How Works Compound Interest? Learn the Secrets of the Dark Side

Summary

  • The compound interest has little effect in short term or by lower interest rates.
  • But compound interest can make you rich in decades or by high yearly returns.
  • The dark side of compound interest is: If you must pay it. In case of high debt or negative real interest rates.
  • Learn how works compound interest and stand on the right side.

There are so many posts and articles on the Internet promising so many wonderful things based on compound interest. Even memes are circulating like this quote by Albert Einstein. Although some sources are questioning its originality.

Compound interest is the most powerful force in the universe. Or, in another version: Compound interest is the eighth wonder of the world.

The Small Side of Compound Interest

Compound interest, also called interests on interests, is very useful in finances. But it isn’t a wonder potion either. It’s meaning is simple. After every year, the actual interest amount is added to the original capital. From that on, interests will be also paid on this amount in all the following years. That creates an effect called exponential growth. Your money won’t increase linear (line shape curve). But exponentially, on a parabolic shaped, acceleratedly rising curve.

For example, if you put $1,000 in the bank for two percent interests. In two years you have $1,040.0 without, and $1,040.4 with the compound interest calculation method. (1,000*1.02*1.02.) The difference is small in this case. But it is growing with time, and higher interest rates make the curve steeper. Compare the next charts with one percent and ten percent compound interests (Chart 1. and 2.).

Chart 1: Simple and compound interest, one percent
Chart 1: Simple and compound interest, one percent

How Do I Calculate It?

The calculation of normal and compound interest is simple, don’t worry. You can do it with the basic mathematics of elementary schools. You add the interest (calculated on a daily, monthly or yearly basis) to the original amount of money. For example, $1,000 capital, five percent interest per year (per annum, p. a.) and three years:

      • Simple method (seldom in use over one year): 1,000 + 3 * (1,000 * 0.05) = 1,000 + 0.15 * 1,000 = 1,000 + 3*50 = 1150. (Dollar, euro, peso, rupees, etc.)
      • By compound interest, you calculate exponentially. You don’t add, you multiply the original funds: 1,000 * 1.05 3 = 1157.625.

Another example, with 547 days, one and a half years of investing period on a daily basis:

      • With the simple method, you calculate first the daily interest. Then, multiply it by the number of days and add to the initial capital: 1,000 + 547 * (1,000 * 0,05/365) = 1,074.932.
      • By compound interest, you calculate a power. You receive the exhibitor dividing the number of effective days by all days (365) in a year: 1,000 * 1.05 (547/365) = 1,000 * 1.05 1,4986= 1,075.856.

(I’m aiming to show you a simple, common-sense calculation method. If you wish a more scientific, more accurate description of the calculation visit Wikipedia.)

Chart 2: Simple and compound interest, ten percent
Chart 2: Simple and compound interest, ten percent

As you see on the charts, your money grows very slowly with only a one percent rate. Even in 30 years, your $1,000 will grow only to 1,300 with simple and to $1348 with compound interests. Moreover, interests are very low in many countries today. Why should you know the compound interest, then, if it has a so small effect on the short term?

  • In the short or middle term, because all banks, companies, institutions and most people are using this calculation method. In fact by all investments with more than one year of maturity. That is the standard, the usual method. If you don’t get your interest payments based on the compound method, you should claim, demand it.
  • In the long term, because it can make a big difference in your investment returns. And in this modern and uncertain world, yes, you should invest in the long term. For various reasons. (Also read:  Which Is Your Best Source of Money? Investing, Saving or Earning?)

How Works Compound Interest on the Bright Side

By ten percent interest and ten years, the picture is much sunnier. In this case, your initial $1,000 grow to 2,000 even with simple interest, but to almost 2,600 with the compound method. In 20 years, the difference is much higher: 3,000 versus 6,727. Here, you can already feel the real power of compound interest.

Some of the data on the third chart may be unrealistic, unlikely to achieve, but dreaming is not forbidden. After decades of investment and double-digit investment returns, our capital would multiply. The original thousand dollars (euros, renminbi, etc.) can grow to tens of thousands or hundreds of thousands, Or, a few million.

