## 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 long-term 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 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.