Discrete and continuous compounding are closelyrelated terms. An interest rate is discretely compounded whenever it is calculated and added to the principal at specific intervals (such as annually, monthly or weekly). Continuous compounding uses a natural logbased formula to calculate and add back accrued interest at the smallest possible intervals.
Interest can be compounded discretely at many different time intervals. The number of and distance between compounding periods is explicitly defined with discrete compounding. For example, interest that compounds on the first day of every month is discrete.
There is only one way to perform continuous compounding â€“ continuously. The distance between compounding periods is so small (smaller than even nanoseconds) that it is mathematically equal to zero.
Compounding is still considered to be discrete if it occurs every minute or even every single second. If it isn't continuous, it's discrete. Simple interest is considered discrete as well.
Calculating Continuous and Discrete Compounding
If the interest rate is simple â€“ no compounding takes place â€“ then the future value of any investment can be written as: Future Value = principal x ((1 + (interest rate) x (time period)); or, more simply, as FV = P(1+rt)
When interest is compounded discretely, its formula is: FV = P (1+ r/m)^mt, where t is the term of the contract (in years) and m is the number of compounding periods per year.
Continuous compounding introduces the concept of the natural logarithm. This is the constant rate of growth for all naturally growing processes. It's a figure that developed out of physics.
The natural log is typically represented by the letter e. To calculate continuous compounding for an interestgenerating contract, the formula needs to be written as: FV = P*e^(rt).

How to calculate compound loan interest in Excel?
Find out about compound interest and how to use the compounding interest formula in Microsoft Excel to calculate the compound ... Read Answer >> 
How do I calculate compound interest using Excel?
Learn what compound interest is, the formula used to calculate it, and how to calculate it using three different techniques ... Read Answer >> 
How can I tell if a loan uses simple or compound interest?
Learn the differences between simple and compound interest and how you can identify which one a loan uses. Read Answer >> 
What is the difference between stated annual return and effective annual return?
Essentially, the effective annual return accounts for intrayear compounding, and the stated annual return does not. The ... Read Answer >>

Investing
Learn Simple and Compound Interest
Interest is defined as the cost of borrowing money, and depending on how it is calculated, it can be classified as simple interest or compound interest. 
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. 
Investing
Calculating Future Value
Future value is the value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. 
Investing
Explaining Interest
Interest is the price charged to borrow money, and is typically expressed as a percentage of the principal, or the amount loaned. 
Retirement
Using Compounding to Boost Retirement Savings
Allowing growth on your investments to compound over time gives you immense returns when saving for retirement. 
Investing
How to Calculate Your Investment Return
How much are your investments actually returning? Find out why the method of calculation matters. 
Retirement
Compounding Is Important in the Later Years Too
The power of compounding is even greater in the later years of saving for retirement. 
Investing
Compounding: My Favorite Term
Vanguard CEO Bill McNabb shares why "compounding" is his favorite financial term. 
Financial Advisor
The Awesome Power of Compounding
The power of compounding. It may not be sexy, but it is the surest way to accumulate wealth over time.

Discrete Compounding
Discrete compounding refers to the method by which interest is ... 
Continuous Compounding
The process of earning interest on top of interest. The interest ... 
Effective Annual Interest Rate
Effective Annual Interest Rate is an investment's annual rate ... 
Periodic Interest Rate
The interest rate charged on a loan or realized on an investment ... 
Compound Return
The rate of return, usually expressed as a percentage, that represents ... 
Compound
The ability of an asset to generate earnings, which are then ...