Rate of Return Calculator with Contributions

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Rate of Return Calculator with Contributions

Determine the annual growth rate required to reach your investment goals with periodic contributions.

Monthly Quarterly Annually
Please ensure all fields are filled with positive numbers. The ending balance must be greater than 0.
Personalized Annual Rate of Return (IRR):
0%

Understanding Rate of Return with Periodic Contributions

Calculating the performance of an investment is straightforward when you make a single one-time deposit. However, when you add money regularly—whether monthly, quarterly, or annually—the math becomes more complex. This calculator uses an iterative numerical method to determine the Internal Rate of Return (IRR), which accounts for the timing and size of every contribution.

The Formula Behind the Calculation

There is no simple algebraic formula to solve for the rate of return (r) when contributions are involved. Instead, we solve for r in the Future Value equation:

FV = PV(1 + r)^n + PMT × [((1 + r)^n – 1) / r]

  • FV: Final Balance
  • PV: Starting Principal (Present Value)
  • PMT: Periodic Contribution
  • n: Total number of periods
  • r: Rate of return per period

Practical Example

Imagine you start with $10,000. Over 5 years, you contribute $200 every month ($12,000 total in contributions). At the end of the 5 years, your account balance is $30,000. Simply looking at the gain ($8,000) doesn't tell the whole story because that $200 you added in the final month didn't have time to grow.

Using this calculator, you would discover that your annualized rate of return for this scenario is approximately 9.82%.

Why Contributions Matter

Contributions act as "fuel" for compound interest. However, because contributions made later in the investment period have less time to benefit from compounding, a high final balance doesn't always mean a high rate of return. This tool helps you separate the growth generated by the market from the growth generated by your own savings habits.

function calculateRateOfReturn() { var pv = parseFloat(document.getElementById('initialBalance').value); var fv = parseFloat(document.getElementById('finalBalance').value); var pmt = parseFloat(document.getElementById('contributionAmount').value); var freq = parseFloat(document.getElementById('frequency').value); var years = parseFloat(document.getElementById('years').value); var errorDiv = document.getElementById('rorError'); var resultBox = document.getElementById('rorResultBox'); if (isNaN(pv) || isNaN(fv) || isNaN(pmt) || isNaN(years) || years <= 0 || fv <= 0) { errorDiv.style.display = 'block'; resultBox.style.display = 'none'; return; } errorDiv.style.display = 'none'; var totalPeriods = years * freq; var pmtPerPeriod = pmt; // We use a Binary Search / Bisection Method to solve for r var low = -0.9999; // -99.99% return var high = 50.0; // 5000% return (extreme upper bound) var r = 0; var precision = 0.0000001; var iterations = 0; var maxIterations = 100; while (iterations < maxIterations) { r = (low + high) / 2; var guessedFV = 0; if (Math.abs(r) fv) { high = r; } else { low = r; } if (Math.abs(high – low) < precision) break; iterations++; } // Convert periodic rate to annual rate // Nominal annual rate = r * freq // Effective annual rate = (1+r)^freq – 1 var annualRate = (Math.pow(1 + r, freq) – 1) * 100; document.getElementById('rorOutput').innerText = annualRate.toFixed(2) + '%'; var totalInvested = pv + (pmt * freq * years); var totalGain = fv – totalInvested; document.getElementById('rorSummary').innerHTML = "Total Amount Invested: $" + totalInvested.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + "" + "Total " + (totalGain >= 0 ? "Profit" : "Loss") + ": $" + Math.abs(totalGain).toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}) + ""; resultBox.style.display = 'block'; }

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