Understanding the arithmetic of wealth is critical to acquiring wealth. It is your passport to wealth. Arguably, knowing this topic is more important than knowledge about markets!

This knowledge makes it easy to draw your path to wealth. It is motivational in the sense that what seems beyond your reach is seen as understandable and attainable. Before my kids went off to college they were introduced to this powerful topic.

Albert Einstein Agrees

The arithmetic of wealth refers to the compounding of money. Albert Einstein was so enamored by compounding that he referred to it as ” the eighth wonder of the world” and “the most powerful force in the universe.” High praise, especially considering the source.

This topic is so important that even if you believe you understand it, reviewing it is strongly encouraged. 

Income Helps, But ….

Becoming a millionaire is not necessarily related to the income you earn. Innumerable stories can be found about janitors or low-skilled laborers who toiled their entire lives in obscurity. Upon death, these unimportant and unheralded people were discovered to be millionaires or multi-millionaires.

The first one who came up on a Google search — Ronald Read, a janitor and gas station attendant never earned much money but died with an estate of $8 million. His story is not that unusual. Here are similar stories.

What is common in these cases is a willingness and discipline to save and invest.  No “keeping up with the Joneses” or pretending you are wealthier than you are. Little if anything is purchased with debt. Lifestyles are sparse. Yet these “nobodies” end up better off than many corporate types who consistently live beyond their means.

These people do not acquire wealth because they have unusual stock market expertise. They do it with regular savings properly invested. These surprise millionaires are not Warren Buffets, nor do they have unusual stock expertise or access to inside information. They are “average Joes” who do something which today is considered extraordinary — they live within their means and create a nest egg to protect against the unexpected. 

High income is no guarantee for wealth creation. You still need prudent habits and behavior. Ostentatious spending reflects personal insecurity and also can offset the advantages of high income, at least for wealth building. If there is one characteristic that tends to identify the “surprise millionaires,” it is humility and self-confidence. The self-assured end up with wealth beyond what their incomes and lifestyles would suggest. They live within or below their means.

The immature and insecure spend what they make (and oftentimes more) to impress and, temporarily, outshine their peers. Whatever produces this insecurity is irrelevant but it always yields a retirement less comfortable than earnings would suggest.

Luck Helps, But ….

Becoming a millionaire does not require luck. Nor does it depend upon an uncanny ability to pick stocks.

Those lucky enough to be in on the ground floor of Microsoft or Apple became millionaires merely by holding the stock. But, depending on wealth creation this way is like counting on winning the lottery to fund your retirement.

For every lottery winner, there are millions of losers. For every start-up company that makes it big, there are thousands (perhaps millions) that you never hear about because they fail.

Playing the lottery is not a way to wealth. Nor is playing the stock market as if it were a lottery.

The Arithmetic of Wealth

The arithmetic of wealth shows the magnifying effects of savings, particular savings done early in one’s career.  The arithmetic of wealth reduces its creation to simple mathematics understandable to virtually all. Knowing how simple the mechanics of wealth creation are makes it possible for many who never thought they could become rich to aspire to such a goal. Learning these simple techniques is motivational.

When you forgo consuming every penny you earn, you are creating wealth. Conversely, borrowing reduces wealth, at least to the extent that the borrowing is for consumption rather than investing. All credit card debt is wealth reducing!

Investing savings enables it to grow beyond what you saved. Paying interest on credit card debt reduces wealth over and above the amount borrowed.

Investing can be as simple as putting money into a savings account. For your funds (you are lending money) the financial institution) pays you interest. Your funds grow over time by the amount of interest you receive. (This is a safe investment but earns very little interest or return.)

A Simple Example of Compound Interest

The future value of your funds depends on three variables — the amount you saved, the interest rate you obtained and the period of time you leave the funds in the investment. Higher values for any of these variables produces a higher future value for your funds. Lower variables decreases the future value.

For simplicity, let’s work with $100 and an interest rate of 10% per annum. (While this interest rate is high given current conditions, not too long ago you likely would have considered it too low.)

At the end of one year, your hundred dollars will have grown to $110. At the end of the second year, your balance will be $121.0. The extra $1.00 in your account reflects the compounding effect. For year two you earn interest on $110, not $100. You earn interest on previously earned interest. This is known as compounding.

Aside: For those interested in formulas, the formula to calculate the future value of a single sum invested at 3% for ten years is (1 +.03)^10 * Single Sum. This formula reads 1 + the interest rate raised to the power of the number of years times the initial deposit (single sum). The formula to the right is used for interest that compounds monthly as opposed to annually.

Table One shows what a $100 grows to at different interest rates and over different time periods:

TABLE ONE

The rate of interest you receive and the number of years you leave the $100 invested make large differences in the ending balances.

• At 3% growth, you will have $438 after 50 years.
• But, at 15% $100 will have grown to more than $100,000.

Aside: There is a rule of thumb that enables you to approximate these relationships. It is referred to as the rule of 72. It turns out that if you divide the interest rate into 72, it provides a reasonable estimate of the number of years to double your money. For example, at an interest rate of 3% it takes about 24 years for you money to double. At 10% it only takes about 7 years. 

