By Michael Paulding Thomas

“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it…” ―Albert Einstein

The Power of Compounding

Let’s look at the incredible power of compounding. An old question that beautifully illustrates this is:

Would you rather have $1,000,000 or a penny that is doubled every day for 30 days?

Doubling a penny 30 times = $5,368,709! (It actually only take 28 days to surpass $1M.)

Let’s see what’s happening here…

What is Compound Interest?

I used to think that the interest rate on an investment was pretty simple — you invest your money at 5% and get “X” in return. Then if your investment returned 10%, it would be “X” times two. Right?

WRONG. That’s when over 35 years ago someone showed me a compound interest table and explained the magic of compound interest, which is one of the most amazing facets of financial management.

Compound interest is the interest calculated on the initial principal and also on the accumulated interest of previous periods. This means that interest is earned on both the initial amount and the interest that has been added to it over time.

For example,

1. If you deposit $100 at a 5% annual interest rate, at the end of the first year, you would have $105.
2. In the second year, you would earn 5% on $105 (not $100), resulting in $110.25.
3. This process of earning interest on interest occurs year after year and leads to exponential growth.

Again, doubling the rate-of-return doesn’t simple double the result. Look at the example below of fully-funding two IRAs for a married couple:

12% earns almost four times as much as 6%. Amazing, isn’t it?

How It Works ― The Rule of 72

The Rule of 72 is a simplified formula that estimates the number of years it will take to double your investment.

The math behind it works because doubling is linked to how percentages compound over time. The exact calculation involves logarithms, which are used in higher-level math to solve problems related to exponential growth. But the Rule of 72 skips all the complicated calculations by relying on a close approximation that works well for most realistic growth rates.

It’s not perfect — its accuracy wobbles with very high or very low interest rates — but for rates between 4% and 15%, it’s remarkably accurate. Economists trace its origins to 15th-century merchants who marveled at the power of compounding long before financial calculators existed.

The correct rule should be:

69.3 / Interest Rate = Years to Double Money

But we use 72 instead of 69.3 because it has a lot of divisors so it can be easier to do mentally. For example, 72 divides cleanly into 1, 2, 3, 4, 6, 8, 9 and 12, allowing for a quick and simple division problem instead of using a calculator.

The High Cost of Waiting

“Never interrupt the compounding.” ―Nick Murray

The power of compound interest is amplified by time ― the longer you keep it going, the more your money grows. But the reverse is also true.

Let’s look at two examples of waiting to invest and thus robbing you of compounding.

Example 1: Delaying One Year Costs You $1.5M

In the above example, we notice the following:

1. Fully-funding two IRAs for a married couple from age 25 to 65 (40 years of saving) and earning an average of 12% rate-of-return, will build them a $13M nest-egg.
2. By waiting just one year to start their IRAs (39 years of saving) it costs them $1.5M!
3. By waiting five years to start their IRAs (35 years of saving) it costs them $6.2M!
4. By waiting 15 years to start their IRAs (25 years of saving) it costs them $11.5M!

At the bottom of chart you can see the amount of extra monthly contributions it would take to catch-up to the original value. Scary.

Example 2: When is $21k > $90k?

Let’s compare Sam and Linda, two 28-year-olds contemplating saving for retirement in a long-term equity mutual fund earning an average of 10%:

1. Sam begin investing immediately and saves $500 per month for seven years. Then he stops contributing due to family and other financial obligations. However, he doesn’t withdraw any money and lets it compound until age 65 and ends-up with $496,636.
2. Linda, due to not having extra cash, decided to delay investing for seven years until she is 35. However, once she starts contributing she doesn’t stop and continues until she is 65. She ends-up with $493,482.

Sam contributed $21,000 and accumulated $496,636. Linda contributed $90,000 and accumulated $493,482.

This demonstrates both the power of starting early, and the high cost of waiting.

“Compound interest is ugly in the early years, but beautiful in the later years.” ―Michael

Conclusion

Even the smallest amount of money, saved systematically over a period of time (Dollar-Cost Averaging), will multiply far beyond your expectations through the magic of compound interest. No amount is too small or insignificant to save. The important thing is to get some money started working for you as soon as possible.

“If you understand the math behind compounding you realize the most important question is not ‘How can I earn the highest returns?’ It’s ‘What are the best returns I can sustain for the longest period of time?’” ―Morgan Housel

If you would like to learn more on how to make compound interest work for you (and where to get long-term, historically defensible, sustainable returns) I invite you to schedule a no-obligation, no-cost conversation with me.

P.S. You may also be interested in my monthly client newsletter

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Michael Paulding Thomas

• Celebrating ,./36 years in the industry
• Investment Advisor • Securities Principal
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