Rule of 72 and Magic of Compounding

“Compound interest is the eighth wonder of the world. He who understands it, earns it, and he who doesn't, pays it.” – Attributed to Albert Einstein (although there is no evidence that he actually said it)

"Save and invest, for someday you’ll be 72." – Anonymous

Rule of 72 is a quick way to estimate the number of years it will take to double your investment at a given annual rate of return. It states that you divide 72 (hence the Rule of 72) by the rate, expressed as a percentage.

If you invest $1,000 today and earn 6% per year, it will take approximately 12 years to double your money to $2,000. You simply divide 72 by 6 and get the answer: 12 years.

Of course, you can use Excel or a financial calculator to get the exact number. However, you don’t always have access to these tools and the Rule of 72 gives the result that is close enough to make a quick decision.

Here are a few more examples:

Rate of Return	Years to double your money	Calculation
8%	9 years	72 / 8 = 9
9%	8 years	72 / 9 = 8
12%	6 years	72 / 12 = 6

The Rule of 72 is an extremely powerful tool that everyone should know. It is a simple but important tool especially for the younger members of our workforce who are just starting their career.

Now consider this. The average annual return of the S&P 500 Index since adopting 500 stocks into the index in 1957 through 2018 is roughly 8%. So, if you invest $10,000 in the S&P 500 Index fund today, with the long-term rate of return of 8%, the value of your investment will double to $20,000 in 9 years and it will continue to double every 9 years. The following table shows the value of your investment.

Number of Years	Value of $10,000 investment in S&P 500 Index Fund
0 years	$10,000
9 years	$20,000
18 years	$40,000
27 years	$80,000
36 years	$160,000

The Rule of 72 and the power of compounding is especially important to understand for young investors.

To illustrate, let us take a look at two individuals Ms. Start Early and Mr. Wait Longer. Ms. Early started investing 12.5% of her salary (including the employer match) in her employer’s 401(k) at the age of 25 when she got her first job that offered 401(k). Note that this translates to 1/8th or her first hour's salary each day! Her starting salary was $40,000 and it grew at 3% each year. Mr. Longer earned the same salary but waited 10 years before he started investing 12.5% of his salary. Both of them invested in the S&P 500 Index Fund (such as the one from Vanguard, Fidelity, or Schwab).

The following chart shows the estimated value of their 401(k) each year until they turn 60.

Estimated value of 401(k) through age 60

Ms. Early will have $1.4 million in her 401(k) whereas Mr. Longer will have a little over half as much ($760,000) – significantly less. This example illustrates the importance of starting to invest early and not waiting. Investing one hour of income each day over the first 10 years resulted in $651,034 additional wealth for Ms. Early. That is the magic of compounding!

If you double your savings rate to 25% (equivalent of 2 hours' salary per day), the value of your 401(k) will grow even faster. The following chart illustrates this.

As you can see from the chart above, doubling the saving rate to 25% will enable you to reach $1 million by age 50.

Of course, if your earnings are higher, you will be able to reach these goals much sooner. For example, if your starting salary is $60,000 and it grows annually at 3%, with a 12.5% saving rate, you will reach $1 million in your 401(k) by age 52. With a 25% saving rate, you will reach this goal by age 45.

Note that the above calculations and charts use the long-term historical stock market rate of return of 8%. Future rate of return may be different.

Here are some additional points to keep in mind.

1. Invest in low-cost index funds (or equivalent ETFs) such as Total Stock Market Index (Vanguard Total Stock Market Index Fund) or S&P 500 (Vanguard 500 Index Fund).

2. Stay the course in the good and bad markets to take advantage of dollar cost averaging. Remember that the stock market does not go up in a straight line, but in the past, it has always gone up over time. Time in the market beats timing the market.

3. The rule can work against you if you borrow on credit cards and personal loans instead of investing.

Note: Technically the rule should be called the rule of 69 because mathematically this is the number that provides a more accurate estimate. However, in many cases 72 is easier to use when you are doing mental math! 72 is divisible by 2, 3, 4, 6, 8, 9, 12, 18 and so on.

Disclaimer: This article is not intended to be investment advice. Consult a duly licensed professional for investment advice. The contents of this article are for educational purposes only and do not constitute financial, accounting, tax, or legal advice. Past performance is no guarantee of future results.