Formula to Calculate Exponential Growth
Exponential Growth formula refers to the formula which is used in order to calculate the final value of the initial value by giving effect of the compounding of the annual growth and according to the formula the final value is derived by adding one to the Annual Growth Rate, then dividing it by the No of Compounding, then resultant is raised with the power of the number of years multiplied by the number of compounding and finally multiplying the resultant with the Initial value.
However, in the case of continuous compounding, 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 annual growth rate into the number of years.
Mathematically, it is represented as below,
Calculation of Exponential Growth (Step by Step)
The exponential growth can be calculated using the following steps:
- Step 1: 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 case of the time value of money calculation.
- Step 2: 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 for the calculation of a future value of a deposit, then the growth rate will be the rate of return expected from the market situation.
- Step 3: Now, the tenure of the growth in terms of number years has to be figured out i.e. for how long the value will be under such a steep growth trajectory.
- Step 4: Now, determine the number of compounding periods per year. The compounding can be quarterly, half-yearly, annually, continuous, etc.
- Step 5: Finally, the exponential growth is used to calculate the final value by compounding 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 a number of 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 a period of 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. 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. value of the deposited money after three years is done using the above formula as,
Final value = $50,000 * (1 + 10%/4 )^{3 * 4}
Calculation will be-
- Final value = $67,244.44
Half Yearly Compounding
No. of compounding per year = 2 (since half yearly)
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. 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
Exponential Growth Formula is used to calculate the final value by compounding the initial value by using an annual growth rate, a number of years and number compounding per year.
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 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 –
- What is Exponential Distribution?
- Advantages of Compound Journal Entry
- Growth Formula in Excel
- Rate Formula in Excel
- Sustainable Growth Rate Formula
- Gordon Growth Model Formula
- Dividend Growth Rate Formula
- GROWTH in Excel
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