DEFINITION of 'Compound Interest'
Interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound interest can be thought of as “interest on interest,” and will make a deposit or loan grow at a faster rate than simple interest, which is interest calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semiannually over the same time period. Compound interest is also known as compounding.
INVESTOPEDIA EXPLAINS 'Compound Interest'
The formula for calculating compound interest is:
Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)
= [P (1 + i)^{n}] – P
= P [(1 + i)^{n }– 1]
(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)
If the number of compounding periods is more than once a year, "i" and "n" must be adjusted accordingly. The "i" must be divided by the number of compounding periods per year, and "n" is the number of compounding periods per year times the loan or deposit’s maturity period in years.
For example:
 The compound interest on $10,000 compounded annually at 10% (i = 10%) for 10 years (n = 10) would be = $25,937.42  $10,000 = $15,937.42
 The amount of compound interest on $10,000 compounded semiannually at 5% (i = 5%) for 10 years (n = 20) would be = $26,532.98  $10,000 = $16,532.98
 The amount of compound interest on $10,000 compounded monthly at 10% (i = 0.833%) for 10 years (n = 120) would be = $27,070.41  $10,000 = $17,070.41
Compound interest can significantly boost investment returns over the long term. While a $100,000 deposit that receives 5% simple interest would earn $50,000 in interest over 10 years, compound interest of 5% on $10,000 would amount to $62,889.46 over the same period.
While the magic of compounding has led to the apocryphal story of Albert Einstein supposedly calling it the eighth wonder of the world and/or man’s greatest invention, compounding can also work against consumers who have loans that carry very high interest rates, such as creditcard debt. A creditcard balance of $20,000 carried at an interest rate of 20% (compounded monthly) would result in total compound interest of $4,388 over one year or about $365 per month.
VIDEO

Compound Annual Growth Rate  CAGR
The yearoveryear growth rate of an investment over a specified ... 
Interest Expense
The cost incurred by an entity for borrowed funds. Interest expense ... 
Anticipated Interest
The amount of interest that a savings vehicle will accrue by ... 
Compound
The ability of an asset to generate earnings, which are then ... 
Interest
1. The charge for the privilege of borrowing money, typically ... 
Interest Rate
The amount charged, expressed as a percentage of principal, by ...

Insurance
What are the tax implications of a life insurance policy loan?
Learn the instances in which you are required to pay taxes on a life insurance policy loan, so you can avoid making a costly mistake. 
Credit & Loans
Will debt consolidation stop debt collectors and creditors from calling me?
Explore different debt consolidation options. Learn the effect that different interest rates have on monthly payments and total cost of borrowing. 
Retirement
Is it easier to save for retirement if you start earlier in life? Can I make up for what I don't save ...
In general, the earlier you start saving for retirement, the easier it will be to afford, given the number of financial obligations that tend to be incurred at that later period in your life. ... 
Savings
It's Never Too Early To Start Saving
The earlier you begin investing, the more stable your future will be in the short and long term. 
Investing Basics
Top 5 Books For Young Investors
Reading these respected tomes will help you begin your journey into investing on the right foot. 
Investing Basics
Understanding The Time Value Of Money
Find out why time really is money by learning to calculate present and future value. 
Investing Basics
Overcoming Compounding's Dark Side
Understanding how money is made and lost over time can help you improve your returns. 
Retirement
For IRAs, Time Is Money
Don't procrastinate. The timing of your contributions can mean thousands more in savings. 
Options & Futures
6 Major Credit Card Mistakes
Avoid these pitfalls to keep your credit score healthy and your debt under control. 
Retirement
Is Investing $25 A Month Worth It?
Find out how small investments can add up over time and how to avoid the fees that can eat tiny returns.