function calculateInflation() {
var startVal = parseFloat(document.getElementById('initialPrice').value);
var endVal = parseFloat(document.getElementById('finalPrice').value);
var years = parseFloat(document.getElementById('timeYears').value);
var resultBox = document.getElementById('result');
var totalChangeDisplay = document.getElementById('totalChangeDisplay');
var diffDisplay = document.getElementById('diffDisplay');
var avgRateDisplay = document.getElementById('avgRateDisplay');
// Validation
if (isNaN(startVal) || isNaN(endVal) || isNaN(years) || years <= 0 || startVal <= 0) {
alert("Please enter valid positive numbers. Start Price and Years must be greater than zero.");
resultBox.style.display = "none";
return;
}
// 1. Calculate Total Percentage Change
// Formula: ((End – Start) / Start) * 100
var totalChange = ((endVal – startVal) / startVal) * 100;
// 2. Calculate Absolute Difference
var difference = endVal – startVal;
// 3. Calculate Average Annual Inflation Rate (Compound Annual Growth Rate – CAGR)
// Formula: ( (End / Start)^(1 / Years) ) – 1
var ratio = endVal / startVal;
var power = 1 / years;
var annualRate = (Math.pow(ratio, power) – 1) * 100;
// Display Results
totalChangeDisplay.innerHTML = totalChange.toFixed(2) + "%";
diffDisplay.innerHTML = difference.toFixed(2);
avgRateDisplay.innerHTML = annualRate.toFixed(2) + "%";
resultBox.style.display = "block";
}
Understanding the Average Rate of Inflation
Calculating the average rate of inflation is essential for investors, economists, and consumers who want to understand how the purchasing power of money changes over a specific period. Unlike a simple average, the average inflation rate is typically calculated using the geometric mean (Compound Annual Growth Rate or CAGR) to account for the compounding effect of price changes year over year.
Why Calculate Average Inflation?
Inflation erodes the value of currency. If you held $100 ten years ago, it would likely buy fewer goods today. By calculating the average rate, you can determine:
Real Investment Returns: Did your portfolio outpace inflation?
Salary Adjustments: Has your income kept up with the rising cost of living?
Historical Comparison: Comparing price stability between different decades.
The Formula
To calculate the average annual rate of inflation, we treat it as a Compound Annual Growth Rate (CAGR). The formula is:
Rate = ( ( Final Value / Initial Value )1/n ) – 1
Where:
Final Value: The price of the item or the CPI (Consumer Price Index) value at the end of the period.
Initial Value: The price or CPI value at the beginning of the period.
n: The number of years between the two values.
Example Calculation
Let's say a basket of goods cost $100.00 exactly 5 years ago. Today, that same basket of goods costs $125.00.
Total Increase: The price rose by $25.00, which is a 25% total increase.
Simple Average (Incorrect method for compounding): 25% / 5 years = 5%. This ignores compounding.
The average annual inflation rate is approximately 4.56%. This is slightly lower than the simple average because the calculation accounts for the fact that the price base grows larger each year.
Using the Consumer Price Index (CPI)
While you can use specific prices (like the cost of milk or a house), economists usually use the Consumer Price Index (CPI) to calculate inflation for an entire economy. The CPI is a measure that examines the weighted average of prices of a basket of consumer goods and services.
To use this calculator with CPI, simply enter the starting CPI index value in the "Start Price" field and the ending CPI index value in the "End Price" field.