Understanding Exponential Growth: Definition, Examples & Applications

Exponential growth is when data rises over a period of time, creating an upwards trending curve on a graph. In mathematics, when the function includes a power (or an exponent), the calculation would be increasing exponentially. For example, if hens lay eggs three times per year and triples every year, then in the second year, there would be 27, and in the third year, there would be 81.

Summary

• Exponential growth can be illustrated as a graph that is flat in the beginning and instantaneously grows in the vertical direction over a period of time.
• Within the realm of finance, exponential growth is mostly seen in compounding interest, which is prevalent in various investment instruments, including stocks and high-interest savings accounts.
• Compound interest is favorable to investors, as they can increase their net worth over time using a small amount of cash flow.

Understanding Exponential Growth

Within the realm of finance, when an individual saves money in a high-yield savings accountSavings AccountA savings account is a typical account at a bank or a credit union that allows an individual to deposit, secure, or withdraw money when the need arises. A savings account usually pays some interest on deposits, although the rate is quite low. for an extensive period of time, the investor will receive compound returns due to exponential growth. It is an example of how investments can grow exponentially with little initial outlay.

If the account provides a compound interest rate, then the investor will receive interest on the principal and interest payment received from the previous period. For example, in the first year, the investor may receive 15% interest on a $100 face value bond that matures in 30 years. Therefore, he would receive $15.

In the second year, the 15% interest rate would then be applied to $115 rather than $100, considering the interest payment given in year one. Thus, as each year passes by, interest payments will continue to accumulate and be considered within the yearly interest payment calculation by the time the financial instrument matures. If illustrated, the growth would be an exponential curve.

Exponential Growth Formula

Illustratively, an exponential graph will begin low and appear flat for some time before increasing almost in the vertical direction. It can be perceived as follows:

V = S * (1+r)^T

Where:

• S = Beginning value or principal amount
• r = Rate of return (or interest rate)
• T = Time that’s passed since the issuance of the financial instrument

Understanding What Compounding Is

To investors, compounding means the ability to grow one’s wealth exponentially over a period of time by earning interest on the additional earnings received from previous interest payments that stem from the principal amount. It contrasts with simple interestSimple InterestSimple interest formula, definition and example. Simple interest is a calculation of interest that doesn't take into account the effect of compounding.  In many cases, interest compounds with each designated period of a loan, but in the case of simple interest, it does not.  The calculation of simple interest is equal to the principal amount multiplied by the interest rate, multiplied by the number of periods., as it does not reflect compounding. Simple interest only pays interest on the original principal, not including the earnings received over the lifetime of the financial instrument.

To calculate compound interest, the formula is as follows:

P[(1+i)^n-1]

Where:

• P = Principal
• i = Nominal annual interest rate
• N = Number of compounding periods

Uses of Exponential Growth

Exponential growth is often used in financial modelingFinancial ModelingFree financial modeling resources and guides to learn the most important concepts at your own pace. These articles will teach you financial modeling best practices with hundreds of examples, templates, guides, articles, and more. Learn what financial modeling is, how to build a model, Excel skills, tips and tricks. Although the concept is apparent in a high-interest savings account, the reason for that is because interest rates tend to not waver or fluctuate as much during different economic states. However, when considering stocks, returns are not as smooth.

Overall, exponential growth models are useful in predicting investment returns when the growth rate is steady and does not oscillate frequently.

More Resources

CFI offers the Capital Markets & Securities Analyst (CMSA)®Program Page - CMSAEnroll in CFI's CMSA® program and become a certified Capital Markets &Securities Analyst. Advance your career with our certification programs and courses. certification program for those looking to take their careers to the next level. To keep learning and advancing your career, the following resources will be helpful:

• Continuously Compounded ReturnContinuously Compounded ReturnContinuously compounded return is what happens when the interest earned on an investment is calculated and reinvested back into the account for an infinite number of periods. The interest is calculated on the principal amount and the interest accumulated over the given periods
• Effective Annual Interest RateEffective Annual Interest RateThe Effective Annual Interest Rate (EAR) is the interest rate that is adjusted for compounding over a given period. Simply put, the effective
• Rate of ReturnRate of ReturnThe Rate of Return (ROR) is the gain or loss of an investment over a period of time copmared to the initial cost of the investment expressed as a percentage. This guide teaches the most common formulas
• Compound Growth RateCompound Growth RateThe compound growth rate is a measure used specifically in business and investing contexts, that indicates the growth rate over multiple time periods. It is a measure of the constant growth of a data series. The biggest advantage of the compound growth rate is that the metric takes into consideration the compounding effect.