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# What is Compound Interest and How Does it Work?

When asked, “What’s your least favorite subject in school?” many people would likely take no time in answering, “Math.” It’s a dreaded subject for most of us, both in K-12, college, and beyond. Although those of us non-math majors still wonder how studying the Pythagorean theorem or knowing what the square root of –i ever benefitted us in our careers, some things from high school math class are surprisingly applicable in real life.

Take compound interest, for example. Although technological advances have increased the prevalence of laziness when it comes to difficult multiplication problems as seen with compound interest, it’s important to recognize how this concept can benefit us in regards to our finances. It’s too easy to assume our bankers and brokers will manage our savings and investments for us; self-sufficiency through in-depth financial education is key to truly making your money work for you. Learning about what Albert Einstein thought was “the greatest mathematical discovery of all time”—yes, compound interest—is a step in the right direction.

### What is Compound Interest?

There are two main types of interest: simple and compound. As you may think, simple interest is really just that: simple. If you invest $1,000 at 5%, you will have $1,050 in one year. Over the course of ten years, the initial investment of $1,000 would be worth $1,500.

When compound interest enters the equation, things become a little muddled. Investopedia explains compound interest quite adeptly in a mathematical sense. For a clear-cut example, consider the following:

#### Scenario One:

You invest $1,000 into savings with a 5% interest rate. You leave it there for ten years, and after one decade, it is now worth $1,629. This is $629 more than what you would’ve had if you had stuffed ten $100 bills under your mattress for a decade and $129 more than if you had invested the same amount and only applied simple interest over the same course of time. See what a difference compound interest makes?

#### Scenario Two:

You invest $1,000 into savings with a 5% interest rate. You continue to add $100 to the account every month for the next ten years. After one decade, you now have $16,722. Without any interest whatsoever, you would’ve only had $13,000 after ten years. Again, compound interest helps you make more on your initial investment, without any extra work required.

### How Does Compound Interest Work?

Once you have a solid grasp on the basics of compound interest (and maybe a calculator nearby, just in case), what next? Time to start applying these principles to your own life by studying your current returns in savings accounts and investments alike. The importance of having a savings account is exemplified through the principle of compound interest: by leaving your funds where they are (rather than constantly depositing and withdrawing, as you would with a checking account), you grow your savings over time. However—thanks to the Federal Reserve keeping interest rates low supposedly to discourage saving and spur spending in the US economy—yields from basic savings accounts are relatively low in status quo. Although there is greater risk in the stock market, the returns are generally higher than ultra-safe savings accounts.

Financial experts generally agree that investing in stocks that pay in dividends. Instead of cashing out these dividends however, you can reinvest these funds in more stocks. Over the course of time, this investment will compound on itself, building up quite a stash of wealth using just the initial investment.

### Compound Interest Calculator

For the most streamlined, easy-to-use calculator, check out Investor.gov’s compound interest calculator. This calculator (provided by the U.S. Securities and Exchange Commission) takes from the current principle input with additional monthly input in the section below, years to grow, followed by the given interest rate. Want to add how many times the interest is compounded per year? This calculator does that as well.

### Further Resources

For the more mathematically-inclined folks out there, Investopedia has another great article on Understanding the Time Value of Money to help you get to the root of how compound interest works and why studying this concept can help you maximize your financial gains both in the realm of savings accounts and investment portfolios.

For those seeking to simply understand compound interest works in a real world context, BetterExplained.com offers an excellent guide on the background and application of compound interest.

Fell asleep during high school math class and are now looking for someone to spell out the intricacies of compound interest much like your old math teacher? Check out this helpful video from the Khan Academy. It’s an easy-to-follow tutorial with audio and visual explanations; perfect for anyone trying to learn more about the mathematical aspect of compound interest.

Photo Credit: Andrew Michaels