What is compound interest and how does it work?

What is compound interest?

Compound interest is the accumulation of returns on top of previous returns. That’s why it’s an investor’s best friend and allows you to accumulate wealth over the long term.

It’s often said that Einstein once defined compound interest as the eighth wonder of the world.

Is it true that Einstein said that? We don’t really know, but we do know for sure that compound interest is a pretty powerful force.

How does it work?

Let’s look at an example of how compound interest works, as this is the best way to understand it.

Let’s say you have €10,000 and you invest it in a financial instrument that pays 10% per year for 30 years.

By reinvesting the annual interest you receive in the same investment, at the end of 30 years you will have accumulated €174,500. This means that your initial capital would have multiplied by a factor of 17.45 and you would have generated interest of €164,500.

Wow! Not bad at all. You’ve multiplied your initial capital by more than 17 times! Let’s see how this is possible.

In the previous example, we considered that all the interest payments you receive during the life of the investment are reinvested.

Now, let’s take the example to the other extreme, we change the way of managing the interest and assume that you do not reinvest the interest; that is, you withdraw it from the investment every year.

Thus, at the end of the 30-year period, you will only have the initial €10,000 plus the annual payment of 10% calculated over 30 years, but on the initial capital of €10,000. This means that without reinvestment you would have €40,000:

Calculation: €10,000 + (€10,000 * 10% per year) * 30 years = €40,000.

To simulate how compound interest would be applied in an inbestMe portfolio, you can use our simulator.

What is compound interest, in detail?

It is clear that the reinvestment of interest results in a large difference in the final capital. More than €135,000 difference must have something to do with the issue of reinvestment of the interest received.

To understand compound interest in more detail, let’s look at the mechanism under which the effect of reinvesting interest is so powerful.

Let’s assume that we start with €10,000, as in the previous example.

At the end of the first year, since the investment pays 10% annually, we will receive a payment of €1,000 (€10,000 * 10%).

To understand compound interest, we will reinvest the payments we receive. So, if we reinvest the €1,000 received, we will start the second year with a capital of €11,000 (€10,000 + €1,000).

On this capital, the €11,000 (not the initial €10,000), a 10% interest payment will be calculated for the second year, which will amount to €11,000* 10% = €1,100.

We see that the interest payment in the second year is higher (€1,100) compared to the first year (€1,000).

The difference of €100 is due to the fact that also the €1,000 received at the end of the first year has been added to the initial capital for the following year, so the interest for the second year is calculated including this €1,000.

The €100 plus interest received at the end of the second year is exactly interest on interest: €1,000 * 10% = €100.

If we look at compound interest in a more mathematical way:

• Initial capital = €10,000
• Interest at the end of year 1 = €1,000 (€10,000 * 10%)
• Capital at the beginning of year 2 = €11,000 (10,000 + 1,000)
• Interest at the end of year 2 = €1,100 (11,000 * 10%)
• Capital at the beginning of year 3 = €12,100 (11,000 + 1,100)
• Interest at the end of year 3 = €1,210 (12,100 * 10%)
• And so on year after year until you reach your financial goal.

As you can see, the large effect on the final value of the investment from reinvesting interest is due to the fact that the annual payments are calculated on the growing capital base. This makes the payments larger.

Simply keeping the example limited to the first 3 years, you can see that 10% interest is initially calculated on an initial capital of €10,000; in the third year, 10% interest is calculated on the €12,100.

If we graph this effect, we can see how the capital growth accelerates as the holding period increases due to the accumulation of interest on interest (green line).

Of course, we have made some simplifications, as investment returns are not always positive. But, at least in past history, a globally diversified portfolio has always shown positive results over the long term.

How can you benefit from compound interest?

We must remember that we have made 2 rather strong assumptions for the power of compounding to develop properly:

1. All cash flows received are reinvested.
2. The investment is maintained over the long term.

Of course, this is not easy to do if you invest on your own, as it requires a certain discipline to regularly reinvest and maintain your investment over the long term, even in tough market times when emotions can lead you to exit the investment.

inbestMe can help you on both counts, systematically reinvesting your profits and helping you stay on track when it is more emotionally difficult. Our portfolios by definition take advantage of the power of compound interest:

• We prefer to use index funds or ETFs that accumulate dividends in the fund itself.
• When this is not the case, they are reinvested again in proportion to your risk profile.

In this way, you will put luck on your side to make your money grow in a systematic, mechanical and accelerated way thanks to what is called the capitalization of returns or the magic of compound interest.