
Albert Einstein called compound interest "the greatest mathematical discovery of all time". We think this is true partly because, unlike the trigonometry or calculus you studied back in high school, compounding can be applied to everyday life.
The wonder of compounding (sometimes called "compound interest") transforms your working money into a stateoftheart, highly powerful incomegenerating tool. Compounding is the process of generating earnings on an asset's reinvested earnings. To work, it requires two things: the reinvestment of earnings and time. The more time you give your investments, the more you are able to accelerate the income potential of your original investment, which takes the pressure off of you.
To demonstrate, let's look at an example:
If you invest $10,000 today at 6%, you will have $10,600 in one year ($10,000 x 1.06). Now let's say that rather than withdraw the $600 gained from interest, you keep it in there for another year. If you continue to earn the same rate of 6%, your investment will grow to $11,236.00 ($10,600 x 1.06) by the end of the second year.
Because you reinvested that $600, it works together with the original investment, earning you $636, which is $36 more than the previous year. This little bit extra may seem like peanuts now, but let's not forget that you didn't have to lift a finger to earn that $36. More importantly, this $36 also has the capacity to earn interest. After the next year, your investment will be worth $11,910.16 ($11,236 x 1.06). This time you earned $674.16, which is $74.16 more interest than the first year. This increase in the amount made each year is compounding in action: interest earning interest on interest and so on. This will continue as long as you keep reinvesting and earning interest.
Starting Early
Consider two individuals, we'll name them Pam and Sam. Both Pam and Sam are the same age. When Pam was 25 she invested $15,000 at an interest rate of 5.5%. For simplicity, let's assume the interest rate was compounded annually. By the time Pam reaches 50, she will have $57,200.89 ($15,000 x [1.055^25]) in her bank account.
Pam's friend, Sam, did not start investing until he reached age 35. At that time, he invested $15,000 at the same interest rate of 5.5% compounded annually. By the time Sam reaches age 50, he will have $33,487.15 ($15,000 x [1.055^15]) in his bank account.
What happened? Both Pam and Sam are 50 years old, but Pam has $23,713.74 ($57,200.89  $33,487.15) more in her savings account than Sam, even though he invested the same amount of money! By giving her investment more time to grow, Pam earned a total of $42,200.89 in interest and Sam earned only $18,487.15.
Editor's Note: For now, we will have to ask you to trust that these calculations are correct. In this tutorial we concentrate on the results of compounding rather than the mathematics behind it. (If you'd like to learn more about how the numbers work, see Understanding The Time Value Of Money.)
Both Pam and Sam's earnings rates are demonstrated in the following chart:
You can see that both investments start to grow slowly and then accelerate, as reflected in the increase in the curves' steepness. Pam's line becomes steeper as she nears her 50s not simply because she has accumulated more interest, but because this accumulated interest is itself accruing more interest.
Pam's line gets even steeper (her rate of return increases) in another 10 years. At age 60 she would have nearly $100,000 in her bank account, while Sam would only have around $60,000, a $40,000 difference!
When you invest, always keep in mind that compounding amplifies the growth of your working money. Just like investing maximizes your earning potential, compounding maximizes the earning potential of your investments  but remember, because time and reinvesting make compounding work, you must keep your hands off the principal and earned interest.
Investing 101: Knowing Yourself

Investing
How does Compound Interest Work?
A quick way to understand the impact of compound interest is to ask yourself if youâ€™d rather receive $100,000 a day for a month, or start with a penny on day one and double it every day for those ... 
Personal Finance
How Interest Rates Work on Savings Accounts
Here's what you need to know to grow your rainyday fund. 
Investing
Learn Simple And Compound Interest
Interest is defined as the cost of borrowing money, and depending on how it is calculated, can be classified as simple interest or compound interest. 
Investing
Understanding Compound Interest
Compound interest is often called one of the most powerful concepts in finance. Find out what it is and how it can work for you. 
Investing
Accelerating Returns With Continuous Compounding
Investopedia explains the natural log and exponential functions used to calculate this value. 
Retirement
Why Investors Should Care About Compound Interest
Learn about compounding interest and how it impacts savings decisions, debt management, investment strategies and retirement planning. 
Investing
5 Best Ways to Earn Interest
Learn how to use tools to increase your interest earnings. Use compounding interest and breakpoints to increase your interest income. 
Personal Finance
APR and APY: Why Your Bank Hopes You Can't Tell The Difference
Banks use these rates to entice borrowers and investors. Find out what you're really getting. 
Managing Wealth
Dissecting the Simple Interest Formula
Simple interest ignores the effect of compounding: it's only calculated on the principal amount. This makes it easier to calculate than compound interest. 
Retirement
Why Save for Retirement in Your 20s?
You're probably paying off your student loans and retirement is 40 years away. Shouldn't you focus on eliminating debt and, maybe, saving for a home?