Sign Convention: Ensure PV (money received) is positive and PMT (money paid out) is negative (or vice versa).
Total number of payment periods.
Payment made each period (negative if paying out).
Total amount the future payments are worth now (loan amount).
Cash balance attained after last payment (default 0).
End of Period (0)
Beginning of Period (1)
Periodic Rate:
Annual Rate (x12):
*Assuming monthly periods for annual calc
function calculateExcelRate() {
// Inputs
var nper = parseFloat(document.getElementById('nper').value);
var pmt = parseFloat(document.getElementById('pmt').value);
var pv = parseFloat(document.getElementById('pv').value);
var fv = parseFloat(document.getElementById('fv').value);
var type = parseInt(document.getElementById('type').value);
var resultArea = document.getElementById('result-area');
// Validation
if (isNaN(nper) || isNaN(pmt) || isNaN(pv)) {
alert("Please enter valid numbers for Nper, Pmt, and Pv.");
return;
}
if (isNaN(fv)) fv = 0;
// Check for no solution scenarios
if (nper 0 && pv > 0 && fv > 0) || (pmt < 0 && pv < 0 && fv < 0)) {
alert("No solution: PV, PMT, and FV cannot all have the same sign. Please verify your cash flow directions (positive for money in, negative for money out).");
return;
}
// Newton-Raphson approximation settings
var rate = 0.1; // Initial guess (10%)
var maxIter = 100; // Max iterations
var eps = 1e-7; // Precision
var found = false;
// Iteration loop
for (var i = 0; i < maxIter; i++) {
var y, f, derivative;
// Function to solve: PV*(1+r)^n + PMT*(1+r*type)*[(1+r)^n – 1]/r + FV = 0
// Avoid division by zero if rate is 0
if (Math.abs(rate) < eps) {
y = pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
} else {
f = Math.pow(1 + rate, nper);
y = pv * f + pmt * (1 + rate * type) * ((f – 1) / rate) + fv;
}
// Numerical derivative (f(r+h) – f(r)) / h
// This is safer than writing the explicit derivative formula inline
var h = 0.00001;
var y_plus_h;
var r_h = rate + h;
if (Math.abs(r_h) < eps) {
y_plus_h = pv * (1 + nper * r_h) + pmt * (1 + r_h * type) * nper + fv;
} else {
var f_h = Math.pow(1 + r_h, nper);
y_plus_h = pv * f_h + pmt * (1 + r_h * type) * ((f_h – 1) / r_h) + fv;
}
derivative = (y_plus_h – y) / h;
// Update rate
var newRate = rate – y / derivative;
// Check convergence
if (Math.abs(newRate – rate) < eps) {
rate = newRate;
found = true;
break;
}
rate = newRate;
}
if (found && isFinite(rate)) {
var percentage = (rate * 100).toFixed(4) + "%";
var annualPercentage = (rate * 12 * 100).toFixed(4) + "%"; // Simple multiplication for estimation
document.getElementById('periodic-rate').innerHTML = percentage;
document.getElementById('annual-rate').innerHTML = annualPercentage;
resultArea.style.display = 'block';
} else {
resultArea.style.display = 'none';
alert("Calculation failed to converge. Please check your input values for realistic financial scenarios.");
}
}
Understanding the Excel RATE Function Calculation
The Excel RATE Calculator allows you to determine the interest rate per period for an annuity, loan, or investment without opening spreadsheet software. This tool replicates the mathematical logic behind the Microsoft Excel =RATE() function.
How It Works
In financial analysis, the interest rate is often the unknown variable. While you might know how much you borrowed (Present Value), how much you pay monthly (Payment), and how long the term is (Nper), the exact effective interest rate might be hidden. This calculator solves for the rate r in the Time Value of Money equation:
Nper (Number of Periods): The total number of payment periods in the annuity. For a 5-year loan paid monthly, this is 5 × 12 = 60.
Pmt (Payment): The payment made each period. This cannot change over the life of the annuity. Important: Use a negative sign (e.g., -500) if this is money leaving your pocket.
Pv (Present Value): The total value of a series of future payments right now. For a loan, this is the loan amount (positive value).
Fv (Future Value): The cash balance you want to attain after the last payment is made. For loans, this is usually 0 (the loan is paid off).
Type: Indicates when payments are due. Select '0' for payments at the end of the period (most loans) or '1' for payments at the beginning.
Why Did I Get an Error?
The most common reason for an error (or a failure to converge) is the Sign Convention. In financial mathematics, cash flows must have directions:
Money received (like a loan check) is Positive (+).
Money paid out (like a monthly payment) is Negative (-).
If you enter both PV and PMT as positive numbers, the calculator (and Excel) cannot find a solution because the balance would grow infinitely rather than being paid down.
Example Scenario
Imagine you take a loan of $10,000 (PV). You agree to pay $200 (PMT = -200) every month for 60 months (Nper). To find the monthly interest rate, you would enter:
Nper: 60
Pmt: -200
Pv: 10000
Fv: 0
The calculator will perform iterations to find the rate that balances the equation to zero.