## The Arithmetic Of Wealth

### 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

 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:

TABLE THREE

 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.

### 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.

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