Formula to Calculate Exponential Growth

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However, in the case of continuous compoundingContinuous CompoundingThe continuous compounding formula depicts the interest received when constant compounding is done for an infinite number of periods. The four variables used for its computation are the principal amount, time, interest rate and the number of the compounding period.read more, the equation calculates the final value by multiplying the initial value and the exponential function, raised to the power of the annual growth rate into the number of years.

Mathematically, it represents as below,

Calculation of Exponential Growth (Step by Step)

On the other hand, the formula for continuous compounding is to calculate the final value by multiplying the initial value (Step 1) and the exponential function raised to the power of the annual growth rate (Step 2) over several years (Step 3), as shown above.

  • Firstly, determine the initial value for which the final value one has to calculate. For instance, it can be the present value of money in the time value of money calculation. Next, determine the annual growth rate, which one can decide based on the type of application. For instance, if the formula is to calculate a future value formula of a deposit, then the growth rate will be the rate of return expected from the market situation. The tenure of the growth in terms of the number of years figured out, i.e., how long the value will be under such a steep growth trajectory. Now, determine the number of compounding periods per year. The compounding can be quarterly, half-yearly, annually, continuous, etc. Finally, the exponential growth is to calculate the final value by compounding the initial value (Step 1) by using an annual growth rate (Step 2), the number of years (Step 3), and the number compounding per year (Step 4), as shown above.

Example

  • MonthlyQuarterlyHalf YearlyAnnuallyContinuously

Monthly Compounding

No. of compounding per year = 12 (since monthly)

The calculation of exponential growth, i.e., the value of the deposited money after three years is done using the above formula,

  • Final value = $50,000 * (1 +10%/12 )3 * 12

The calculation will be-

  • Final value = $67,409.09

Quarterly Compounding

No. of compounding per year = 4 (since quarterly)

The calculation of exponential growth, i.e., the value of the deposited money after three years, is done using the above formula as,

Final value = $50,000 * (1 + 10%/4 )3 * 4

  • Final value = $67,244.44

Half Yearly Compounding

No. of compounding per year = 2 (since half-yearly)

The value of the deposited money after three years done using the above formula:

Final value = $50,000 * (1 + 10%/2 )3 * 2

Calculation of Exponential Growth will be-

  • Final value = $67,004.78

Annual Compounding

No. of compounding per year = 1 (since annual)

Final value = $50,000 * (1 + 10%/1 )3 * 1

  • Final value = $66,550.00

Continuous Compounding

Since continuous compounding, the value of the deposited money after three years money is calculated using the above formula as,

Final value = Initial value * e Annual growth rate * No. of years

Final value = $50,000 * e 10% * 3

  • Final value = $67,492.94

Calculator

You can use the following Exponential Growth Calculator.

Relevance and Uses

A financial analyst needs to understand the exponential growth equation since it primarily calculates compound returns. The enormity of the concept in finance demonstrates the power of compounding to create a large sum with a significantly low initial capital. For the same reason, it holds great importance for investors who believe in long holding periods.

This article is a guide to the Exponential Growth Formula. Here, we discuss calculating exponential growth with examples and downloadable Excel sheets. You can learn more about financing from the following articles: –

  • Exponential DistributionExponential DistributionExponential distribution refers to the continuous and constant probability distribution which is actually used to model the time period that a person needs to wait before the given event happens. This distribution is a continuous counterpart of a geometric distribution that is instead distinct.read moreGrowth Formula in ExcelCalculate Sustainable Growth RateFormula of Dividend Growth Rate