Compound Interest
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One of the most powerful forces in economics and finance is compound interest. Not everyone understands compound interest, even though they may reap its benefits or suffer its consequences. Compounding has the potential to build fortunes and wreck empires. The effects of compounding are also not limited to interest payments. It can apply to a great many things in and out of the financial world.

Learn more about compound interest, how it works, and its awesome potential on this episode of Everything Everywhere Daily. This episode is sponsored by NerdWallet. When it comes to general knowledge and history, you know I've got you covered. But who do you turn to when you need smart financial decisions? If your answer is NerdWallet, then you're absolutely right. And if it's not, let me change your mind.

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But from the start, internal strife and infighting threatened the colony's survival. Wondery's American History Tellers takes you into the events, times, and people that shaped America. Its values, struggles, and dreams. In the latest series, after their arrival, the English colonists quickly established a fort, but their quest for wealth and status soon led to conflict with Virginia's native people and the powerful Powhatan. Violence, disease, and starvation would soon follow, leaving the colony on the edge of collapse.

Follow American History Tellers on the Wondery app or wherever you get your podcasts. Listen to all the episodes ad-free and get early access to the latest season on Wondery Plus. Start your free trial today in the Wondery app, Apple Podcasts, or Spotify. Albert Einstein was reported to have been asked what the most powerful force in the universe was. And his answer was compound interest.

Actually, he probably never said that, but it's still a great quote. And there's an alternative version floating around in which he calls it the eighth wonder of the world. Perhaps the simplest explanation as to what compound interest is was given by the early American statesman Benjamin Franklin, who said, quote, money makes money and the money that money makes makes money, end quote. It sounds a bit convoluted the way he puts it, but he's fundamentally correct.

Compound interest is the interest on a loan or deposit that's calculated based on both the initial principal and the accumulated interest from previous periods. Unlike simple interest, where the interest is only calculated on the principal amount, compound interest grows faster because each period's interest is added to the principal, and future interest is calculated on this newer, larger amount.

So, essentially, you're earning interest on your interest. This might not sound like a big deal at first, but as we'll see, that simple idea has enormous potential and enormous dangers. There's a formula you can find for compound interest that I'm not going to explain in detail here, simply because equations like children are better seen and not heard. Suffice it to say, there are several variables that go into calculating compound interest.

the interest rate, the compounding frequency, the principal amount, and time. I'll illustrate the concept using a very simple example. Let's say you have $100 in a savings account that earns 5% per year in interest. And just to make the math easy, let's assume that the interest is calculated once per year. At the end of the first year, you will make $5 on your initial principal of $100.

If you're compounding, then you take that $5 you made in interest and put that into the savings account. So in year two, you now make 5% on $105, not 100. The amount of interest you earn in year two would be $5.25, not $5.00.

In year three, you now make 5% on $110.25, which would be $5.51. And in year four, you make 5% on $115.76, which would then be $5.79. The amount you make in interest keeps going up because you keep making money on the interest you previously earned. This example is assuming that you only calculate the interest once per year. But what if you did it every month?

In that case, you divide 5% by 12, the number of months in a year, and calculate 0.417% interest every month. If you compound interest monthly rather than annually, in the first year you will make $5.12 in interest, not $5. The shorter the compounding period, the more money you can make, although there is a limit to it. Using calculus, you can actually calculate continuous compounding.

If you didn't compound interest, it would take 20 years to double your principal, making only 5% a year. However, if you compound your interest annually, it would take only 14.2 years to double your principal. In 20 years, you would have made $165.33 in interest, 65% more than without compounding. In the examples I'm using, the differences in numbers might not seem like a lot, but over time they become enormous.

Before I get into the implications of compound interest and why it can be so powerful, I want to provide a brief history of compound interest. Compound interest, or at least the idea of it, has been around for a very long time. The first known examples of interest being charged on loans came from the Sumerians, Babylonians, and Assyrians. In ancient Mesopotamian societies, loans were often issued in the form of grain or livestock and interest was applied.

Some ancient records from Babylon indicate that interest was compounded annually. The famous Babylonian legal document, the Code of Hammurabi, from around 1750 BC, regulated the rates of interest, especially for agricultural loans. In some cases, farmers would borrow seeds and the interest would be calculated based on future harvests, making these early cases of pseudo-compounding.

The Greeks were known to study mathematical principles that relate to geometric progressions, which is essential to understanding compounding, but were not known to use compound interest itself. The Romans did know about compound interest and occasionally used it. The famed orator Cicero once wrote to a friend, "...I had success in arranging that they should pay with interest for six years at the rate of 12% and added yearly to the capital sum."

The Romans had laws putting limits on interest in place, but they never had any laws regarding compounding of interest. The main thing which prevented the use of compound interest was mathematics. It was much more difficult to calculate than simple interest, so it was seldom used.

For centuries, compound interest was infrequently used, mainly because of the calculation problem, but also because most loans were shorter than they are today. A loan would often be paid back in months, not years. Over shorter periods, compounding just wasn't worth the effort. The calculation problem began to be solved with the development of a formal banking system in Italy, especially around the city of Florence.

In 1340, the Florentine merchant Francesco Balducci Pegalotti created a table of compound interest for interest rates from 1 to 8% for periods up to 20 years. In the 15th century, the Medici Bank, one of the most powerful banks of the time, played a crucial role in financing large projects, including governments and monarchs. The practice of compounding interest became more formalized as the Medici developed sophisticated accounting techniques for managing long-term debts and investments.

