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.

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.

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.