The magic of compound interest

So you want financial independence? Want your money to work for you? But how? Well, investing is definitely a good place to start. Specifically, value investing. But how can we really grow wealth into a sum large enough to claim financial independence? The answer – using compound interest.

Talking points

  • What is compound interest and why is it important for investors?
  • Break down compound interest into equations and examples.
  • The magic of compound interest.

What is compound interest?

The basic and boring definition of compound interest is interest on the original principal plus accrued interest 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 on interest.

Whichever way you want to see it, compound interest will grow your investment much faster than simple interest, interest calculated on the principal only. We will see an example later in this article.

The concept of compound interest has been around for quite 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, this cannot work without two crucial elements: reinvested earnings and time.

For example, let’s say you have $10,000 earning 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 becomes $12,100 ($11,000 * 1.10). Note that if you reinvest your earnings, you earn $100 more over two years than if you took them out ($12,100 – $12,000). This is important for two reasons. First, you made more money using compound interest. And, second, you didn’t have to work at all; your money has worked for you. Although $100 may not seem like much, after many years, as I will demonstrate later, using compound interest will inflate your investment compared to using simple interest.


Allocation of compound interest

Before we continue, let’s take a brief look at the math behind this seemingly magical concept. It is important to understand the formula so that you can use it in different ways. It also allows you to modify some aspects of the formula to suit what you are calculating. I have a free spreadsheet that contains several financial calculators available with a click here.

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

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

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

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’ll add the monthly deposits. This solution actually calls for two equations; however, one of them we have already seen: FV=P*(1+r/n)^(t*n). The other equation concerns the aspect of the monthly addition. This equation is:

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

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

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

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

I know, your eyes are bright 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
  • FV = $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 equals a difference of nearly $30,000 over 10 years.

The magic of compound interest

Compound interest can transform your investments, but as you can see, monthly deposits and time really affect how it works. Let’s take two examples,

First, let’s say Red invests $10,000 and gets 10% annual returns for 20 years. Now suppose his 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 the entire term. The chart below shows the difference these monthly deposits can make.

02may2017164052.jpg

Notice how Blue’s investment more than doubles Red’s after 20 years. What a difference $100 a month can make! Also note how the curves show a significant increase in the second half of the graph. We will examine this in more detail next.

Now let’s say Red and Blue decide to invest the same amount ($10,000) and get the same annual returns (10%), but 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.

02may2017164053.jpg

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

Summary

  • 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 three crucial things: reinvested earnings, monthly deposits, and time.
  • As the graphs above show, these components can increase your investments by two to three times in as little as 10 years.

Start a seven day free trial Premium subscription to GuruFocus.

About the author