# How does compound interest work?

**What you will get from this article:**

- Understand the power of compounding
- Learn the true meaning of 3 common financial terms
- Discover what can happen with $1 when compound interest is maximized
- Find out how to access the ultimate financial resource, Unshakeable by Tony Robbins

Why does it seem that when you’re in the early stages of growing your wealth, low monthly contributions barely make a dent in your financial goals? Many young investors get impatient when they don’t see instant results and either stop investing altogether or try to come up with ways to put huge chunks of money away. They think this will be more effective in easing their financial fears for the future and lead them to financial freedom. However, these individuals are then missing out on the power of compound interest.

What is compound interest, and why bother with it when you could get a greater return sooner through other means? It might seem easier to make a larger, riskier decision right off the bat, but in truth, the power of compound interest is one of the most effective ways to grow your wealth.

Even though it might appear that investing $1 right now is silly, even that small compound interest investment is powerful and suddenly that $1 is worth a whole lot more. Here’s how a compound interest investment puts time on your side and helps you generate more wealth in the long run.

##### What is compound interest?

Compound interest is perhaps the most powerful tool in your investment arsenal. Albert Einstein once called it the most important invention in all of human history. So why do so few of us take advantage? For most people, they simply don’t take the time to fully understand the concept.

##### Compound interest definition

**COMPOUND INTEREST, DEFINED.**

Let’s start with a dictionary compound interest definition to establish a core meaning of the term:

1. A method used to calculate interest paid on both the principal and on accrued interest.

In other words, compound interest is interest on interest. It occurs when you reinvest interest rather than take it as a payout. This means that interest in the next period is earned not only on the principal sum, but also on any interest that was previously accumulated. The amount you earn is based on how much money you have invested, the percentage of interest that is paid on that amount and on the compounding frequency or number of times per year interest is paid out. Compounding frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily or continuously. The more frequently interest is compounded, the more interest you will earn.

Let’s start with how compound interest works. First, you must understand these definitions:

##### What is simple interest?

Simple interest is interest that is only earned on the principal. For example, if you had $100 and a simple interest rate of 3%, you’d earn $3 each year. Your interest earnings would never change because the principal stays the same – so you’d earn $3 in year one, $3 in year two, etc. After 20 years you’d have $100 + ($3*20), so $160 total.

##### What is compound interest?

Compound interest is interest that lets you earn interest on your interest, not just the principal. No wonder Einstein loved it. If you had $100 and an annual compound interest rate of 3%, suddenly the numbers change. At the end of year one you’ll have $103. For year two, you earn interest on all $103, meaning you’ll earn $3.09 in interest that year. For year three you’ll earn interest on $106.09, and so on. After 20 years you’d have $100 * (1+.03)20, so $180.61 total. Notice how compound interest investment gives $20 more than with simple interest over the same time period.

##### What is APY?

APY stands for Annual Percentage Yield. This is a percentage rate that reflects the total amount of interest paid on the account. It’s based on the interest rate compounded daily for a 365-day period. You’ll see this rate mentioned on some types of investments, like savings accounts.

##### How does compound interest work?

The formula for calculating compound interest may look complicated at first, but it’s actually relatively simple. The formula is A = P (1 + r/n) (nt). To calculate, enter the principal amount (money you’ve initially invested) into the P section, interest rate with r as the decimal, n as the number of times the interest is compounded and (nt) as the time the money is invested for.

For example, if you invested $5,000 into an account with an annual interest rate of 5% that is compounded monthly, it would look like this: A = 5000 (1 + 0.05/12) (12 (10)), which equals 8235.05. This means that your financial investment of $5,000 is now worth over $8,000 in 10 years’ time.

##### Compound interest examples

Do you want to use the power of compound interest to become financially unshakeable? Here are some compound interest examples that better illustrate the answer to the question, “How does compound interest work?”

1. You make an initial investment of $10,000 for a period of five years and that investment earns the return of 3%, which is compounded monthly. At the end of the five-year term, your initial $10,000 investment has grown to $11,616.17.

2. You make an initial investment of $10,000 for a period of two years and that investment earns a return of 2%, which is compounded quarterly. At the end of the short 2-year term, your initial investment has grown to $10,404.07

3. You make an initial investment of $1,000 for a year and that investment earns a return of 5%, which is compounded twice a year. At the end of the year, your $1,000 investment has grown to $1,050.63.

##### Why make a compound interest investment?

Clearly, it pays to make a compound interest investment as early as possible to maximize your earnings. So why not start now? Perhaps you want to take that big bonus or raise and take a vacation or buy a new car. Or maybe the reason you’re not saving now is you’re already squeezing the most out of every paycheck. But by setting aside a dedicated percentage every check or every month, you’ll be able to gain financial freedom with a compound interest investment – even if it’s a small amount of money. Just see what can happen to $0.10 if you doubled it 19 times:

As you can see in the video, with each round you play, the number gets remarkably bigger:

Tony’s golf analogy shows that the power of compound interest can make a huge difference in your investments, whether in savings, bonds or stocks.

##### What can happen to $1 with compound interest investment?

To further explain how compound interest works, let’s go back to that $1 from the start. What would happen if you started with $1 and contributed $1 every week to a savings account with an APY of 0.25%? In 10 years, you’ll have $527. In 20 years, you’ll have $1,067.

If you started with $1 and contributed $10 every week to a savings account with an APY of 0.25%, how much would you have in 10 years? A few hundred maybe?

You’d actually have $5,266.60. In 20 years, it would be $10,665.

The power of compound interest is that the more you continue to add to your savings, the more money you have to earn interest. Basically, the more you put into your compound interest investment, the faster it grows. This is hands-down the best way to achieve one of Tony’s financial resolutions of speeding up savings.

Unfortunately, U.S. savings accounts now generally have extremely low APYs; most of them have been below 1% since the Great Recession. However, as our example shows, even a few tenths of a percentage point plus regular savings contributions can make a huge difference due to how compound interest investment works. Other investment types like index funds or stocks can have much higher rates of return, but can also carry greater risks of loss. With a compound interest investment, there is no threat of loss and a guaranteed rate of return.

##### Save early and often: The true power of compound interest

Other compelling advice to save early comes from financial expert Burton Malkiel, who created the idea of index funds. His story of two brothers investing is another great example of a money machine in action.

**Take two brothers, we’ll call them William and James. Both are 65 years old. Based on the information below, which brother has more money in his account at the age of retirement when they compare their returns? William, who invested for 20 years, or James, who invested for 25? Click below to find out.**

Yes, William earned a whopping 600% more than his brother even though he invested the exact same amount for less time. This illustration makes it clear to see why compound interest is part of the language of the wealthy. Even if you’re no longer in your 20s, you can still take advantage of compound interest investment by putting away what you can now. Every day you wait, you’re losing out on extra income.

Curious to learn more about smart investing and gaining your financial freedom? Check out how to plan your financial future and smart ways to plan for retirement. Harness the power of compounding interest and see just where $1 can take you.

### Want to discover more investing secrets from the smartest minds in finance today?

Get all the details in Tony Robbins’ *Unshakeable* audio. Unlock secrets on how to compound wealth, make smart investing decisions and master your personal finances today.