Compounding Concepts4 分钟阅读

Compounding and the Rule of 72

Compounding, which Einstein reportedly called "humanity's greatest invention." With a single number, 72, you can instantly calculate just how powerful it is.

What Is Compounding?

Simple interest accrues only on the principal. At 10% simple interest per year on about $7,400, you earn about $740 in interest each year.

Compound interest accrues on interest too. After 1 year, the $740 of interest is added to the principal, making it about $8,100. After 2 years, the interest is 10% of about $8,100, or about $810. This difference grows enormous over time.

After 20 years: simple interest, about $7,400 becomes about $22,200 (about $14,800 gain). Compounding, about $7,400 becomes about $49,800 (about $42,400 gain). Compounding delivers more than double.

The Rule of 72

The time it takes for your principal to double is found by dividing 72 by your annual return.

Annual return 7%: 72 / 7 approximately 10.3 years to double Annual return 10%: 72 / 10 = 7.2 years to double Annual return 4%: 72 / 4 = 18 years to double Annual return 1% (a deposit): 72 / 1 = 72 years to double

This rule is an approximation of the exact formula (ln(2)/ln(1+r)), but it is accurate enough for everyday use. In the 6-10% return range, the error is under 1%.

Used in reverse: if inflation is 3% per year, the value of money halves after 72/3 = 24 years.

The Snowball Effect: Why Starting Early Matters

The real power of compounding appears in the later years. If you invest about $7,400 at a 7% annual return: After 10 years: about $14,600 After 20 years: about $28,700 (an increase of about $14,100 between years 10 and 20) After 30 years: about $56,400 (an increase of about $27,700 between years 20 and 30) After 40 years: about $110,900 (an increase of about $54,500 between years 30 and 40)

It grows nearly 4 times faster in year 40 than in year 10. This is why people say "starting 10 years late is the same as cutting your contribution in half."

The Preconditions for Compounding

To enjoy the compounding effect, two things are required: time and reinvestment.

When gains occur, you must reinvest rather than spend for compounding to work. For stocks, reinvesting dividends and not selling your gains are the conditions for compounding. And along the way, you must endure drawdowns of -30% or -50%. The benefit of compounding is the reward for patience.

常见问题

Q. Does compounding apply to stock investing too?

Yes, in two forms. First, price appreciation: when a stock price rises, there is a compounding effect as it rises again from the higher price. Second, dividend reinvestment: reinvesting dividends increases the number of shares you hold, maximizing the compounding effect. Note that unlike a deposit, stocks have no fixed interest, so the return fluctuates.

Q. What are the limits of the Rule of 72?

The Rule of 72 is an approximation of compound-interest calculation. The error grows when the return is very high (above 30%) or very low (below 1%). It also assumes the annual return is constant. In real investing, returns vary each year and losses occur, so use this rule to get a "rough sense" only.