Present Value Rate of Return Calculator

Present Value Rate of Return Calculator

Results

The implied annual rate of return is:

0%

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Understanding the Present Value Rate of Return

The Present Value Rate of Return Calculator is a specialized financial tool used to determine the efficiency of an investment. In financial mathematics, this represents the discount rate at which the future value of an asset equals its initial cost (present value).

The Mathematical Formula

This calculator solves for the rate (r) using the standard time value of money formula. The calculation is derived from:

r = [(FV / PV)^(1 / n)] – 1

• r: Annualized Rate of Return
• FV: Future Value of the investment
• PV: Present Value (the initial amount invested)
• n: Number of years or time periods

Practical Example

Suppose you purchase a rare collectible for 10,000 (Initial Investment). After 6 years, you sell it for 18,000 (Future Value). To find your performance:

1. Divide Future Value by Present Value: 18,000 / 10,000 = 1.8
2. Raise the result to the power of (1 / 6 years): 1.8^(0.1667) ≈ 1.1029
3. Subtract 1 to get the decimal: 0.1029
4. Multiply by 100 to get the percentage: 10.29%

Why Use This Calculator?

Unlike simple ROI (Return on Investment), which ignores time, the Rate of Return calculated here accounts for the compounding effect over years. This allows you to compare different investment opportunities with varying durations on a level playing field.

function calculateROR() { var pv = parseFloat(document.getElementById('initialInvestment').value); var fv = parseFloat(document.getElementById('futureValue').value); var n = parseFloat(document.getElementById('timePeriod').value); var resultDiv = document.getElementById('rorResult'); var output = document.getElementById('rorOutput'); var summary = document.getElementById('rorSummary'); if (isNaN(pv) || isNaN(fv) || isNaN(n) || pv <= 0 || n <= 0) { alert("Please enter valid positive numbers. Initial investment and time period must be greater than zero."); return; } // Calculation: r = ((FV / PV)^(1 / n)) – 1 var r = Math.pow((fv / pv), (1 / n)) – 1; var rPercentage = (r * 100).toFixed(2); resultDiv.style.display = 'block'; output.innerHTML = rPercentage + "%"; var totalGain = fv – pv; var growthMultiple = (fv / pv).toFixed(2); summary.innerHTML = "Over " + n + " years, your investment grew by a factor of " + growthMultiple + "x, resulting in a total net gain of " + totalGain.toLocaleString() + "."; // Scroll to result smoothly resultDiv.scrollIntoView({ behavior: 'smooth', block: 'nearest' }); }