The term Rate Per Annum (RPA) refers to the annualized rate of growth, return, or change over a one-year period. While frequently used in finance to describe interest, it is a universal mathematical concept used to standardize measurements of change so that different timeframes can be compared accurately.
Standardizing a rate "per annum" allows you to compare a 5% gain over 3 months against a 12% gain over 14 months by bringing both figures to a consistent 12-month baseline.
The RPA Formula
To calculate the annualized rate of return (CAGR method), we use the following formula:
Rate Per Annum = [(Final Value / Initial Value)^(1 / Years) – 1] × 100
How to Use This Calculator
Initial Value: Enter the starting amount or the value at the beginning of the period.
Final Value: Enter the ending amount or current value.
Duration: Specify how long it took to reach the final value, selecting Days, Months, or Years.
Example Calculation
Imagine you purchased a collectible item for 1,200 and sold it 18 months later for 1,500. To find the rate per annum:
function calculateRPA() {
var initial = parseFloat(document.getElementById('initialValue').value);
var final = parseFloat(document.getElementById('finalValue').value);
var timeVal = parseFloat(document.getElementById('timeValue').value);
var unit = document.getElementById('timeUnit').value;
var resultBox = document.getElementById('rpaResultBox');
var resultDisplay = document.getElementById('rpaValue');
var description = document.getElementById('rpaDescription');
if (isNaN(initial) || isNaN(final) || isNaN(timeVal) || initial <= 0 || timeVal <= 0) {
alert("Please enter valid positive numbers for all fields.");
return;
}
// Convert time to years
var years = 0;
if (unit === 'days') {
years = timeVal / 365;
} else if (unit === 'months') {
years = timeVal / 12;
} else {
years = timeVal;
}
// Calculation: CAGR formula (Compound Annual Growth Rate)
// Rate = ((Final / Initial) ^ (1 / years) – 1) * 100
var rate = (Math.pow((final / initial), (1 / years)) – 1) * 100;
// Handle edge case where final value is less than initial (negative growth)
var formattedRate = rate.toFixed(2);
resultDisplay.innerHTML = formattedRate + "%";
var totalReturn = ((final – initial) / initial * 100).toFixed(2);
description.innerHTML = "This reflects a total absolute change of " + totalReturn + "% over the specified period, normalized to a 12-month annual cycle.";
resultBox.style.display = 'block';
}