Per Annum Rate Calculator

Per Annum Rate Calculator

Days Months Years

Calculation Result

function calculatePerAnnumRate() { var start = parseFloat(document.getElementById('startValue').value); var end = parseFloat(document.getElementById('endValue').value); var duration = parseFloat(document.getElementById('durationValue').value); var unit = document.getElementById('durationUnit').value; var resultContainer = document.getElementById('pa-result-container'); var resultText = document.getElementById('pa-result-text'); var summaryText = document.getElementById('pa-summary'); if (isNaN(start) || isNaN(end) || isNaN(duration) || start <= 0 || end <= 0 || duration <= 0) { alert('Please enter valid positive numbers for all fields.'); return; } var years; if (unit === 'days') { years = duration / 365; } else if (unit === 'months') { years = duration / 12; } else { years = duration; } // CAGR (Compound Annual Growth Rate) formula: ((End/Start)^(1/t) – 1) * 100 var rate = (Math.pow((end / start), (1 / years)) – 1) * 100; var totalGainPercent = ((end – start) / start) * 100; resultText.innerText = rate.toFixed(2) + "% p.a."; summaryText.innerHTML = "Your total growth of " + totalGainPercent.toFixed(2) + "% over " + duration + " " + unit + " translates to an annualized rate of " + rate.toFixed(2) + "%."; resultContainer.style.display = 'block'; }

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Understanding the Per Annum (p.a.) Rate

The term "Per Annum" is Latin for "by the year." In mathematics and finance, the per annum rate represents the geometric progression of a value over a single year. It is the most standardized way to compare growth rates across different time periods, whether the actual duration was 50 days or 10 years.

Why Use an Annualized Rate?

Raw growth percentages can be misleading. For instance, if Asset A grows 10% in 6 months and Asset B grows 15% in 2 years, which performed better? By converting both to a per annum rate, you can compare them on equal footing.

• Standardization: It aligns all metrics to a 12-month calendar.
• Compounding Logic: Unlike simple averages, the per annum rate accounts for the "growth on growth" effect.
• Performance Analysis: Essential for evaluating business KPIs, population changes, and investment returns.

The Per Annum Formula

This calculator uses the Compound Annual Growth Rate (CAGR) formula, which is the industry standard for determining a per annum rate:

Rate = [(Final Value / Initial Value)^{(1 / Years)} – 1] × 100

Practical Example

Imagine you have a business metric that started at 500 units. After 18 months, that metric grew to 750 units. While the total growth is 50%, the per annum rate is calculated as:

1. Final / Initial = 1.5
2. Years = 18 / 12 = 1.5 years
3. (1.5)^{(1 / 1.5)} – 1 = 0.3103
4. Result: 31.03% p.a.

Frequently Asked Questions

Is "Per Annum" the same as APR?
In many financial contexts, they are related, but "per annum rate" is a broader term used for any growth metric, whereas APR (Annual Percentage Rate) often includes specific fees and regulations related to lending.

Can the rate be negative?
Yes. If the Final Value is lower than the Initial Value, the calculator will return a negative percentage, indicating an annualized rate of decline.