Also in the 15th century, the Italian mathematician Luca Petroli developed what is known as the Rule of 72. The Rule of 72 is a simple rule of thumb used to establish how long it will take for an investment to double given a fixed annual rate of return using compound interest. For example, if you have a 6% interest rate, 72 divided by 6 will give you 12, the approximate amount of time it would take to double your money.

The rule of 72 is only approximate. 72 is just a nice round number, which is evenly divisible by 1, 2, 3, 4, 6, 8, 9, and 12. For continuous compounding, 69.3 works much better than 72. The formalization of compound interest can be traced back to the 17th century. Mathematicians like Jacob Bernoulli were pioneers in developing the theory of compound interest.

Bernoulli's studies in the late 1600s contributed to the mathematics of exponential growth and the early foundations of modern financial mathematics. The establishment of the Bank of England in 1694 led to the widespread use of compound interest in bonds and other financial products. Government borrowing began to rely heavily on interest-bearing loans, where compound interest helped increase the return for lenders.

By the 20th century, the calculation problem of compound interest had been solved, and it was common in most transactions that calculated interest. During World Wars I and II, many governments, especially in the United States and Europe, issued war bonds that used compound interest to attract investors. By the mid-20th century, all the way to today, compound interest is used almost everywhere as computers have made the calculation of compound interest trivial.

So let's get into some examples which demonstrate just how powerful compound interest is. The secret ingredient for taking advantage of compound interest is time. Imagine someone 20 years old investing $10,000 in a retirement account with an average annual interest rate of 7% compounded annually. They leave the money untouched for 40 years and they don't add any additional money to the account.

When they turn 60, that initial $10,000 investment would have turned into $149,745, an almost 15-fold increase in wealth. But let's say you don't have $10,000 to invest when you're 20. Instead, let's assume that you have $200 and you just add $200 a month to an account accruing interest at 6%, compounded annually over 30 years. When you turn 50, you will have

$200,896, even though only $72,000 was ever actually deposited. This is why the sooner you start saving, the more money you can make. The money has longer to compound, which makes the end value larger. Given enough time, compound interest can become staggering. Consider for a moment this.

Let's say you started a savings account way back when the Great Pyramid was completed about 4,700 years ago. This savings account would be pretty horrible. Let's say it only earned 1% interest compounded annually and the only thing you had to put into the savings account was 1 cent.

The question is, how much would one penny invested at 1% interest compounded annually be worth today 4,700 years later? Well, it wouldn't be in the millions or the billions or even trillions of dollars. The final amount would be 2 quadrillion 43 trillion 886 billion 515 million 503 thousand 186 dollars. To put this into perspective,

The total gross domestic product of the world is estimated to be around $142 trillion. The total amount of debt in the world is about $220 trillion, which is approximately the same as the total value of all the real estate in the world. Compounding isn't just something that affects interest rates. It affects many other things as well. And one is economic growth. Let's suppose you have two countries that have economies of the exact same size.

Economy A grows at 2% and Economy B grows at a rate of 3%. That might not sound like much of a difference. And over the course of a single year, it isn't much of a difference. However, if that 1% difference in economic growth were sustained for a century, after 100 years, Economy A would be 7.24 times larger. But Economy B would be 19.22 times larger.

A 1% difference in growth over 100 years will result in one country being 2.65 times richer than the other. Inflation is also subject to compounding effects. Every year's increase in prices is on top of the increase in prices which came before. Most developed economies try to shoot for an annual inflation rate of about 2-4%. Yet, over time, there are huge differences between those two numbers.

At a 2% rate of inflation, prices after 50 years would be 2.7 times greater. But with a 4% rate of inflation, prices after 50 years would be 7.1 times greater. Compounding effects also occur in population growth and decline. The more offspring there are, the more people there are to produce even more offspring.

Compounding effects can also work in reverse. So far, I've talked about investing money and earning a return. However, if you're in debt, compound interest can work against you, and the results can be devastating. Suppose someone has $5,000 in credit card debt with an annual interest rate of 20%, compounded monthly, and let's assume they don't make any payments for a year.

After one year, the debt will grow to $6,095, showing how high interest compounding debt can spiral quickly out of control. When you don't pay down your debt, you begin paying interest on the unpaid interest. And this is as true for individuals as it is for nations. As the United States national debt has gotten larger and larger, the percentage that is spent on interest keeps getting larger and larger due to compounding effects.

As of the recording of this episode, interest payments have surpassed national defense and will probably surpass Medicare next year. Within a few years, unless there is a dramatic reversal, the compound interest effect will result in interest payments becoming the largest single component of the national budget, overwhelming everything else. As I mentioned before, the effect of compound interest is dependent upon principal, time, and interest.

Regarding the national debt, interest rates can change over time. So if interest rates increase even slightly, it can result in a massive increase in the cost of interest and hence the size of the debt. Compound interest isn't hard to understand conceptually, but many people fail to recognize the dangers or benefits of allowing compound interest to work over time.

So regardless if Einstein actually ever said it, it might very well be the case that compound interest is the most powerful force in the world. The executive producer of Everything Everywhere Daily is Charles Daniel. The associate producers are Benji Long and Cameron Kiefer.

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