# Compound interest – what is it?

When it comes to investing and saving, compound interest is a major topic. But what is it in practice?

EUR

## Compound interest calculator

€500

200

20 years

7 %

### Would you like to use interest rate variance?

Range of interest rates (above and below the rate set above),
that you desire to see results for

## How does the Sortter's compound interest rate calculator work?

If maths isn’t your favourite subject, the easiest way to find out how much you could end up with is to use a compound interest calculator. The calculator shows how much you would earn over the years if you deposited a certain amount in a cash-generating savings account, such as a securities account/book-entry account or a fund.

There are several compound interest available for consumers, and Sortter has its own. The different calculators work in much the same way, but may differ in their infographics and how they present the accrual of interest.

Use the compound interest calculator in the way that suits your own goals.

For example, you might want to:

1. Find out how much you could save in 10 years.
2. See how long you would have to save to have €5,000.

The Sortter's compound interest calculator will ask for the following information:

• Starting amount
• Monthly savings amount
• Expected return
• Investment period
• Variation in expected return

The starting amount is the initial sum you invest.

The monthly savings amount is simply the amount you add to your investment each month.

The expected return on investment is based on current interest rates. The higher the expected return, the more you will add to your savings, but the risks are also accordingly higher.

Investment time is simply the length of time you plan to save and invest. If you’re planning to save for your retirement and are now around 30, you could set the investment period to 30 years, for example.

The calculator also has an option for variation in the return on investment. You can activate this additional function if you wish.

Sortter’s compound interest calculator gives an estimate of the amount of interest that is compounded over the investment period. The calculation does not take into account factors that may reduce performance, such as inflation or fees charged by the investment fund. A good rule of thumb is that the administrative costs of the investment should not exceed 0.5%.

To minimise these costs, you should consider opting for a low-cost fund. In general, passive index funds are the cheapest, and Nordnet, for example, offers a completely cost-free index fund.

The compound interest calculator gives you a summary in both figures and graphs. The bar chart also shows, in different colours, the variation of the expected return (+/- 2%) and the value of your investment, provided you have chosen to include it in the calculation.

## Compound interest – what is it?

When it comes to investing and saving, compound interest is a major topic. But what is it in practice?

No doubt you’ll have heard of compound interest, as it has long been the subject of much discussion in the investment world in particular.

It can rightly be said to be the cornerstone of investing. Interest rates on deposits in ordinary bank accounts and savings accounts are now so low that the return is meagre. Because of this, it’s a better idea to invest your savings.

Many people considering investing wonder whether they can benefit from the compounding of interest. Even if you start with only a small investment, over the years the savings and the return on them can add up nicely.

A compound interest calculator can give you a better grasp of your investment over the long term. It tells you how much your investment could yield over a certain number of years.

But what is compound interest all about? How much extra money can it make you? What is the compound interest formula? And how does the compound interest calculator work?

We’ll look at these shortly, after a quick run-through of the basics.

## What is compound interest?

It is often repeated that none other than Albert Einstein is said to have referred to compound interest as “the eighth wonder of the world.”

Compound interest is a means of growth, and is not hard to understand: it is the interest that is earned on interest. When you invest a certain amount of money, interest on it slowly starts to accrue in the same way that the total outstanding amount of a loan, for example, increases due to the accumulation of interest. The difference, however, is in who benefits: in the case of a loan you pay interest to the bank, whereas with an investment the interest is added to your investment capital.

Compound interest really starts to come into its own over a longer period. After a year or so, you’ll start to see some results as interest starts to compound on the amount you invested.

How compound interest works can be better understood by way of an example.

Let’s say you start by investing €500 in a fund. If the interest rate were 5%, a year later you would have €525. This amount will increase again by 5%, leaving you with €551.25 after another year. And after a third year, the amount will be €578.81.

So, even if you do not add to the investment, by compounding over the course of time the interest rate will increase the return on your investment, for as long as you keep your capital and the accumulating returns on it invested.

## What does interest on a loan mean?

Although I’ll discuss compound interest mainly from the perspective of saving and investing, it can also work the other way round. This is the case when you take out a bank loan, for instance, where you are the payer instead of the recipient.

In practice, interest is the cost of taking out consumer credit that you will only pay back later. In saving and investing, the reverse is true: you save money first so you can spend it later, and best of all, your patience is rewarded by the wonders of compounding.

For a lender, compound interest means that you pay simple interest on your loan. And the longer the repayment period, the larger the amount of interest accrued will be. So to avoid the interest burden becoming too large, it makes sense to pay off your loan as soon as possible. More interest will begin to accrue if loan repayment instalments are not paid in full.

If you have difficulty replaying a loan, or you have several consecutive debts, such as part-payment agreements, credit card debt, instant loans or consumer credit, taking out a lower-interest loan to pay off all these debts could be less costly and more convenient.

## Media appearances

If you decide to put your savings to work by taking advantage of compound interest and if all goes well, you could even earn extra, passive income.

