Compounding

Why this matters

Compounding is the reason long-term investing works the way it does. It explains why small amounts can grow large, why starting early matters so much, and why things like fees and debt can quietly cost more than they seem to.

Returns on returns

Say you invest $10,000 and it earns 7% in a year. You gain $700 and now have $10,700. In the second year, 7% is earned on the whole $10,700, not just the original $10,000. So you gain $749, not $700.

That extra $49 is small, but it's the start of compounding:¹ your earlier gains are now earning gains of their own. Each year, the amount doing the earning is a little bigger than the year before.

After	Gains taken out each year	Gains left to compound
10 years	$17,000	$19,672
20 years	$24,000	$38,697
30 years	$31,000	$76,123

In the first column, the $700 of gains is taken out every year, so only the original $10,000 keeps earning. The total grows in a straight line. In the second column, the gains stay invested. After 30 years, the difference is more than $45,000, and almost all of it arrives in the later years.

A shortcut: the Rule of 72

To estimate how long money takes to double, divide 72 by the yearly growth rate. This is the Rule of 72.

• At 7% a year: 72 ÷ 7 ≈ 10 years to double.
• At 4% a year: 72 ÷ 4 = 18 years.
• At 9% a year: 72 ÷ 9 = 8 years.

It's an approximation, but a close one for ordinary rates.² It also shows how much the rate matters: at 9%, money doubles more than twice as fast as at 4%.

Why starting early matters

Because compounding does most of its work in the later years, time can matter more than the amount you invest. Here's a hypothetical example, using a steady 7% a year to keep the math clear.

	Priya	Marcus
Invests each year	$2,000	$2,000
Ages	25 to 34, then stops	35 to 64
Total put in	$20,000	$60,000
Value at 65	about $210,000	about $189,000

Priya puts in a third as much money and stops after ten years, yet finishes ahead. Her money simply had ten more years to compound. The numbers are hypothetical, and real returns would vary year to year, but the pattern holds: early dollars have the most time to grow.

Try it yourself

Change the numbers below. Try adding ten years without changing anything else, then try doubling the monthly amount instead, and compare the two.

Key takeaways

• Compounding means earning returns on earlier returns, so growth speeds up over time.
• Most of compounding's effect arrives in the later years, which is why time matters so much.
• The Rule of 72 estimates doubling time: divide 72 by the yearly rate.
• Compounding also magnifies losses, fees, and debt interest.

Check your understanding

Using the Rule of 72, roughly how long does money take to double at 6% a year?

1. 6 years
2. 12 years
3. 17 years

Two funds hold the same investments. One charges 0.1% a year in fees, the other 1%. Over 30 years, what happens to the difference?

1. It stays about 0.9% of the value, since that's the fee gap.
2. It disappears over time, because the investments and their returns are the same.
3. It grows much larger than 0.9% of the value, because the fee compounds.

What's next

So far, every dollar has been treated as a dollar. But a dollar in 20 years won't buy what it buys today. The next lesson, Inflation and Purchasing Power, looks at what your money is actually worth over time.