Chart 3: Higher interest rates and compound interest (logarithmic scale)
Chart 3: Higher interest rates and compound interest (logarithmic scale)

We can see this on the graph, where some the lines were so steep, like exploding, that they didn’t look good. So we had to use a logarithmic scale. In an extreme case, if 30 percent p. a. were achieved in thirty years, the value of thousand dollars would increase to 2.619 million, or 2,619 times. But in reality, this can be achieved only by very few people. Only some multi-billionaires, entrepreneurs, gurus made it in the past regularly.

How Much Interest or Return is Real?

But which interest rate is real then? That depends on the country, the economic environment, the base interest rate of the central bank, the risks of the investments and much more. At the beginning of 2020 and some years before, low-risk interest rates were mostly very low in developed countries. (Like government bonds, insured bank deposits, in US, EU, Japan.) Often by zero, or in negative territories.

The good news is, the long-term returns of stock market indexes are mostly much higher than the returns of low-risk assets. The bad news is, stocks surged a lot in the recent decade. Many investors are afraid of a bubble on the market – and a new crash.

Compound interest or real interest?

Another problem is inflation. Let’s assume you make a five percent return with your investments. But the inflation, the devaluation of your money reaches also five percent. (The real interest rate, the part over the inflation, is zero.) So, you gain nothing. And if the inflation surges to seven percent, you lose two percent yearly. I say, if you live in a country where you can reach 1-3 percent of real interest by really low risks, you can be happy.

How Works Compound Interest on the Dark Side

Many articles about compound interest are talking only about the positive effects. How can your wealth grow? But there is also a negative side. How works compound interest if you get only a negative real interest rate? Or, if you have to pay your debts? Or, if your debt is growing, accumulating over time? I call this the “dark side.”

Skull sculpture with pound signs. (Image in the negative. By Mariusz Matuszewski from Pixabay)
Skull sculpture with pound signs. (Image in the negative. By Mariusz Matuszewski from Pixabay)

It sounds very nice that you can double your money with the compound interest. But if you pay the same with compound interests, you can lose all. Your debt also can grow double. If you receive less interest than inflation, you can lose a couple of percent every year. That can also accumulate to a greater sum if it continues in the long term. Unfortunately, loan rates you pay, are much higher than the rates you receive on your savings. Always.

The basic mechanism of debt traps

On Chart 4, you can view how your wealth decreases over time in the bad case. With only one percent of negative annual real interest rate, in 30 years, you will have only 74 percent of the initial capital. Or, $740 of the $1,000 at the beginning. By a five percent negative rate, you lose 78.5 percent in 30 years. Almost all you had.

Chart 4: Compound interest of negative rates (for example, negative real interests)
Chart 4: Compound interest of negative rates (for example, negative real interests)

Perhaps you have a house worth $2,000, but bought the half on credit, and you don’t pay the interests. Or you need newer and newer credits to pay. With the compound interests accumulating, your debt grows and grows. The real value of your wealth decreases.

In 5-7 years, the nominal value of your house may be still $2,000 worth, but you have also a debt of 1,500-1,800. In reality, you would have only a couple of hundreds of dollars of net wealth. In 8-9 years, the debt reaches the value of the house. And your net asset value will be around zero, or slightly negative.

Conclusion

See, it’s better to learn how compound interest works. Avoid all situations where you are paying the compound interest. In the actual global environment, be happy if some real interest, about inflation, can be obtained. If not, please read this article: Eight Ways How Inflation Threatens Your Income and 13 Ways to Fight It. In particular, you should avoid all high-interest debts (like credit cards or other consumer credits). But also be careful with all other loan forms, even with lower interest rate mortgages.

More Important Readings About Your Money

References:

Disclaimer

I’m not a certified financial advisor nor a certified financial analyst, accountant nor lawyer. The contents on my site and in my posts are for informational and entertainment purposes and reflecting my collection of data, ideas, opinions. Please, make your proper research, or consult your advisors before making any investment or financial or legal decisions.

(Cover image by Tumisu from Pixabay, in negative)

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