Long-Term Growth Rate Calculator
Understanding Long-Term Growth Rate
The long-term growth rate is a crucial metric for understanding how an investment, asset, or any quantifiable entity has performed over an extended period. It measures the average annual percentage increase in value. This calculator helps you determine this rate based on the starting value, ending value, and the duration over which this change occurred.
Formula Used:
The compound annual growth rate (CAGR) formula is used to calculate the long-term growth rate. It smooths out volatility and provides a single, representative rate of return.
CAGR = ((Ending Value / Starting Value)^(1 / Number of Years)) – 1
Where:
- Ending Value: The final value of the investment or asset at the end of the period.
- Starting Value: The initial value of the investment or asset at the beginning of the period.
- Number of Years: The total number of years over which the growth occurred.
Why is it Important?
Understanding long-term growth rates is essential for:
- Investment Analysis: Comparing the performance of different investments over time.
- Financial Planning: Projecting future values of assets based on historical growth.
- Business Valuation: Assessing the historical growth trajectory of a company.
- Economic Indicators: Tracking the growth of economies or specific sectors.
Example Calculation:
Let's say you invested $10,000 (Starting Value) in a stock that grew to $50,000 (Ending Value) over 10 years (Number of Years).
Using the formula:
CAGR = (($50,000 / $10,000)^(1 / 10)) – 1
CAGR = (5^0.1) – 1
CAGR = 1.1746 – 1
CAGR = 0.1746 or 17.46%
This means the investment grew at an average annual rate of 17.46% over the 10-year period.
function calculateGrowthRate() {
var initialValue = parseFloat(document.getElementById("initialValue").value);
var finalValue = parseFloat(document.getElementById("finalValue").value);
var numberOfYears = parseFloat(document.getElementById("numberOfYears").value);
var resultDiv = document.getElementById("result");
if (isNaN(initialValue) || initialValue <= 0) {
resultDiv.innerHTML = "Please enter a valid Starting Value greater than zero.";
return;
}
if (isNaN(finalValue) || finalValue <= 0) {
resultDiv.innerHTML = "Please enter a valid Ending Value greater than zero.";
return;
}
if (isNaN(numberOfYears) || numberOfYears <= 0) {
resultDiv.innerHTML = "Please enter a valid Number of Years greater than zero.";
return;
}
// CAGR = ((Ending Value / Starting Value)^(1 / Number of Years)) – 1
var growthRate = Math.pow((finalValue / initialValue), (1 / numberOfYears)) – 1;
if (isNaN(growthRate) || !isFinite(growthRate)) {
resultDiv.innerHTML = "Calculation error. Please check your inputs.";
} else {
resultDiv.innerHTML = "
Result:
" +
"Starting Value: " + initialValue.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 }) + "" +
"Ending Value: " + finalValue.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 }) + "" +
"Number of Years: " + numberOfYears.toLocaleString() + "" +
"
The calculated Long-Term Growth Rate (CAGR) is: " + (growthRate * 100).toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 }) + "%";
}
}
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