What is compound interest and how does it work?

Albert Einstein famously referred to compound interest as ‘the eighth wonder of the world’. But what does it really mean? Compound interest is the interest you earn on your initial principal amount, plus the interest that has been added over previous periods. In simple terms, it’s ‘interest on interest’. Unlike simple interest, which is calculated only on the principal amount, compound interest considers the accumulated interest, allowing your money to grow at a faster rate. This makes compound interest a crucial concept in saving and investing.

How compound interest works

The power of compound interest lies in its ability to accelerate the growth of your money. By compounding more frequently—whether daily, monthly, quarterly or annually—your investment's value increases exponentially over time. The formula for calculating compound interest is:

A=P(1+ r/n)^nt

Where:

A: This is the amount of money accumulated after n years, including interest.
Principal (P): This is your initial investment or the amount you are starting with. For example, if you invest €1,000, this will be the basis of your calculations.
Annual interest rate (r): This is the percentage at which your investment will grow each year. It's important to convert this percentage into a decimal for the formula. For example, a 9% interest rate would be expressed as 0.09.
Compounding frequency (n): This is how often the interest is calculated and added back to the principal. Interest can be compounded annually, semi-annually, quarterly, monthly or even daily. The more often interest is compounded, the more interest you will earn over time. For annual compounding, n would be 1; for monthly compounding, it would be 12.
Time (t): This is the length of time the money is invested or borrowed, measured in years. The longer you keep your investment, the more you can benefit from compounding.

How to calculate compound interest

Let's look at a practical example to illustrate how to use the compound interest formula. Suppose you decide to invest €1,000 in an exchange-traded fund (ETF) that will provide an annual return of 9%, compounded annually. You want to find out how much your investment will grow over 30 years.

Identify the variables:
- P = €1,000 (the capital)
- r = 0.09 (9% expressed as a decimal)
- n = 1 (compounded once a year)
- t = 30 (the investment period in years)
Insert these values in the formula:
A = 1,000*(1 + (0.09/1))^(1*30)
Simplify the equation:
A = 1,000*(1.09)^30
Calculate 1.09^30:
Using a calculator, you would find that 1.09^30 = 13.26768
Finally, calculate A:
A = 1,000*13.26768 = 13,267.68

After 30 years, your initial investment of €1,000 would grow to approximately €13,267.68, resulting in a total increase of €12,267.68 due to the power of compounding. This example illustrates how significant the growth can be if you invest your money over a long period of time, especially with a reasonably high interest rate.

The rule of 72

The rule of 72 is a quick way to estimate the time it takes to double your investment. Here’s the formula:

72/r=Y

Where r is the annual interest rate and Y is the number of years to double your investment. For instance, at a 5% interest rate, your money would double in approximately 14.4 years. While this is an estimation, it provides a useful guideline for understanding the impact of compound interest.

This rule is particularly effective for interest rates in the 6% to 10% range, where it tends to give reasonably accurate estimates. However, it can still provide insights for rates outside this range, albeit with slightly less precision.

Compound interest vs. simple interest

Simple interest is calculated solely on the initial principal, while compound interest considers both the principal and the accumulated interest. This difference can lead to significantly varied outcomes over time, making compound interest a more powerful tool for growing savings and investments.

The key difference lies in the frequency of compounding. Interest can be compounded annually, semi-annually, quarterly, monthly or even daily, which can significantly impact the total amount of interest earned over time. The more frequently the interest is compounded, the greater the amount of interest you will earn.

Over longer periods, the difference between compound and simple interest becomes even more pronounced. For instance, if we extend the investment period to 30 years, the disparity becomes remarkable. With simple interest, you would earn a total of €1,500 on the original €1,000 investment (5% of €1,000 for 30 years). However, with compound interest, the growth can lead to significant wealth accumulation. The same €1,000 invested at 5% compounded annually for 30 years would grow to approximately €4,321.94, illustrating the exponential growth potential of compound interest.

Pros and cons of compound interest

Pros

Builds wealth: Unlike simple interest, which only applies to your initial investment, compound interest allows you to earn interest on both your principal and any accumulated interest. This means your money can grow significantly, especially if you start investing early and let it compound over time.
Wealth preservation: In a world where inflation can erode your savings, compounding helps to preserve the purchasing power of your money.
Repaying loans: When it comes to loans, making larger payments can actually work in your favour. By paying off your loans faster, you'll reduce the principal amount, which in turn reduces the total interest you'll pay overtime.

Cons

Debt accumulation: On the downside, compound interest can work against you if you have high-interest debt, such as credit cards. If you only make minimum payments, your debt can grow quickly, leading to a cycle of escalating payments.
Tax implications: While the returns from compounding can be substantial, they often come with tax implications. Interest earned is usually taxable, which can reduce your net returns.
Complex calculations: Although the concept of compound interest is simple, the calculations can become complex, especially with varying interest rates and compounding frequencies. This complexity can be a challenge for many, so it is important to use resources or financial tools to help you make accurate calculations.

Key takeaways

Compound interest, often referred to as ‘interest on interest’, accelerates the growth of your investments by allowing you to earn interest on both your initial principal and any previously accumulated interest.
The longer you invest and the more often interest is compounded - whether annually, monthly or daily - the greater the growth of your investment.
The rule of 72 provides a simple way to estimate how long it will take to double your investment based on a fixed annual interest rate. For example, at an interest rate of 5%, your investment would double in approximately 14.4 years.
Unlike simple interest, which is calculated only on the principal, compound interest takes into account both the principal and the accumulated interest, leading to very different results over time. This difference becomes particularly important over longer investment periods.
While compounding can significantly increase wealth and help preserve purchasing power against inflation, it can also lead to debt accumulation for borrowers with high interest debts. In addition, the tax implications of the interest earned, and the complexity of the calculations can be challenging for investors.

The information in this article is not written for advisory purposes, nor does it intend to recommend any investments. Please be aware that facts may have changed since the article was originally written. Investing involves risks (e.g., price volatility, currency or liquidity risk). You can lose your invested funds. Consider your knowledge and experience when making investment decisions. Past performance is not a reliable indicator of future results. Markets are volatile and can fluctuate significantly due to economic, political, regulatory, or other developments.