You may be thinking things like “where can I get 15% return?” or “I am already in my forties so I don’t have the luxury of investing for 50 years.” These concerns will be addressed in the future chapters. Our purpose here is to understand why Albert Einstein was so impressed with the power of compounding and what it can do for you.

Using $100 in Table One makes it easy to adjust to any other starting figure. Multiples of $100 can be applied to the end numbers to determine their results. For example, if you used $500 as your starting investment, each number in the table would be five times larger than shown. Thus, a one-time $500 investment that earned 15% per year would be worth over $540,000 fifty years in the future.

Let’s Get Real

If you look at Table One you might be discouraged because the numbers seem rather small. Further, if you know much about markets, you will know that a 15% return, long-term, is unlikely to be possible. No one should enter the stock market expecting to make only 3%  or 15% over a long period of time. Both returns can be exceeded in individual years and losses can also be incurred.

A more realistic expectation, over the long-term, is that you will average somewhere between 7 and 12% in the stock market. Lots of factors determine this range, including general economic conditions and the amount of risk you are willing to assume. Risk will be ignored in this article but dealt with in a future chapter.

Table One is unrealistic in the sense that it doesn’t reflect the way people save. Most budget and save (or should) annually. That is, they don’t only save once and then forget it. They typically set a savings goal of so much per year.

For simplicity, let’s recreate Table One above to reflect a savings of $100 not just one time but every year. (Mathematical nerds will recognize this as an annuity for which formulas, tables, and spreadsheets can easily handle calculations). The table from above is recast to reflect the value of a $100 annual deposit that compounds forward.

TABLE TWO

The numbers are larger because the savings of $100 occurs every year. One cannot multiply the number of years by the amounts from table one and come up with a correct entry for Table Two. The number is less than that because each subsequent savings has fewer years to earn interest. This illustrates an important point: Early savings are worth more than later savings.

Table Two produces significantly larger amounts than those in Table One. However, they still appear small because the savings assumption is only $100 per year. A more realistic assumption might be that you save $100 per month. A quick approximation of what that would do can be obtained by multiplying the above table by 12:

TABLE THREE

Note: multiplying by 12 assumes somewhat overstates the final results. For this table to be correct, $1200 would have to be deposited each year at the beginning of that year. 

The numbers shown in Table Three are beginning to look attractive. The goal of becoming a millionaire now seems in reach, especially for those who have time on their side.

Are You Already a Millionaire and Don’t Know It?

Let’s look at two examples to illustrate why you might already be a millionaire in the sense that you don’t need to save anything from here out to end up as such.

“Dear Aunt Tillie”

When I taught introductory courses in Finance, I tried to use colorful and relevant examples to demonstrate compound interest for students. One such example involved “Aunt Tillie,” a distant and virtually unknown relative who passed away and left $25,000 to one of the students (her niece of nephew). Of course that made the barely-known relative “dear Aunt Tillie,” the student’s favorite. The student, say 20 years old, is now asked to explore two options: 1) the student grabs the money and immediately goes out and buys a hot car becoming the envy of his classmates, or 2) the student accepts the money and invests it.  Let’s examine the implications of these two decisions.

The shiny new car is great. It’s a chick magnet (if the heir is a male) and provides great popularity, dates, and memories he could not have otherwise have gotten. Ten or 15 years down the road the car is old, dinged up and becoming more costly to keep running. Eventually, it is junked and the student is left with his memories.

The alternative, difficult for college students to envision, is to take the $25,000 and invest it. Let’s suppose it is put into an investment that earns 10% per year. When he turns 60, he will do so without any of the memories the car may be produced, but he will have (from Table One above) (25,000/100)*($4,526) = $1,131,500. At age 70, if still untouched, it would be worth more than $4.5 million. (Taxes were not factored into these calculations.)

The point is that “dear Aunt Tillie” made this young student a millionaire, had he known and been able to exercise restraint. I would like to believe that examples like this influenced some students.

“The Average Joe”

You are 40 years old, just an “average Joe.” You might be a millionaire already, in the sense that the student above was/could have been.

You have never thought of being a millionaire; never even considered it possible. But, take a look at your personal balance sheet. You have savings of $10,000, a 401K with $70,000 in it and a $400,000 home with a $250,000 mortgage. Are you already a millionaire like a student above was? Let’s see.

We make the following assumptions:

1. You earn 10% per year on your savings and 401K.
2. Your house is appreciating at 3% per year and your mortgage will be paid off in twenty years.

What will be your financial situation be at age 65? Based on the assumptions above, let’s extend these numbers to their future values. As you will see, you are already a millionaire so long as you don’t act like the college student. That is, merely the passage of time ensures that. No additional saving is necessary. No additional 401K contributions are needed. (Additional savings and 401K contributions are always recommended but not reflected below).

1. $10,000 in savings will grow to $108,000
2. 401K will grow to $758,000
3. Home mortgage-free will be then be worth $656,000

You are today, without any additional savings, headed for retirement watching what you already have grow to $ 1.5 million

These assumptions regarding interest rates, time horizons and your particular circumstances can easily be altered.

Conclusions

Einstein was properly impressed by the power of compounding. None of us are Einsteins but all of us should be equally impressed if not overwhelmed. Knowing this power, you can go out and get wealthy. Use this knowledge to plot your road map to wealth.