Compound Growth Rate Calculator
Understanding Compound Growth Rate
The Compound Growth Rate (CGR) is a measure of how an investment or a metric grows over a specific period, assuming that the gains are reinvested. It's essentially the average annual growth rate over a period longer than one year, considering the effect of compounding. This is different from simple growth rate, which does not account for the snowball effect of growth on previous growth.
The formula used to calculate the Compound Growth Rate is:
CGR = (($\frac{Final Value}{Initial Value}$)$^{\frac{1}{Number of Periods}}$ – 1) * 100%
Where:
- Initial Value: The starting value of the investment or metric.
- Final Value: The ending value of the investment or metric after a certain number of periods.
- Number of Periods: The total number of periods over which the growth occurred (e.g., years, months).
The CGR is a powerful tool for understanding long-term trends and comparing the performance of different investments or metrics. For example, if an investment grows from $1,000 to $2,500 over 5 years, the CGR will give you a consistent annual growth rate that smooths out any fluctuations within those 5 years.
Example Calculation:
Let's say you invested an initial amount of $1,000 (Initial Value) and after 5 years (Number of Periods), your investment has grown to $2,000 (Final Value).
Using the formula:
CGR = (($\frac{2000}{1000}$)$^{\frac{1}{5}}$ – 1) * 100%
CGR = (2$^{0.2}$ – 1) * 100%
CGR = (1.1487 – 1) * 100%
CGR = 0.1487 * 100%
CGR = 14.87%
This means your investment grew at an average compound rate of 14.87% per year over the 5-year period.
function calculateCompoundGrowthRate() {
var initialValue = parseFloat(document.getElementById("initialValue").value);
var finalValue = parseFloat(document.getElementById("finalValue").value);
var numberOfPeriods = parseFloat(document.getElementById("numberOfPeriods").value);
var resultDiv = document.getElementById("result");
if (isNaN(initialValue) || isNaN(finalValue) || isNaN(numberOfPeriods) || initialValue <= 0 || numberOfPeriods <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields.";
return;
}
var cgr = (Math.pow(finalValue / initialValue, 1 / numberOfPeriods) – 1) * 100;
if (isNaN(cgr)) {
resultDiv.innerHTML = "Calculation error. Please check your inputs.";
} else {
resultDiv.innerHTML = "
Result:
The Compound Growth Rate is: " + cgr.toFixed(2) + "%";
}
}
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