The phenomenon of compounded growth is truly remarkable. If we put it to work for us, it can do glorious things.

Most importantly, it can help us grow wealthier and amass a necessary and sizable nest egg, all without massive effort on our part. Here's a closer look at compounding and what it can do.

A couple is looking at an open laptop and looking amazed and happy.

Image source: Getty Images.

On compounded growth and compounding

While compound interest is a classic example of compounding, compounded growth also occurs elsewhere, such as in our investments in stock. Here are what some of history's best investors have said about compounding:

"Enjoy the magic of compounding returns. Even modest investments made in one's early 20s are likely to grow to staggering amounts over the course of an investment lifetime."
-- John C. Bogle

"Understanding both the power of compound interest and the difficulty of getting it is the heart and soul of understanding a lot of things."
-- Charlie Munger

"My wealth has come from a combination of living in America, some lucky genes, and compound interest."
-- Warren Buffett

How compounding works

Let's get back to the example of interest. Money in an account might grow via simple interest or compound interest. With simple interest, you keep earning a rate of return on your original principal. With compound interest, as your balance grows, you earn that rate of return on ever-larger amounts. Here's an example, featuring 10% growth:

Year

$1,000 Earning 10% Simple Interest

$1,000 Earning 10% Compound Interest

1

$1,100

$1,100

2

$1,200

$1,210

3

$1,300

$1,331

4

$1,400

$1,464

5

$1,500

$1,611

6

$1,600

$1,772

7

$1,700

$1,949

8

$1,800

$2,144

9

$1,900

$2,358

10

$2,000

$2,594

11

$2,100

$2,853

12

$2,200

$3,138

13

$2,300

$3,452

14

$2,400

$3,798

15

$2,500

$4,177

Data source: author.

The next table shows what's happening in more detail -- noting how much the account grew by in each year when compounding was at work:

Year

$1,000 Earning 10% Compound Interest

How Much the Account Grew By

1

$1,100

$100

2

$1,210

$110

3

$1,331

$121

4

$1,464

$133

5

$1,611

$147

6

$1,772

$161

7

$1,949

$177

8

$2,144

$195

9

$2,358

$214

10

$2,594

$236

11

$2,853

$259

12

$3,138

$285

13

$3,452

$314

14

$3,798

$346

15

$4,177

$379

Data source: author.

You can see that the amount by which the account grows is increasing from year to year. That's the magic of compounding. It's kind of like how a snowball gets bigger and bigger as it keeps rolling.

Putting compounding to work for yourself

So how can you tap into this amazing power of compounding? Well, one great way is to have it help you amass a hefty nest egg for retirement. (Social Security will only get you so far, after all, with a recent average annual retirement benefit of about $22,860, as of December.)

Much of the compounded-growth wonder happens kind of automatically, but for best results, it does require two things from you: investing money regularly and then being patient. Really patient.

Here's how your money might grow over time at an average annual rate of 8%:

Growing at 8% For:

$7,000 Invested Annually

$15,000 Invested Annually

5 years

$44,351

$95,039

10 years

$109,518

$234,682

15 years

$205,270

$439,864

20 years

$345,960

$741,344

25 years

$552,681

$1,184,316

30 years

$856,421

$1,835,188

35 years

$1,302,715

$2,791,532

40 years

$1,958,467

$4,196,716

Data source: author.

You'll see that the amount by which your nest egg grows will itself grow from year to year, on average. (The stock market doesn't go up in a straight line, though -- there will be down years, though they have generally been eclipsed by up years.)

Much depends on your growth rate, too. You are never guaranteed any rate with stocks, but know that over many decades, the stock market has averaged annual returns of close to 10%. Over your particular investing period, though, it might average 6% or 12% or some other rate.

The next table shows how $10,000 invested annually will grow and compound at several different rates.

Growing For:

Growing at 6%

Growing at 8%

Growing at 10%

10 years

$139,716

$156,455

$175,312

15 years

$246,725

$293,243

$349,497

20 years

$389,927

$494,229

$630,025

25 years

$581,564

$789,544

$1.1 million

30 years

$838,017

$1.2 million

$1.8 million

35 years

$1.2 million

$1.9 million

$3.0 million

40 years

$1.6 million

$2.8 million

$4.9 million

Data source: author.

If you're not already watching your investment accounts grow over time, it's a great time to start. The best way to maximize your growth is to sock away meaningful sums regularly. The more you save and invest, and the earlier you do so, the more money you might amass. Your earliest invested dollars are your most powerful ones -- as they have the most time in which to grow for you.