will argue that taxes must be raised on everybody, mostly the poor and middle-class, and that so-called "entitlements" — Social Security and Medicare — needs to be reduced or even eliminated. Of course, working people have been paying heavy taxes for these entitlements all of their working lives, but the Republicans still call them entitlements. On the other hand, the unified tax credit is a free gift to the wealthy, and unlike the child tax credit, has no onerous requirements!

A few of my articles also have summaries, although most of my articles are already concise. From Money Growth, Money Velocity, and Inflation:

Money Growth, Money Velocity, and Inflation

I also provide resources and links to additional information, such as the following:

Most pages do not have all of these features, since many articles do not benefit from them, but they are used when they improve the article. (And, of course, when I think of it!).

Responsive Website

This website is designed to respond to different screen sizes, so that the articles remain readable from phones to oversized high resolution monitors. Many of the articles contain equations, which I write using tables rather than using images, because tables are designed to be responsive for different screen sizes. Using SVG images also improves responsiveness to screen sizes and orientation.

My website has style sheet sections for printing and for viewing on mobile devices. If a page is printed, it will not include any advertising, navigational links, or any other content not useful on the printed page. On screens wider than 1,400 pixels, there is a fixed sidebar with a search box at the top followed by navigational links to major sections of the site. At the bottom of the sidebar of each page are sharing tools, such as for Facebook, Google+, or Twitter. On smaller screens, the pages have no sidebar so that all the screen space can be devoted to the article. In this case, the search box is located below the footer near the bottom of each page.

Update Policy

I continually update my articles with new information or to improve readability or comprehension. Some information may be dated, but I continue to use it because they provide the same pedagogical value. Because many of my examples take a lot of work, I will not update the examples themselves as long as they reflect current understanding and procedure. For instance, in my article on Butterfly and Condor Option Spreads, I use real bid and ask prices for specific stocks, such as Microsoft and Facebook, to illustrate how these option strategies work. This takes time to do, but there is no advantage to using more recent prices, since the principle of option spreads remains the same. But it does allow me to construct many graphs and show actual results of using different options strategies based on real bid and ask prices for a specific period. Here is an example of a long-put butterfly for Facebook, using prices from 2014:

Example: Long Put Butterfly for Facebook Established on July 31, 2014
Stock Price $73.06
Long Put Butterfly
October, 2014 Puts Strike Price
1 Long K1 70 -$3.10
2 Short K2 72.5 $8.30
1 Long K3 75 -$5.60

Debit $0.40
Maximum Loss $0.40
Maximum Profit $2.10
Line chart showing the potential profit/loss of a long put butterfly option spread for Facebook at options expiration for underlying stock prices ranging from $69.50 to $76.
Line chart showing the potential profit/loss of a long put butterfly option spread for Facebook at options expiration for underlying stock prices ranging from $69.50 to $76.

As of May 11, 2018, the price of Facebook stock now exceeds $185. I could update the above example and the many other examples in the article with higher prices, but it would make no difference in illustrating how option spreads work. On the other hand, continually updating these tables and graphs would take a lot of work, but without adding pedagogical value.

A valuable resource for me is my own readers. I have been writing articles for this website for 12 years, as of May 2018, so I often receive emails about mistakes in my articles or other problems with the article or website. This allows me to make corrections and improvements continually. It always helps to have a diversity of opinion. When I write, I am often editing different parts of the document, editing here and there, striving for perfection. But in doing so, I often become blind even to obvious mistakes, so it helps to have fresh eyes looking at the articles. You can find my email address in the sidebar or at the bottom, in the footer section of every page, or right here: Contact Me!

So, if you see any mistakes, or if you have suggestions, please email me.

A Note to the Grammarian Police

Originally, grammar was the study of how a language was constructed, how the individual words are put together to form meaning. Then, in time, some people have dubbed themselves to be the grammarian police — grammandos! — and have asserted that writing must follow the rules of grammar rigorously, and, nowadays, we even have grammar software to ensure that our writing is so constructed. I disagree with maintaining a rigid grammatical structure.

