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Understanding compound interest

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To build wealth over the long term, you should understand the compound interest effect. It is the basis for making your money “work for you”.

It is often considered the most important basic investment concept. Albert Einstein described compound interest as the “Eighth Wonder of the World.”* He said that those who understand it make the money – and the others pay the money for it. The following article explains how you can use the compound interest effect for a successful investment.

*Although this quote is regularly attributed to Einstein, I have not found any reliable proof that he really made this statement.

💡 What you should know 1. The most relevant variable when using compound interest is time. 2. If you want to accumulate wealth, you must let compound interest work for you. 3. If you have debts, compound interest will have the same negative effect on your wealth.

The idea behind compound interest

The concept behind compound interest is to make more money with money. This is what is meant by the phrase “making the money work for you.” While many people are familiar with the concept of compound interest, they do not understand its powerful effect and therefore misapply it.

Examples for a simple understanding

The best way to learn and understand is by looking at examples. So, let’s do that! To check them yourself, there are free compound interest calculators available on the Internet. Using them, you can easily simulate the development of your capital with different interest rates, terms and savings rates.

Simple InterestYou want to invest $100 for one year at an interest rate of 5%. Your capital increases by the $5 interest after one year to $105 ($100 x 1,05 = $105).
In absolute terms, $5 is not a lot of money. But it makes a big difference in the long run if you withdraw this $5 and buy something with it or if you reinvest the earned interest.
For example, once a year you could afford a movie ticket for $5. Since your capital of $100 earns 5% interest every year, you also have $5 at your disposal every year. This effect is called simple interest. (The problem of the simple interest with an annual interest distribution is obvious: Your starting capital of $100 does not grow and never produces more than 5 interest per year.)
Compound Interest​Instead of spending the $5 interest on consumption, you can reinvest it. So after the second year your capital increases to $110.25 ($105 x 1,05 = $110.25).
What we see here ist that the yearly interest increased by 25 cents. Not only the $100 of capital worked for you, but also the $5 of interest from the first year (compound interest = $5 x 1.05 = $5.25).
To continue to profit from the compound interest effect, you do not withdraw the 10.25 interest, but reinvest it again. If you do this for a total of ten years, your capital will grow significantly. After ten years your capital equals $163.00 ($100 x 1,05^10 = $163). For the sake of simplicity, these example calculations do not take into account the influence of inflation. Inflation can cause $163 to have less purchasing power in ten years than it does today.
If you invest the money including interest for another 10 years, the result is $265 ($100 x 1,05^20 = $265).
The comparison with the simple interest makes the compound interest effect after this time particularly clear:
Simple interest: capital = $100 + 20 x 5 = $200.Compound interest: capital = $100 + 165 = $265
As you can see, after 20 years there is a difference of $65 between the simple interest effect and the compound interest effect.

What factors influence the compound interest effect?

The two factors of the compound interest effect that you can influence the most are time (investment period) and the invested capital.

The earlier you start investing and the higher your monthly savings rate, the more you benefit from the compound interest effect.

TimeIf you start saving at the age of 20 and invest $100 every month, your capital will have grown to $367,000 by the time you are 65, assuming a fixed interest rate of 7%. If you had not reinvested the interest received during that period, you would end up with only $141,000. The compound interest effect in this example amounts to $226,000.
Invested CapitalIf you increase your monthly savings rate to $250 at a 7% return, your assets will already amount to 1 million $ at the age of 65. If you then invest this capital at 5% interest, you can have a monthly pension of $4,100 paid out.
Timing of the interest paymentAnother factor that leads to better compound interest is the timing of the interest payment. A monthly or quarterly payment is better, since the interest received is directly reinvested and thus earns interest earlier.
In the above example, $100 was invested with an annual interest rate of 5%, with the interest payment taking place at the end of the year. Now how does the calculation change if the interest is paid once a quarter?
Since the compound interest effect also works within the year, the following applies (if the interest is immediately reinvested each quarter).
5% effective interest rate > 5% annual interest rate > the quarterly interest rate for the example is 1.25% (interest per quarter = 5%/4 = 1.25%).
To calculate the effective interest rate for the whole year, you must multiply each quarterly interest rate: 1.25% x 1.25% x 1.25% x 1.25% = 5.09%.
As you can see, the effective interest rate is 0.09% higher than the simple annual interest rate just because of the quarterly interest payment.
If you get the interest paid every month instead, the effective interest rate is 0.12% higher than if the interest is paid annually. Monthly interest > effective interest = 5.12%.

When is the effective interest rate an advantage, when a disadvantage?

If you are faced with a choice between two identical financial products that differ only in the period between interest payments, you should always opt for the investment that pays out its interest at shorter intervals. If instead you must pay off a loan at the bank, the shorter the period between interest payments, the more negatively the interest payment will affect you.

Another factor where compound interest plays against you is high transaction costs on your investment. If every year a certain percentage of your invested capital must be paid as a fee, your profit will be greatly reduced.

Summary

The compound interest effect has a huge impact on your investment. When you receive interest payments or dividend payments from stocks, you better reinvest the profit instead of spending the money on consumption. Otherwise, your wealth will not grow.

Statistics show that about half of the return from the S&P 500 comes from reinvested dividends. Therefore, take advantage of the “Eighth Wonder of the World” effect as much as possible.

On the other hand, compound interest has a negative effect if you have debt. Therefore, avoid taking out expensive loans and paying excessive overdraft interest.

For these reasons, you should start investing as early as possible.

PS: Do you want to know more about compound interest? Start with the corresponding Wikipedia article: Compound interest – Wikipedia

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