Finance

Calculating compound interest: the compound interest effect explained in simple terms

With compound interest you earn money with more money. How this works and how to calculate compound interest – our guide shows you step by step.

For Albert Einstein, compound interest was supposedly the greatest invention of human thought, and Wall Street legend Warren Buffett is said to have described it as the most important success factor in investing. But how exactly does the compound interest effect actually work? And what is the difference to simple interest? Our overview explains it to you – step by step and with sample calculations.

What is compound interest?

Of the compound interest describes the Interest you on interest receive. He is your best friend when it comes to growing your wealth. Because compound interest means that you earn more money with money – without having to do anything yourself.

What sounds too good to be true is called Compound interest effect. Every euro in interest that you do not have paid off but reinvested leads to the fact that your capital grows faster. Because then not only will your initial capital be paid interest in the next year, but also the reinvested interest.

What is the difference to simple interest?

The great advantage the compound interest effect brings you becomes clear when we compare it with the simple interest rate. Let’s say you invest $ 10,000 for a year at an interest rate of 5 percent. Then your wealth will develop as follows:

10,000 euros x 1.05 = 10,500 euros

So by letting your money work for you, you earn 500 euros in interest. This money could be paid out and used, for example, as pocket money for the next vacation.

It could be like this every year. Your 10,000 euros always yield 500 euros in so-called simple interest.

The problem is just: Your 10,000 euros will no longer be and the interest will never exceed 500 euros. It looks different when compound interest comes into play.

Instead of hitting the 500 euros on your head while on vacation, you can put it back on again right away. Your assets then grow to EUR 10,500 in the second year – which means that interest rates also rise in the third year:

10,500 euros x 1.05 = 11,025 euros

So you have now not only earned another 500 euros in simple interest, but also 25 euros on top – your first compound interest. They arose because the 500 euro interest from the first year also worked for you.

Compound interest = 500 euros x 1.05 = 25 euros

The nice thing about compound interest is that the longer you invest your interest, the more it affects your account. Because you get higher compound interest from year to year – not just 25 euros every time. It’s called exponential growth.

Calculate compound interest: what is the compound interest formula?

You can use the compound interest formula to calculate how much you will actually earn from compound interest:

Kn = K0 x (1 + i) ^ n

Kn is the final capital that you want to find out. K0 is the starting capital that you use. The letter i denotes the interest rate and the letter n the investment period in years.

Let’s stick with our example: You invest 10,000 euros at an interest rate of five percent for ten years. The calculation would then look like this:

K10 = 10,000 euros x (1 + 5/100) ^ 10 = 16,288.94 euros

For comparison: if you alternatively have the interest paid out every year, your investment with the simple interest rate would be worth 15,000 euros after ten years – that is almost 1,300 euros less (10,000 euros + 10 x 500 euros = 15,000 euros).

Are there also compound interest calculators?

Yes. You do not necessarily have to calculate your possible compound interest yourself – even if you now know the formula. You can find compound interest calculators online that do the work for you.

Simply enter the necessary key figures there: the capital you want to invest, the interest rate and the planned term.

How do I benefit most from the compound interest effect?

To put it simply: by investing as much money as possible at the highest possible interest rate for as long as possible. The investment period and the invested capital therefore play a role. A convenient and promising way to do this is through a ETF savings plan.

ETFs are special equity funds, i.e. equity baskets in which a computer algorithm tracks a stock index such as the Dax. The value of your invested money develops in parallel with the modeled stock index.

Yields of 5 percent per year are quite realistic over a long period of time. The compound interest effect has the strongest impact on so-called accumulating ETFs. Because they automatically reinvest the income, so the value of your ETF shares increases.

With a savings plan, you also ensure that you invest money regularly. ETF savings plans are particularly well suited for those starting out on the stock market, as they are cheap and relatively low-risk.

What difference does the investment period make?

The longer you hold onto the investment, the greater the effect of compound interest. Two sample calculations for ten and 20 years respectively illustrate the difference it makes if you remain patient – regardless of whether you invest a larger amount or keep paying in smaller sums.

For a single deposit:

Let’s take the example from above again. We have calculated that if you start with 10,000 euros, you will get 16,288.94 euros, invest it at an interest rate of 5 percent and then reinvest the interest over and over again for ten years.

With simple interest, you would only have come out at $ 15,000. The compound interest effect amounts to more than 1,200 euros.

Now double the investment period, so if you stay invested for 20 years, you will end up with EUR 26,532.98 – compared to EUR 20,000 with simple interest. The compound interest effect amounts to more than 6,500 euros. With twice the investment period, compound interest has not only doubled, but more than quintupled.

With regular deposits:

The investment period also makes a difference with a savings plan: For example, if you invest 100 euros every month with an interest rate of 5 percent, you will have 15,848.14 euros after ten years. But you have only paid in 12,000 euros – so it makes a profit, too Return called, from 3,848.14 euros.

On the other hand, if you expand your savings plan to 20 years, you will get EUR 41,663.10. 24,000 euros of your own deposits are compared to a return of 17,663.10 euros – four and a half times as much as with half the investment period.

By the way: Also the Time of interest payment brings you better compound interest. Because the sooner you receive interest and invest directly again, the earlier this income is compounded with interest.

So if you have the choice between two investment products that only differ in the type of interest payment, you should prefer a monthly or quarterly interest payment to an annual one. The situation is different when you have to pay off a loan. Then an annual interest payment is cheaper for them.

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