Discrete and continuous compounding are closely related 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 – 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 – no compounding takes place – 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).

What formula can I use to calculate interest on interest?
Find out more about compounding interest, what it measures and how to calculate the amount of compound interest accrued using ... Read Answer >> 
How do I use the rule of 72 to calculate continuous compounding?
Find out why the rule of 72 does not accurately reflect the growth caused by continuous compounding, and which number can ... Read Answer >> 
How do mutual funds compound interest?
Learn how mutual funds can grow wealth over time through the magic of compound interest by reinvesting dividends back into ... Read Answer >> 
What is the difference between compounding interest and simple interest?
Learn about simple interest and compound interest, how to calculate the two types of interest and the main difference between ... Read Answer >> 
What does it mean when interest "accrues daily?"
Find out what it means when an interestbearing account accrues interest daily and how different compounding periods change ... 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. 
Investing
Overcoming Compounding's Dark Side
Understanding how money is made and lost over time can help you improve your returns. 
Investing
The Effective Annual Interest Rate
The effective annual interest rate is a way of restating the annual interest rate so that it takes into account the effects of compounding. 
Personal Finance
How Interest Rates Work on Savings Accounts
Here's what you need to know to grow your rainyday fund. 
Financial Advisor
Compound Annual Growth Rate (CAGR)
The compound annual growth rate is an important tool for measuring investment performance and comparing it across asset classes. Discover how it is calculated and how it can inform your investment ... 
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. 
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. 
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.

Compound Interest
Compound Interest is interest calculated on the initial principal ... 
Compound Return
The rate of return, usually expressed as a percentage, that represents ... 
Front Fee
The option premium paid by an investor upon the initial purchase ... 
Stated Annual Interest Rate
The return on an investment that is expressed as a peryear percentage, ... 
Time Value of Money  TVM
The idea that money available at the present time is worth more ... 
Compound Probability
A mathematical term relating to the likeliness of two independent ...