I believe that the main purpose of language is to communicate. If there is a better way to communicate, then it should be done, even if it breaks the rules of grammar. Case in point: writing numbers as actual numbers rather than as words, because numbers can be read much faster when they are written as numbers rather than as words, including the numbers 1 through 10. (The only problem with 1 is that it looks like I, depending on the font family of the letters, and my voice recognition software seems to prefer "one" over 1.) However, I only use the number 1 when referring to the number, not when it is being used to refer to a person or thing, such as "any one of you". I also know that grammandos are not gonna like "gonna" nor the fact that I put the period after the apostrophe. (Okay, I only used "gonna" here to make the grammandos cringe a little.) I also often write first as 1st and second as 2nd, etc. I don't always write ordinal numbers this way, since I have to consider how people will search for certain topics. So in those cases where the ordinal number may be part of popular search terms, I will continue to write it out as a word.

I think language can be improved in many ways to speed comprehension. For instance, using mathematical symbols for some words, such as = for equals. I don't do this on my site because I believe that too many people would probably have a negative opinion of what would probably look awkward to them. However, I believe the awkwardness is only because people are not accustomed to seeing things written that way, but if they were, they would become accustomed to it. But I do believe that people would be able to comprehend written words faster if documents were so written. It might be worthwhile to have some scientists measure the differences in comprehension speed between a document that used all words and a document that used other common symbols.

In fact, I believe that a committee should be formed that should seek ways to improve language in much the same way as the works to improve HTML and CSS.

I would like to make 1 suggestion right now. In the English language, no word refers to either male or female in the 3rd person singular. Hence, writers are reduced to saying he or she, his or her, or him or her, or they are forced to alternate between the references to avoid being labeled sexist. Sometimes this is useful when using 2 people in examples, since this removes any ambiguity in pronoun referents, but usually, it results in superfluous language. Therefore, I propose the following: e to refer to the 3rd person singular for either sex and er to refer to the objective case, as her does for the pronoun she, and ers for the possessive case. Maybe this new 3rd person singular should be capitalized as the pronoun I is, to distinguish it from the natural logarithm base e, although, context should clarify the meaning. In any case, this is just a suggestion. I will also probably use singular they more, if the meaning is clear.

This is not to say that there are not unintended grammatical errors on this site that do impede comprehension. Although I do run the documents through a grammar checker for a 2nd opinion, even if I don't always follow that opinion, I am sure that errors slip through anyway. Nonetheless, if you want to comment on this, please e-mail me. I would be interested in your opinion. Maybe I should set up a Facebook page for this topic, but, alas, I do not have the time.

Since there are over 800 articles on this site written over more than 12 years, my thoughts on grammar and my propensities have changed through the years, yielding some inconsistencies in the rules that I have used, something that grammandos the world over are definitely not gonna like, but considering that what is acceptable and not acceptable in grammar has changed throughout the years, as evidenced by the changing results of Usage Panel surveys, and as evidenced by literature itself, my main objectives are clarity and conciseness. You can at least be consoled that there is no Beowulf here.

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My Credentials

I am a financial writer who has been writing about financial topics since at least 2005. I have a degree in philosophy and business from Millersville University, located in Lancaster County, Pennsylvania, but most of my knowledge comes from constantly reading, writing, and thinking, and doing examples. I continually read textbooks, magazine articles, and other news sources about economics, personal finance, and investments. Unlike most other sites, I continually edit my articles to provide more or updated information and to make it clearer, especially when my readers alert me to mistakes or ambiguities. I also provide worked out examples for many of the articles. In my opinion, writing is the best education, because it forces you to think deeply about the topic, to research it thoroughly, and to ensure that it coheres with other principles and facts. I do sometimes disagree with the consensus and I will point out why I believe it is so, allowing you to decide if my argument has merit. I also get feedback from readers like yourself, pointing out mistakes, which I correct immediately — one of the many benefits of reading from a website rather than a book, even an ebook.

I also provide many references to my topics, including to individual facts, such as points of law, where you can review that information instantly by clicking on the link, which will open in a new window. For instance, in my tax articles, I provide direct links to all the referenced IRS forms and provide a direct link to many of the individual provisions of the tax code and to the many instructions and other publications provided by the IRS.

Another source of my knowledge, of course, is from personal experience, although it is, by necessity, much more limited than the many topics that I cover. Nonetheless, writing about many topics gives me a greater perspective and better insight into each individual topic, since they are interrelated.