Compounding Is Beautiful

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Time Is On Your Side

Compounding is a fascinating notion.

For example, if you delay a problem and ignore it, the worse the result will be. Likewise, the sooner you start something, the more benefit you will reap.

However, what does compounding have to do with investing? I’m glad you asked; compounding means that time is on your side, so stop waiting and invest!

What about an imminent crash, though!? Ignore the talkshow hosts. If you choose to slack, any missed returns will compound, too. These forgone returns are the opportunity cost of not investing. Hence, Buy Now & Tomorrow, But Don’t Buy The Drop!

Defining Compound Interest

Compound interest refers to growing your principal and previously earned growth concurrently. I.e., you receive gains on your total portfolio, not only the original principal.

Beautiful, Isn’t It?

The beauty of compounding is that your portfolio will double and someday reach a point where interest earned exceeds your initial principal. Now that is powerful.

Example: You invest $1,000, growing at 10% yearly. By year seven, your money has doubled. During year twenty-three, annual cumulative interest payments exceed $1,000. All while your portfolio has grown over $10,000 without further contributions!

Rule of 72

For those new to compound interest, let me introduce the Rule of 72. Simply put, to determine how often your money will double at a given growth or interest rate, divide the rate by 72. The answer will be a close estimate concerning how long your cash takes to double.

Example: 10%/72=7.2 years

Dean Interest Principle Equation

To determine how long it will take for your annual growth to exceed initial principal requires more effort than the Rule of 72, and frankly, I couldn’t find a capable equation. I tried to use my mathematic skills learned from university, but that was a lost cause. Thankfully, my friend, a former rocket scientist and now a data engineer, loves math. Enter the equation I named after him that solves for when annual growth exceeds the initial principal.

Starting on the day this equation generates, you begin the year when the sum of interest payments will be equal to your initial principal. If that is not a mouthful, I don’t know what is.

English translation: Every trading day subsequently for one year will generate interest that totals your initial principal.

Entering this equation into a calculator is tedious, so don’t. Instead, copy this text:

\frac{-\log\left(\left(1+\left(\frac{interest\ rate}{compounding\ periods}\right)\right)^{compounding\ periods}-1\right)}{compounding\ periods\cdot\log\left(1+\frac{interest\ rate}{compounding\ periods}\right)}

Then, paste it into this online scientific calculator, located here.

In my example, you begin receiving interest that will eclipse your initial principal amount on the one-hundredth thirty-third trading day of the twenty-second year of investing. I.e., trading day 133 of year 22.

Equation Terms Defined

Compounding Periods: How frequently interest compounds annually. I use two-hundred-fifty-two periods since there are approximately this many trading days in a year.

Interest rate: The return you expect over the future period, and in my example, I used 10%.

Closing Thoughts

Compound interest is a force that can bring rewards or regrets. In our example above, had you invested another $1,000 each consecutive year, you would have had over $100,000 by year twenty-three – all with only $24,000 in contributions.

For the curious minds that desire to play around with compound interest on their own, try this calculator provided by the Securities and Exchange Commission on Investor.gov. It is a great tool that can help chart out your potential future, and I use it regularly.

Thanks for reading, and as always, have a great day.

Quick Note On Variability Of Returns

Compound interest is a fanciful topic when discussing investing, as stock prices never go up predictably. Instead, prices fluctuate up, down, and sideways in random. Nevertheless, on average, the US stock market has returned ~10% annually since 1926. While we can never bank on the past for the future, it is a starting place to map out the future.