Compound interest

Why it’s the eighth wonder of the world

So you want Financial independence? Want your money to work for you? But how? Well, investing is definitely a great place to start. More specifically, investing in value. But how can we really grow wealth into a sum substantial enough to claim financial independence? The answer… using compound interest.

The basic and boring definition of compound interest is interest on the original principal plus interest accrued from previous periods. Or, in our case, an investment that earned interest (or dividends) that we reinvested in the original principle. It can also be thought of as interest over interest. Whichever way you want to think of it, compound interest will grow your investment much faster than simple interest, which is interest calculated solely on the principal. We will see an example later in this article.

The concept of compound interest has been around for some time. It is believed that Albert Einstein called it “the greatest mathematical discovery of all time” and “the eighth wonder of the world”. Compound interest can turn a small amount of money into a powerful, income-generating machine. However, it cannot function without two crucial elements: reinvested profits and time.

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For example, suppose you have $ 10,000 that earns 10% interest per year. After one year, you will have $ 11,000 ($ 10,000 * 1.10). If you reinvest the $ 1,000 you earned on interest rather than withdrawing it, your $ 11,000 increases to $ 12,100 ($ 11,000 * 1.10). Note that if you reinvest your earnings, you will earn $ 100 more over 2 years than if you had withdrawn them ($ 12,100 – $ 12,000). This is important for two reasons. First, you made more money using compound interest. And two, you didn’t have to work at all … you are money worked for you. While $ 100 may not seem like a lot, after many years, as I will demonstrate later, using compound interest will inflate your investment compared to using simple interest.


BREAKDOWN OF COMPOUND INTEREST

Before we continue, let’s briefly take a look at the math behind this seemingly magical concept. It is important to understand the formula so that you can use it in various ways. It also allows you to change certain aspects of the formula to match what you are calculating. I have a FREE spreadsheet which has several financial calculators available with a click here.

Let’s start with the basic formula for annual compound interest:

FV = P * (1 + r / n) ^ (t * n)

  • VF = Future value of the investment
  • P = Principal amount (initial deposit)
  • r = Annual interest rate
  • t = Number of years
  • n = Number of times compounded per year (12 = monthly; 1 = annually)

For example, if you invest $ 10,000 and get an annual return of 15% for 10 years, you would calculate:

  • VF = 10,000 * (1 + 0.15 / 12) ^ (10 * 12)
  • VF = 10,000 * (1.0125) ^ 120
  • VF = 10,000 * (4.44)
  • VF = 44,402.13

The investment balance after 10 years would be $ 44,402.13.

Next, let’s look at the same calculation, but this time we’re going to add monthly deposits. This solution actually calls 2 equations, however, one of them we have already seen: FV = P * (1 + r / n) ^ (t * n). The other equation concerns the monthly addition aspect. This equation is:

(DEP * (((1 + r / n) ^ (t * n) – 1)) / (r / n))

  • DEP = Deposit
  • r = Annual interest rate
  • t = Number of years
  • n = Number of times compounded per year (12 = monthly; 1 = annually)

So, the final compound interest formula with monthly deposits is:

VF = [P * (1 + r) ^ (t * n)] + [DEP * (((1 + r / n) ^ (t * n) – 1) / (r / n))]]

I know, your eyes are shining now. But let’s go through a quick example, and then we’ll end this section. If you invest the same $ 10,000, earn the same 15% per year for 10 years, and deposit $ 100 per month for 10 years, the formula would look like this:

  • VF = [10,000 * (1 + 0.15 / 12) ^ (10 * 12)] + [100 * (((1 + 0.15 / 12) ^ (10 * 12) – 1) / (0.15 / 12))]
  • VF = 44,402.13 + [100 * ((1.0125 ^ 120 – 1) / 0.0125)]
  • VF = 44,402.13 + [100 * ((4.44 – 1) / 0.0125)]
  • VF = 44,402.13 + [100 * (3.44 / 0.0125)]
  • VF = 44,402.13 + [100 * 275.22]
  • VF = 44,402.13 + 27,521.71
  • VF = $ 71,923.84

I love this formula because you can really see the power of compound interest as well as the magic of adding monthly deposits. A deposit of $ 100 per month equates to almost $ 30,000 difference over 10 years.


THE MAGIC OF COMPOUND INTERESTS

As I mentioned earlier, compound interest can really transform your investments, but as you can see monthly deposits and time really affect how it works. Let’s look at two examples,

First, let’s say Red invests $ 10,000 and earns 10% annual return for 20 years. Now let’s say her buddy Blue invests the same amount and also earns 10% annual return for 20 years. The only difference being that Blue also deposits $ 100 per month. for all the time. The graph below shows the difference these monthly deposits can make.

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Monthly deposits, no matter how small, make a huge difference

Notice how Blue’s investment more than doubles Red’s after 20 years. What a difference $ 100 a month can make! Notice also how the curves show a significant increase in the second half of the graph. We will come back later.

Now let’s say Red and Blue decide to invest the same amount ($ 10,000) and get the same annual returns (10%), only this time, Red decides to invest 10 years after Blue. In this example, Red and Blue also contribute $ 100 per month. The chart below shows the importance of the time component in compound interest.

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Time is of the essence when it comes to compound interest

Starting just 10 years earlier than Red, Blue’s investment has more than tripled in value. Blue appears to be a smart man. And these charts show the importance of monthly deposits and getting an early start when it comes to investing.


ABSTRACT

  • Albert Einstein called compound interest “the greatest mathematical discovery of all time” and “the eighth wonder of the world”
  • But to get the most out of it, you need 3 crucial things: reinvested earnings, monthly deposits, and time.
  • As the charts above show, these components can increase your investments 2-3 times in as little as 10 years.

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