DEFINITION of 'Exponential Growth'
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. On a chart, this curve starts out very slowly, remaining nearly flat for a time before increasing so swiftly as to appear almost vertical, and it follows the formula:
V = S * (1 + R) ^ T
The current value, V, of an initial starting point subject to exponential growth can be determined by multiplying the starting value, S, by the sum of one plus the rate of interest, R, raised to the power of T, or the number of periods that have elapsed.
BREAKING DOWN 'Exponential Growth'
In finance, exponential growth is caused by compounding returns. The power of compounding is one of the most powerful forces in finance. This concept allows investors to create large sums with little initial capital.
The most commonly used example of this is the growth produced by a savings accounts that carries a compounding interest rate.
Compound Interest Example
Assume you deposit $1,000 in an account that earns a guaranteed 10% rate of interest. If the account carries a simple interest rate, then the amount of interest earned each year is 10% of $1,000, or $100. The amount of interest paid does not change each year as long as no additional deposits are made.
If the account carries a compound interest rate, however, interest is earned on the cumulative account total. Each year, the interest rate is applied to sum of the initial deposit and any interest previously paid. In the first year, the interest earned is still 10% of $1,000, or $100. In the second year, however, the 10% rate is applied to the new total of $1,100, yielding $110. With each subsequent year, the amount of interest paid grows, creating rapidly accelerating, or exponential, growth. After 30 years, with no other deposits required, your account would be worth $17,449.40.
With larger sums and higher interest rates, the impact of compounding can be even greater.
Real World Application
While exponential growth is often used in financial modeling, reality is often much more complicated. The application of exponential growth works well in the example above because the rate of interest is guaranteed and does not change over time. In most investments this is not the case. For instance, stock market returns clearly do not smoothly follow longterm averages each year as predicted in simple financial calculations.
Exponential growth, however, has many applications outside the world of finance. The exponential growth formula is often used to predict population growth and inflation.
Accounting for the Unaccountable
Using exponential growth to predict investment returns is primarily useful when the rate of growth is steady and established. Producing accurate estimates for less predictable investments requires more sophisticated formulas designed to account for changing conditions. Thus, other methods of predicting longterm returns â€” such as the Monte Carlo simulation, which uses probability distributions to determine the likelihood of different potential outcomes â€” have seen increasing popularity.

Compound Interest
Compound Interest is interest calculated on the initial principal ... 
Future Value  FV
The value of an asset or cash at a specified date in the future ... 
Triple Exponential Moving Average ...
A technical indicator used for smoothing price and other data. ... 
Data Smoothing
The use of an algorithm to remove noise from a data set, allowing ... 
Compound Return
The rate of return, usually expressed as a percentage, that represents ... 
Stated Annual Interest Rate
The return on an investment that is expressed as a peryear percentage, ...

Investing
Accelerating Returns With Continuous Compounding
Investopedia explains the natural log and exponential functions used to calculate this value. 
Markets
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 ... 
Managing Wealth
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. 
Markets
How Interest Rates Work on Savings Accounts
Here's what you need to know to grow your rainyday fund. 
Personal Finance
The Difference Between Compounding Interest and Simple Interest
Interest is the cost a borrower pays to use someone elseâ€™s money. Interest can be either simple or compounded. 
Markets
Use The Percentage Price Oscillator: The "Elegant Indicator" For Picking Stocks
Technical analysis is basically an attempt to disprove the credo that "Past performance is not indicative of future results." The percentage price oscillator, which measures momentum, is among ... 
Markets
Explaining Interest
Interest is the price charged to borrow money, and is typically expressed as a percentage of the principal, or the amount loaned. 
Managing Wealth
Overcoming Compounding's Dark Side
Understanding how money is made and lost over time can help you improve your returns. 
Markets
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.

How does the compound interest concept vary between a basic savings account and an ...
I understand compound interest as it relates to a basic savings account. If you get 5% interest on $1000 each year, it will ... Read Answer >> 
Other than my savings account, what other types of holdings compound my interest?
Understand the benefits of compounding interest, and learn the types of investments that offer compounding in addition to ... Read Answer >> 
How often is interest compounded?
Understand what compound interest is and how the compounding of interest applies to the benefit of investors or creditors, ... 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 can I tell if a loan uses simple or compound interest?
Learn the differences between simple and compound interest and how you can use mathematical calculations and lender disclosures ... Read Answer >> 
How is compound interest taxed?
Understand the concept of compound interest as opposed to simple interest and learn the usual tax rate at which compound ... Read Answer >>