Loading the player...

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 slowly, remaining nearly flat for a time before increasing swiftly as to appear almost vertical. 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, compound returns cause exponential growth. 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. Savings accounts that carry a compounding interest rate are common examples.

Application of Exponential Growth

Assume you deposit $1,000 in an account that earns a guaranteed 10% rate of interest. If the account carries a simple interest rate, you will earn $100 per year. The amount of interest paid will not change as long as no additional deposits are made.

If the account carries a compound interest rate, however, you will earn interest on the cumulative account total. Each year, the lender will apply the interest rate to sum of the initial deposit, along with any interest previously paid. In the first year, the interest earned is still 10% 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.

While exponential growth is often used in financial modeling, reality is often 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 do not smoothly follow long-term averages each year many models assume.

Other methods of predicting long-term returns – such as the Monte Carlo simulation, which uses probability distributions to determine the likelihood of different potential outcomes – have seen increasing popularity. Exponential growth models are more useful to predict investment returns when the rate of growth is steady.

RELATED TERMS
  1. Triple Exponential Moving Average ...

    The triple exponential moving average, or TEMA, was developed ...
  2. Periodic Interest Rate

    The periodic interest rate is the interest rate charged on a ...
  3. Triple Exponential Average - TRIX

    The triple exponential average (TRIX) indicator is an oscillator ...
  4. Growth Curve

    A growth curve is a graphical representation of how a particular ...
  5. Effective Annual Interest Rate

    The effective annual interest rate is an investment's annual ...
  6. Compounding

    Compounding is the process in which an asset's earnings, from ...
Related Articles
  1. Investing

    Exponential: My Favorite Term

    John Mauldin shares why "exponential" is his favorite financial term.
  2. Trading

    Do Adaptive Moving Averages Lead To Better Results?

    These complex indicators can help traders interpret trend changes, but are they too good to be true?
  3. Personal Finance

    Where to Put Your Cash: Call Deposit vs. Time Deposit Accounts

    Time deposit accounts and call deposit accounts allow customers to earn higher interest in exchange for less access to their cash.
  4. Personal Finance

    Simple Interest Loans: Do They Exist?

    You'll find simple interest loans offered by a variety of loan products, including car loans. Use them to your advantage.
  5. Personal Finance

    Handling High-Yield Savings Accounts

    Is a high-yield savings account right for you? Read on to find out what they have to offer.
  6. Retirement

    What Your 401(k) Can Look Like in the Next 20 Years

    Discover how time and compounded growth of earnings can help even a modest 401(k) balance grow to a significant sum over 20 years.
  7. Investing

    Investing $100 a month in stocks for 30 years

    Find out how you could potentially earn hundreds of thousands of dollars just by investing $100 a month in stocks during your working years.
  8. Personal Finance

    Banking 101

    Do you really need a bank account? A quick survey of banking and how a relationship with a bank can organize your financial life.
RELATED FAQS
  1. What formula calculates interest on interest?

    Find out about compounding interest, what it measures, and how to calculate the amount of compound interest accrued using ... Read Answer >>
  2. 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 >>
  3. How do I calculate compound interest using Excel?

    Learn how to calculate compound interest using three different techniques in Microsoft Excel. Read Answer >>
  4. What is the difference between a simple moving average and an exponential moving ...

    The only difference between simple moving average and an exponential moving average is the sensitivity each one shows to ... Read Answer >>
  5. Simple versus compound interest

    Different methods in interest calculation can end up different interest payment. Learn the differences between simple and ... Read Answer >>
Trading Center