Let’s take a look at how compound interest works, and how much it could add to your savings. Both of the examples below use an expected return of 7%, which reflects the average return on equity market investments over a long period.

Example 1 shows how much money you could have in 20 years if you saved €60 every month on top of your starting capital of €100.

### Example 1

Initial investment €100, monthly savings deposited €60, expected return on investment 7%, investment period 20 years

Starting pointYear 1Year 2Year 5Year 10Year 15Year 20
100 €877 €1 709 €4 571 €10 841 €19 635 €31 970 €

Due to compound interest, your savings will have increased to €31,970 after 20 years. If you were to save in a regular savings account, practically no interest would accumulate, as few banks pay a deposit rate in savings accounts nowadays. In 20 years, you could have around €15,200.

### Example 2

This example shows how much you could save in 20 years if you invested only an initial sum of €1,000, without adding any more money to it during that time.

And if you don’t want to invest more every month but instead just put the money to rest in an investment account, this is also possible.

Initial investment €1,000, monthly savings deposited €0, expected return on investment 7%, investment period 20 years

Starting pointYear 1Year 2Year 5Year 10Year 15Year 20
1 000 €1 070 €1 145 €1 403 €1 967 €2 759 €3 870 €

As the calculation shows, your investment would have grown to €3,870 without any effort on your part. This is a very significant increase over 20 years on the initial investment of €1,000.

Interest will of course also accrue on a smaller investment, such as €100, even if you do not add to it monthly, but will not be very significant. So naturally, the more you invest at the beginning, the more you will accumulate over the years.

As example 1 shows, the best way to get the most out of the compounding of interest is to add monthly to the initial investment. Every little helps to create a larger pot over time.

## What is the compound interest formula?

Compound interest is just plain mathematics, and has its own formula.

### The compound interest formula

In the diagram, the letter ‘k’ represents the capital, ‘p’ represents the annual interest rate, and ‘t’ indicates the investment period in years.

If you want to calculate the amount of compound interest using the formula, note that the interest rate must be the same throughout the entire period. Otherwise, the formula won’t work.

However, how the compounding of interest works can be difficult to understand with just a formula. This is because it seems simpler to just add a percentage to the starting capital: for example, €100 plus 10% is €110.

What makes compound interest such an important concept, however, is that the capital and the interest accrued on it both accrue interest – it is not just the capital that accumulates interest. The compound interest formula can be better understood by considering the Fibonacci sequence of numbers.

### The Fibonacci sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55

In this sequence, each number is the sum of the two preceding numbers. The more numbers there are in the sequence, the larger the number gets.

0+1=1

1+1=2

1+2=3

2+3=5

5+8=13

To understand how interest is compounded, the numbers in the Fibonacci sequence could be thought of as years: the more years pass, the more compound interest accumulates.

• When you invest or deposit a certain amount, it increases over time as the interest on it accumulates. However, at the same time as this simple interest is building up, it is gradually accumulating interest of its own. That’s compound interest.

• For example, if you deposit €1,000, with an expected return of 10%, you will have €1,100 the following year. A year after that, the capital increases and compound interest has accumulated to bring the total to €1,210.

• Saving with a long-term view bears fruit over the years as compound interest starts to pay off. The gain will be modest in the early years, but will gather momentum slowly but surely, giving you more and more the longer your investment period.

• Interest rates vary from year to year, so obviously the value of your investment will vary accordingly. If you only invest small amounts, with a low expected return, the risk will be moderate. For example, if you choose a fixed income fund with an expected return of around 2 to 4% per year, the risk is lower, but the return is also lower. The riskiest funds are equity funds, where the expected return is also higher, above 7%. However, these have the potential for higher returns.

• Start early – the later your start, the less time you have for your savings to accumulate compound interest.  If your goal is to save for 30 years, for example, now is the time to begin.

• The calculator tells you how much interest you can earn based on the amount invested, the amount you add monthly, your expected return on the investment, and the duration of your investment.

## Compound interest needs time to work – start saving early

If you are looking for high returns, the most important element to make sure you get the most from the compounding of interest is time. Miracles don’t happen in a year, or even two. Patience brings rewards. This is why you should start saving and investing as early as possible.

And if the amounts you invest are modest, the need for time becomes especially clear. In such cases, growth will be slight, but over the years may still add up to a nice little nest egg in your golden years on top of your initial savings.

However, you’ll get more benefit from the compounding of interest if your initial investment is reasonably significant, say €1,000. If you then add €100 every month, over the years the amount will be quite substantial, particularly if you’re lucky to have had a large return on your investment.

## How can I make compound interest work for me?

The option of putting your savings to work – of getting out more than you put in – is open to everyone, at any time or any age.

Naturally, the earlier you start the more you will benefit from compound interest. If you are 30 now, let’s say, you could build up a handsome sum for your retirement, or to make a far-off dream come true some day.

Saving money in a high-yield account, with a higher interest rate, is suitable for anyone, regardless of income. Even if your budget is tight, saving what you can each month – even as little as €15 – will eventually go a long way.