A Decreasing Rate Calculator is an essential tool for understanding exponential decay, depreciation, and reduction trends over time. Unlike simple subtraction where a fixed amount is removed, a decreasing rate implies that a percentage of the current value is lost during each period. This concept is widely used in finance, physics, and biology.
How It Works
The logic follows the exponential decay model. At each step, the value is multiplied by the remaining percentage. For example, if something decreases by 10%, it retains 90% of its value from the previous period.
The mathematical formula used is:
Vfinal = Vinitial × (1 – r)t
Vfinal: The value after time t.
Vinitial: The starting amount.
r: The rate of decrease expressed as a decimal (e.g., 5% = 0.05).
t: The number of time periods (years, hours, steps).
Real-World Applications
This calculator is versatile and can be applied to various scenarios:
Asset Depreciation: Calculating the book value of a car or machinery as it loses a percentage of its value every year.
Radioactive Decay: Estimating the remaining amount of a radioactive isotope based on its decay rate.
Population Decline: Modeling populations in biological studies where growth is negative.
Cooling Rates: In physics, understanding how temperature drops over time (Newton's Law of Cooling approximations).
Example Calculation
Imagine you have a piece of equipment worth 10,000. It depreciates at a rate of 15% per year. We want to know its value after 5 years.
Initial Value: 10,000
Rate: 15% (0.15)
Time: 5 periods
Using the calculator, the formula would be 10,000 × (1 – 0.15)5. This results in a final value of approximately 4,437.05, meaning the equipment lost over half its value in 5 years.
function calculateDecay() {
// 1. Get Input Elements
var initialInput = document.getElementById("initialValue");
var rateInput = document.getElementById("decayRate");
var periodsInput = document.getElementById("periods");
var resultsDiv = document.getElementById("results");
var tableBody = document.getElementById("tableBody");
var finalValDisplay = document.getElementById("finalValResult");
var totalLostDisplay = document.getElementById("totalLostResult");
var percentLeftDisplay = document.getElementById("percentLeftResult");
// 2. Parse Values
var initial = parseFloat(initialInput.value);
var ratePercent = parseFloat(rateInput.value);
var time = parseFloat(periodsInput.value);
// 3. Validation
if (isNaN(initial) || isNaN(ratePercent) || isNaN(time)) {
alert("Please enter valid numbers for all fields.");
return;
}
if (ratePercent 100) {
alert("Decrease rate must be between 0 and 100.");
return;
}
// 4. Main Calculation (Exponential Decay)
// Formula: V = P * (1 – r)^t
var rateDecimal = ratePercent / 100;
var finalValue = initial * Math.pow((1 – rateDecimal), time);
var totalDecrease = initial – finalValue;
var remainingPercentage = (finalValue / initial) * 100;
// 5. Update Summary UI
// Helper to format numbers nicely
function formatNum(num) {
return num.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 });
}
finalValDisplay.innerHTML = formatNum(finalValue);
totalLostDisplay.innerHTML = formatNum(totalDecrease);
percentLeftDisplay.innerHTML = formatNum(remainingPercentage) + "%";
// 6. Generate Breakdown Table
var tableHTML = "";
var currentVal = initial;
// Loop through periods. If time is a decimal, we floor it for the loop, or handle steps.
// Usually breakdown is shown per integer step.
var steps = Math.floor(time);
for (var i = 1; i <= steps; i++) {
var prevVal = currentVal;
// Calculate value at this step
currentVal = prevVal * (1 – rateDecimal);
var decreaseAmount = prevVal – currentVal;
tableHTML += "
";
tableHTML += "
" + i + "
";
tableHTML += "
" + formatNum(prevVal) + "
";
tableHTML += "
" + formatNum(decreaseAmount) + "
";
tableHTML += "
" + formatNum(currentVal) + "
";
tableHTML += "
";
}
// Handle partial period if time is not an integer (e.g., 5.5 years)
if (time > steps) {
var prevVal = currentVal;
// Calculate final remainder exact match
currentVal = finalValue;
var decreaseAmount = prevVal – currentVal;
tableHTML += "