Understanding the Arithmetic of Wealth Is Critical to Increasing Your Wealth

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.

Understanding the arithmetic of wealth is…your passport to wealth… This knowledge makes it easy to draw your path to wealth…[and] is motivational in the sense that what seems beyond your reach is seen as understandable and attainable…

Becoming a millionaire is not necessarily related to the income you earn…[but, rather, the] willingness and discipline to save and invest. [There is] no “keeping up with the Joneses” or pretending you are wealthier than you are. Little if anything is purchased with debt. Lifestyles are sparse. [In fact,] high income is no guarantee for wealth creation. You still need prudent habits and behavior…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 Arithmetic of Wealth

The arithmetic of wealth shows the magnifying effects of savings, particular savings done early in one’s career…[and] 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…

• 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:

1. the amount you saved,
2. the interest rate you obtained
3. 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.

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

ONE-TIME INVESTMENT		$100
		Number of Years
Interest Years	10	20	30	40	50
3.00%	$134	$181	$243	$326	$438
5.00%	$163	$265	$432	$704	$1,147
10.00%	$259	$673	$1,745	$4,526	$11,739
15.00%	$405	$1,637	$6,621	$26,786	$108,366

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.
• At 5% $100 will have grown to more than $1,147.

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[r] money to double. At 10% it only takes about 7 years. 

…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 5% per year would be worth over $5,735 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 [as Table Two] 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.

INVEST EACH YEAR		$100
		Number of Years
Interest Years	10	20	30	40	50
3.00%	$1,146	$2,687	$4,758	$7,540	$11,280
5.00%	$1,258	$3,307	$6,644	$12,080	$20,935
10.00%	$1,594	$5,727	$16,449	$44,259	$116,391
15.00%	$2,030	$10,244	$43,475	$177,909	$721,772

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 is shown in Table Three below.:

INVEST EACH YEAR		$1,200
		Number of Years
Interest Years	10	20	30	40	50
3.00%	$13,757	$32,244	$57,090	$90,482	$135,356
5.00%	$15,093	$39,679	$79,727	$144,960	$251,218
10.00%	$19,125	$68,730	$197,393	$531,111	$1,396,690
15.00%	$24,364	$122,932	$521,694	$2,134,908	$8,661,260

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…

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.

The above summary* of the original article by Monty Pelerin (economicnoise.com) has been edited ([ ]), restructured and abridged (…) by Lorimer Wilson, editor of munKNEE.com, for a 48% faster – and much easier – read. (Please note that the previous sentence must be included in any article re-posting to avoid copyright infringement.)

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*The author’s views and conclusions are unaltered and no personal comments have been included to maintain the integrity of the original article. Furthermore, the views, conclusions and any recommendations offered in this article are not to be construed as an endorsement of such by the editor.

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