It is difficult for us to envision growth of our investments as they sit in funds as intangible assets. Comprehending, and forecasting, such growth, requires basic conceptual tools. To understand how much wealth one can accumulate through passive investments, one should understand the** Rule of 72**, an equation which illustrates the powers of time and compound interest, the basic principles of investing. While it is difficult, if not impossible, to forecast investment growth in the short-term, the Rule of 72 can assist in predicting growth over long periods.

__Rule of 72__

The Rule of 72 is an equation by which one determines when their investment will double. For the purposes of this article, we will discuss the __nominal, rather than real return__, on investments. The Rule is based on the principle of annual compound interest. As stated, it should be utilized for understanding long-term investment planning.

The Rule of 72 holds that the years it will take for one’s investment to double can be found as follows:

**Years=** __72__

**Interest Rate**

Thus, if one has invested $100, and the Interest Rate of the investment (also called a Return on Investment, or “ROI”) is 7%, one’s investment will double after 72/7 years (approximately 10 years). In about 10 years, you will have $200. When one invests in a diversified index fund, the historical ROI, including dividends, is about 7%, and so this particular example is pertinent for understanding the practical application of the Rule of 72.

__72__**=** **10(ish) years for investment to double**

**7**

*Hypothetical 1: Carl invests $10 in a diversified index fund, with a 7% ROI, in 2010. When he looks at the investment in 2020, he finds it has grown to $20.*

If the ROI is higher than 7%, the principal will double in a shorter time period.

*Hypothetical 2: David is 11 years old, and is astute about saving for college. His grandparents give him $100 for his birthday. He asks his parents to place this in his college fund, which is a tax-free investment plan. Growth is very strong, and this investment grows at 10% over the next 7 years. When David is ready for college in 7 years, at age 18, his $100 is now $200, which can be applied to his tuition fees. The equation for this hypothetical would thus appear as follows:*

__72__**=** **7(ish) years for investment to double**

**10**

The longer one invests, the greater the accumulation becomes. Drawing on the principle that one’s investment doubles every 10 years, one can see tremendous growth over their investment lifecycle. If one invests $100 in a diversified index fund for 10 years, their investment will become $200. If one invests this amount in the same fund for 20 years, their investment will become $400. And if one invests $100 at 7% for 30 years, their investment will become $800. To further expound on this point, if one invests for 30 years in a diversified index fund with a 7% ROI, their investment will multiply x8. Note that these numbers cannot be applied to the Rule of 72 above, as the Rule of 72 is an equation for how long it takes the principle to double.

The Rule of 72 should be readily applied to one’s saving plan. If one views an $1,000 expenditure today, it should be considered that this principle may be $2,000 in 10 years, $4,000 in 20 years, and $8,000 in 30 years. Capital is more valuable in earlier years due to its growth potential than it is in later years of one’s investing career.

*Hypothetical 3:* *Anna is 25 years old in 2020.* *She looks at a new Macbook that costs $2,500, but instead decides to buy a refurbished one for $500.* *She takes the $2,000 she saves and invests it in a diversified index fund.* *When she decides to retire when she is 65, she looks at her investment, to plan her withdrawal.* *She can see that her principal grew as follows:*

*2020:* *$2,000*

*2030:* *$4,000*

*2040:* *$8,000*

*2050:* *$16,000*

*2060:* *$32,000*

*Anna has $32,000 in 2060, 40 years after she saved the $2,000 on her one purchase.*

The Rule of 72, and the underlying concept that one’s investments grow over time, can readily be utilized to build one’s wealth. Minor expenditures are not minor, and small periods of unemployment are not inconsequential, assuming one is always willing to save and invest their income. If one is able to envision the growth of their investments in a diversified index fund, it may encourage one to save and invest.

The major takeaways from the Rule of 72 should thus be that money earned today is worth more tomorrow if invested, and money spent today would have been valued more tomorrow if invested.

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