### compounding

### compounding explained

Called the "eighth wonder of the world" by Albert Einstein, **compound interest** is not always understood, but crucially important. Nowhere less so than in the protection of your hard-earned wealth. When comparing investment returns of stocks, bonds, bank deposits, real estate, gold, or cryptocurrency, you must compare them not by the *gross return*, but by the **compound return**. The fancy terms in the financial world, such as "compound interest", "annual percentage rate" (APR), "internal rate of return" (IRR), "yield-to-maturity" (YTM), and "compound annual growth rate" (CAGR) actually all mean the same thing: the **compound return**!

Important: **compound return** is always stated as an annual figure.

Let's take a simple example then, comparing Bitcoin's *gross return* and **compound return**, versus the US dollar. Assume you bought Bitcoin 2.5 years ago with US dollars:

Notice the *gross return*. A fantastic return and a current appeal of crypto. But it's not the number you need to know, to understand what it means versus other investments. That's where **compound return** comes in. To understand that, you need to take into account those *2 years and 6 months which have passed*, and "smooth out" your return to a **compounded, geometric rate of return**. Don't worry about how to calculate it. It's not simply dividing the gross return by 2.5 (though doing that does get you pretty close). Notice then, how the correct answer for **compound return** is quite different from *gross return*. This is the figure you must know to accurately compare your investment return to all others, such as interest rates, APRs, deposit rates, IRRs, bond yields, or even holding US dollars (as in this example).

**Doubling time**. Another very important, and simple way to look at **compound return*** *is to use the **Rule of 72**. This is a back-of-the-envelope way to see how long it takes your investment to *double,* according to its **compound return**. Very simply, to find an investment's doubling time, divide 72 by its **compound return**, without its '%' sign! Notice how it's calculated above.

Here are the doubling times for various **compound returns** using the Rule of 72:

Investment yielding a

**2% compound return**= 36 years to doubleInvestment yielding a

**10% compound return**= 7.2 years to doubleInvestment yielding a

**300% compound return**= 0.24 years or 3 months to double

Note that these are *approximate*. The actual calculation for doubling time is more complex, but the Rule of 72 gets you close. It's most accurate around a **10% compound return**—the further your **compound return** is from this number, the less accurate the Rule of 72 is.

Another point. The world is awash with *negative interest rates*, and *central bank inflation*. Therefore, by charging you a negative bank deposit rate of say, 1%, and increasing prices by about 2% each year via central bank inflation, this adds up to a 3% "invisible tax" to you (in reality, it's likely much more). Both of these costs, *negative interest rates* and *central bank inflation*, are generally promoted around the world as standard, monetary *policy* today. This means that the authorities actually target—according to their own policies—a *halving of your purchasing power*—for your dollar, euro, rupee or yen—at least every 24 years.

These are some reasons why cryptocurrency is so different, and so important.

The charts above graph the **compound returns**—*as of** **today*—for various cryptocurrencies versus the US dollar. Note that these returns will change as the days roll by. Unlike a traditional chart, the "history" of this chart will change over time, based on **today's **price. To find your **compound return** from a crypto investment at any given time, simply find the approximate date you purchased a coin. The displayed % figure reflected in the green line ** at that time** is your

**compound return**, if you held the investment

*until today*. The calculations always start more than 180 days ago (i.e. one must have at least a 180 day "holding period" to see their returns in this chart).

Keep the Rule of 72 in mind.

Source: Coin Metrics, CoinMarketCap, Blockchain, BitInfoCharts