Formula to Calculate Exponential Growth
Exponential Growth refers to the increase due to compounding of the data over time and therefore follows a curve that represents an exponential function.
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For eg:
Source: Exponential Growth Formula (wallstreetmojo.com)
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 is used to calculate the final value by multiplying the initial value and the exponential function, which is raised to the power of the annual growth rate into the number of years.
Mathematically, it is represented as below,
Calculation of Exponential Growth (Step by Step)
Exponential growth can be calculated using the following steps:
- Firstly, determine the initial value for which the final value has to be calculated. For instance, it can be the present value of money in the time value of money calculationTime Value Of Money CalculationThe Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read moreThe Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read moreThe Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read more.
- Next, try to determine the annual growth rate, and it can be decided based on the type of application. For instance, if the formula is used to calculate a future value formula of a deposit, then the growth rate will be the rate of return expected from the market situation.
- Now, the tenure of the growth in terms of number years has to be 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 used to calculate the final value by compoundingCompoundingCompounding is a method of investing in which the income generated by an investment is reinvested, and the new principal amount is increased by the amount of income reinvested. Depending on the time period of deposit, interest is added to the principal amount.read more of the initial value (step 1) by using an annual growth rate (step 2), number of years (step 3), and number compounding per year (step 4) as shown above.
On the other hand, the formula for continuous compounding is used to calculate the final value by multiplying the initial value (step 1) and the exponential function, which is raised to the power of annual growth rate (step 2) into several years (step 3) as shown above.
Example
Let us take an example of David, who has deposited a sum of $50,000 in his bank account today for three years at a 10% rate of interest. Determine the value of the deposited money after three years if the compounding is done:
- Monthly
- Quarterly
- Half Yearly
- Annually
- Continuously
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 as,
- 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}
The calculation will be-
- 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 is done using the above formula as,
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)
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%/1 )^{3 * 1}
Calculation of Exponential Growth will be-
- 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}
Calculation of Exponential Growth will be-
- Final value = $67,492.94
Calculator
You can use the following Exponential Growth Calculator.
Initial Value | |
Annual Growth Rate | |
No. of Compounding | |
No. of Years | |
Exponential Growth Formula = | |
Exponential Growth Formula = | Initial Value * (1 +Annual Growth Rate/No. of Compounding)^{No. of Years*No. of Compounding} | |
0 * (1 +0/0)^{0*0} = | 0 |
Relevance and Uses
It is very important for a financial analyst to understand the concept of exponential growth equation since it is primarily used in the calculation of compound returns. The enormity of the concept in finance is demonstrated by 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.
Recommended Articles
This article has been a guide to the Exponential Growth Formula. Here we discuss how to calculate exponential growth with examples and downloadable excel sheets. You can learn more about financing from the following articles –
- Exponential Distribution
- Growth Formula in Excel
- Calculate Sustainable Growth Rate
- Formula of Dividend Growth Rate
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