# What is compound interest and how does it work?

Albert Einstein described compound interest as “the eighth wonder of the world”, but what exactly is it? Compound interest is the interest that you receive on a principal amount, including the accumulated interest from previous periods of a deposit or loan. Simply put, it is the interest gained on money that was already earned as interest or the “interest on interest”. In contrast, simple interest is only paid on the principal amount and not on any accrued interest. In practice, compound interest is more common in comparison to simple interest.

## Factors that influence compound interest

• Frequency: Compounding frequency, or the number of times per year that interest payments are distributed, impacts compound interest. Interest is often compounded on an annual, semiannual, quarterly or monthly basis, but it can also be compounded daily or even continuously. For the most part, the more compounding periods there are, the greater the future value of your money will be.
• Interest rate: Interest rates can have a considerable effect. Higher interest rates will contribute more to an investment compared to a lower rate.
• Time: Compound interest has a greater impact on investments with a longer timeframe compared to a shorter one.

### How to calculate compound interest

If you are trying to figure out how to work out compound interest, it is relatively easy with the compound interest formula. Compound interest is calculated using the following formula:

A=P(1+ r/n)nt

In the formula, ‘A’ is the future value, ‘P’ is the principal, ‘r’ is the interest rate, ‘n’ is the number of compounding periods and ‘t’ is the time in years.

For example, say you deposit €1,000 in a savings account at the bank and you leave it there for 20 years. Your bank pays a 5% interest rate and interest is compounded annually. Without doing anything else, in 20 years, you will have €2,653.30.

Compound interest in investing works similarly. Say you invest €1,000 in an ETF that hypothetically has a 9% annual return. After the first year, your investment would grow to €1,090. While a €90 gain does not seem like much, time in the market can significantly grow your investment. After 30 years, your same investment would grow to be €13,267.68. This is an increase of €12,267.68 from your initial investment of €1,000.

### The rule of 72

The rule of 72 is a quick way to be able to estimate the time it takes to double an investment. Moreover, it is a shortcut to find out the approximate impact of compound interest. The rule of 72 formula is:

72/r=Y

Where r is the compound annual interest rate and Y is the number of years it will take to double your investment. Taking the 5% interest rate from above and using the rule of 72 formula, you would be able to double your money in 14.4 years. It is important to keep in mind that the rule of 72 is just an estimation. In this case, the actual amount of years it would take to double your money if interest was compounded annually would be 14.21 years. Although there is a small discrepancy in these figures, the rule of 72 can be used for easy estimation.

### Pros and cons of compound interest

The effect that compound interest can have can either positively impact you or cost you, depending on the circumstances. You can reap the benefits of compound interest in the scenario that you are the investor, whereby an investment can exponentially grow over time.

On the other hand, when you are the borrower, compound interest can be costly. This is most commonly the case with credit cards. Some credit card companies charge interest for borrowing money and on the amount of interest that has accumulated. Therefore, you can end up owing your credit card company significantly more than you initially borrowed.

### Risks involved

At DEGIRO, we are open and transparent about the risks that come with investing. Before you start to invest, there are a number of factors to consider. It helps to think about how much risk you are willing to take and which products match your knowledge. Additionally, it is not advisable to invest using money that you may need in the short term or to enter into positions that could cause financial difficulties. It all starts with thinking about what kind of investor you want to be. You can read more about the risks of investing on our dedicated risk page.  