Step 1: Change Your Life With One Calculation

If there were an eighth wonder of the world, we’d nominate the equation for compound interest:

Your money x (1 + i)^n

(If you’re not a math wizard, don’t worry; we’re going to decipher that for you.)

Albert Einstein called this deceptively simple formula the “greatest mathematical discovery of all time.” We call it your ticket to financial independence.

That’s right, just three straightforward inputs can change your life: the amount of money you invest; the rate of return you get (i); and how much time you have to let your money grow (n, in years).

Hate math but like money? Read on.
Since words cannot adequately describe the magical nature of compound interest, let’s try a few visuals.

Here’s how a single €2,000 investment grows over time in four savings scenarios.

How a single €2,000 investment grows

  Savings Account (0.5%) FestinsSparen (1.5%) Deutsche Bund (2.5%) Stock Market (9%*)
Initial Investment € 2,000 € 2,000 € 2,000 € 2,000
5 years € 2,051 € 2,208 € 2,553 € 3,077
10 years € 2,102 € 2,438 € 3,258 € 4,735
15 years € 2,155 € 2,692 € 4,158 € 7,285
20 years € 2,210 € 2,972 € 5,307 € 11,209
25 years € 2,266 € 3,281 € 6,773 € 17,246
30 years € 2,323 € 3,623 € 8,644 € 26,535

* The annual return of the DAX over the last 30 years.

As you can see, simply socking away one lump sum and leaving it put could turn €2,000 into more than €26,500 over 30 years. Not only have you earned interest, but you’ve earned interest on your interest. And all you had to do was invest your first paycheck.

But let’s be honest: €26,535 won’t even buy a decent car these days. So let’s make one small revision and invest €2,000 every year. Behold the power of compound interest with regular contributions!

A more compelling table than the previous one 

  Savings Account (0.5%) FestinsSparen (1.5%) Deutsche Bund (2.5%) Stock Market (9%)
Initial Investment € 2,000 € 2,000 € 2,000 € 2,000
5 years € 12,202 € 12,824 € 14,156 € 16,124
10 years € 22,661 € 24,775 € 29,671 € 37,855
15 years € 33,384 € 37,970 € 49,473 € 71,292
20 years € 44,378 € 52,539 € 74,745 € 122,738
25 years € 55,649 € 68,623 € 107,000 € 201,894
30 years € 67,206 € 86,382 € 148,165 € 323,686

Now we’re at more than €300,000. Not bad, right? Still, we think you can top it. In fact, it’s not a stretch to get near that magical €1 million milestone. All you have to do is save €7,000 a year (or just €584 per month), and at 9% you’ve got a million euros in 30 years. Or stick with the €2,000 annual contribution but improve your investing skills (which the rest of this series will show you how to do). If you are able to best the DAX’s average annual returns by 6 percentage points, the €1 million prize is yours.

And the best part about compound interest is that it works the same for everyone, whether you have €200 to invest or €200,000. Go ahead, tinker with this compounding calculator to see what we mean. If you don’t believe you can become a millionaire with just the resources you have right now, keep reading.

The amazing tale of the washer woman
Oseola McCarty was born in the southern part of the USA in 1908. For nearly 75 years, she lived in the same simple house, washing other people’s clothes for a living and putting whatever money she could into savings accounts at local banks.

In the summer of 1995, Oseola made national news when she donated $150,000 to a local university to establish a fund to help new students. “I just figured the money would do [the students] a lot more good than it would me,” she said. It soon came out that this washer woman had managed to amass nearly one quarter of a million U.S. dollars over her lifetime.

Time — a key part of the compounding equation — helped turn her meager early investments into hundreds of thousands of dollars.

We like this ending better
As remarkable as the Oseola McCarty story is, the ending could have been a blockbuster. After she died in 1999, one of her bankers wrote to us saying: “Time was able to turn even the modest returns of her early investments into hundreds of thousands of dollars. If we had been able to introduce her to stocks earlier, she would have left millions instead of thousands.”

Remember, the amount you save and your time horizon — how long you have until you need the money you’ve invested — are only two-thirds of the compounding equation. Oseola excelled in both. But she did pay a price for ignoring the rate of return on her investments.

Typically, the more risk you are willing to take on (by, say, investing in stocks rather than bonds), the higher your potential return. But risk is not something many people are comfortable with: They’re happy to settle for lesser returns to avoid it.

Bad idea. Stuffing all your savings into a metal box — or sticking only with safer investments like FestinsSparen or Deutsche Bunds — is even more disastrous. It’s not simply that they return less. It’s that they barely keep up with the rate of inflation, and that means your savings are not going to go as far as you think. We Fools believe the best place for your long-term (key word … as you’ll discover in Step 4) savings is the stock market.

Your golden ticket to financial independence
There you have it: Financial independence is just three variables away. So start saving now (as much as you can), and invest it well. Because the sooner you get the wonder of compounding working for you, the sooner you’ll reach your financial dreams. And that’s exactly what this series will help you do.

Action: Are you ready for more? We’ll keep it easy: Now, you should go ahead and read the rest of the “How to Invest” series. Just click the link below for Step 2.