# PSU Insight

## The Awesome Power of Compounding

I’ve saved the most impressive — and arguably the most important — concept of “running the numbers” for last.

As you know, Albert Einstein was one of the most brilliant men of the past century. Most people associate Einstein with the discovery of the equation E = mc^{2} which led to the development of atomic energy. But atomic energy didn’t impress Einstein nearly as much as our next “running the numbers” idea — compounding.

In fact, Einstein maintained that compounding is **“the greatest mathematical discovery of all time.”** As you’ll shortly see, Einstein wasn’t exaggerating.

Now “compounding” can sound complicated, but it’s really not. It’s simply applying a percentage, over and over again. That is, you increase something by a percentage. Then you increase that increased amount by the same percentage. Then you again increase that new increased amount by that same percentage. The percentage of increase stays the same, but the actual amount of the increase increases.

That may still sound confusing, but it’s a lot easier to see an actual ‘run the numbers’ example….

Let’s suppose that you create an e-commerce site. Like many e-commerce sites, it’s slow going at the beginning. In fact, business is so slow, you show a profit of only $1 your first day of operation. (One dollar is a nice round number.)

One dollar for one day’s activity isn’t much. What about the second day? If you have no growth, it’s easy to see that you’re not going to make much money through that venture. (If your business stays constant at $1 per day, you’ll make $365 per year, a relatively paltry sum.)

So let’s be optimistic and imagine that your on-line business grows. First, let’s consider a constant growth. Let’s say that your income grows by $1 per day every week. That means that in the first week, you make $1 per day; in the second week, you make $2 per day; in the third week you make $3 per day; in the fourth week, you make $4 each day, and so on.

An increase of a dollar a day per week is not an unreasonable growth rate to anticipate. Unfortunately, it doesn’t produce much in the way of impressive results either.

It doesn’t take a calculator to see that starting with $1 a day in income, by the end of the first year (52 weeks) of operation, you’re making slightly over $50 per day. Now if that’s in addition to your other income, that’s not bad money. (But if that’s your total income, you’re hurting.)

So let’s give your on-line business another year of the same weekly increases — $1 per day. That means by the end of your second year (another 52 weeks), you’re making slightly over $100 per day. That’s not bad money, but it’s far from a fortune. At the end of three years, you’re making over $150 a day. You’re getting there, slowly but surely.

Let’s say you’re in this for the long-term, so you stick with it. If you increase your income by $1 per day every week, after ten years you’re making over $500 per day. Hooray! Now we’re finally talking about some serious money.

But it took you ten years to get here. Isn’t there another approach? Fortunately, there is….

Let’s consider another type of growth, growth by a percentage. Starting with your original $1 per day in income, let’s imagine that your income grows by 10% (a nice round — and not unreasonable — number) each week (instead of the $1 weekly increase that we just considered).

In this example, that means that the second week you make $1.10 per day; the third week, you make $1.21 per day; the fourth week, you make $1.33 per day, and so on.

Now the “obvious” conclusion is that this is a poorer growth rate. In the fourth week you’re only making $1.33 per day, where you were already making $4 per day in the previous example. In fact, you’re near the end of your second month before you reach $2 per day in income, the amount you reached in your second week in the first example.

But here’s where the “magic” occurs. If you keep increasing your income by 10% every week, by the end of your first year your income will have reached slightly over $140 per day… **almost triple your income using the original dollar-a-week rate of growth.**

But why should we stop with one year? Let’s imagine that you continue your 10% per week growth rate. By the end of your second year, your income will have reached (are you ready for this?) a whopping twenty thousand dollars… per day.

(If you don’t believe this — and I don’t blame you for doubting it — it only takes a minute or two with a calculator to verify. Or you can search for “compound interest calculators” on the Internet to make the task even easier.)

Here’s what that means —

If your business levels off after two years and never grows after that, that’s still an income of **over seven million dollars a year**… starting with an income of only $1 a day, and increasing by only 10% each week for only two years.

Now you may be protesting that 10% is still a hefty percentage. Does this work with smaller percentages? Yes, it does! Not as quickly, of course, but it still works.

Let’s consider another example. Like before, you have an e-business that starts off by producing $1 a day in income. What happens if you increase your income by a mere 1 %, each and every day?

Now a one-percent increase is tiny. That means that if you make $1 on January 1, you make one penny more on January 2, $1.02 (technically $1.0201) on January 3, and so on. Certainly not much money to start with. But by December 31, you’re making almost $40 a day. Not bad.

But wait, there’s more. By December 31 of the second year, you’re making over $1400 per day. And by the end of the third year, you’re making almost $54,000... per day! All it takes is a one-percent increase, each and every day.

Is that still too much growth for you? How about a 1% growth per week (not per day)? Starting with $1 per day our first week, you make a measly $1.01 per day the second week, $1.02 per day the third week, and so on. Your growth is barely perceptible — but it’s there.

It will take two decades, but I think you’ll agree that it’s worth the wait. Starting with an income of $1 a day and increasing your income by a mere 1% per week, after 20 years your business will be producing over thirty-one thousand dollars. Per day!

So it all comes down to this — if you increase your income by a percentage instead of by a constant amount (like the $1 per week in the first example), your cumulative increase over time is staggering.

As you would expect, the higher your percentage increase, the less time it takes. But even a small percentage, applied over a sufficiently long period, can yield impressive results.