This tool replicates the functionality of the Microsoft Excel =RATE() function online. In financial modeling, the RATE function is essential for calculating the interest rate per period of an annuity. It is most commonly used to determine the interest rate of a loan given the loan amount and payment, or the compound annual growth rate (CAGR) of an investment given regular contributions.
Understanding the Inputs (Syntax)
To use this calculator accurately, you must understand the five primary variables used in Time Value of Money (TVM) calculations:
Nper (Number of Periods): The total number of payment periods in the annuity. For a 5-year monthly loan, this would be 60 (5 × 12).
Pmt (Payment): The payment made each period. Important: In standard cash flow conventions, money leaving your pocket is negative, and money entering is positive. If you borrow money (Pv is positive), your payments back (Pmt) should be negative.
Pv (Present Value): The total amount that a series of future payments is worth right now. For a loan, this is the loan amount. For an investment, this is your starting principal.
Fv (Future Value): The cash balance you want to attain after the last payment is made. For loans, this is usually 0 (loan paid off). For savings, this is your target goal.
Type: Indicates when payments are due. '0' means payments are due at the end of the period (standard for mortgages), while '1' means due at the beginning (common for leases).
Real-World Example: Mortgage Interest
Suppose you take a loan of 200,000 (Pv) to be paid off over 30 years (360 months, Nper). The bank tells you the monthly payment is -1,073.64 (Pmt). To find the interest rate:
Nper: 360
Pmt: -1073.64
Pv: 200000
Fv: 0
The calculator will return a periodic rate of approx 0.416% (monthly). Multiplied by 12, this reveals an annual interest rate of 5.0%.
function calculateExcelRate() {
// 1. Get Inputs
var nper = parseFloat(document.getElementById('excel_nper').value);
var pmt = parseFloat(document.getElementById('excel_pmt').value);
var pv = parseFloat(document.getElementById('excel_pv').value);
var fv = parseFloat(document.getElementById('excel_fv').value);
var type = parseInt(document.getElementById('excel_type').value);
var guess = parseFloat(document.getElementById('excel_guess').value);
var alertBox = document.getElementById('rateAlert');
var resultBox = document.getElementById('resultContainer');
// 2. Validate Inputs
if (isNaN(nper) || isNaN(pmt) || isNaN(pv)) {
alertBox.style.display = 'block';
alertBox.innerHTML = "Error: Please fill in Nper, Pmt, and Pv fields.";
resultBox.style.display = 'none';
return;
}
if (isNaN(fv)) fv = 0;
if (isNaN(guess)) guess = 0.1; // Default 10%
// 3. Logic: Newton-Raphson Iteration to solve for Rate (r)
// Equation: PV * (1+r)^N + PMT * (1+r*type) * ( (1+r)^N – 1 ) / r + FV = 0
var rate = guess;
var maxIter = 150;
var precision = 1e-8;
var found = false;
for (var i = 0; i < maxIter; i++) {
var y, y_derivative;
if (Math.abs(rate) PV * n * (1+r)^(n-1)
// Derivative of term with PMT is complex.
// Let's use Secant method or clean Newton with formula:
var t1 = Math.pow(1+rate, nper-1);
var t2 = Math.pow(1+rate, nper);
var term1_d = pv * nper * t1;
// Derivative of PMT component: PMT * [ ( (1+r*type)*((1+r)^n – 1) ) / r ] '
// var U = (1+r*type)
// var V = ((1+r)^n – 1) / r
// This gets messy. Let's use numeric derivative (Secant method approach step within Newton)
// f'(x) approx (f(x+h) – f(x)) / h
}
// Numeric Derivative for stability and simplicity in embedded script
var h = 1e-6;
var r_plus = rate + h;
var f_plus, y_plus;
if (Math.abs(r_plus) < precision) {
y_plus = pv + pmt * nper + fv;
} else {
var base_plus = Math.pow(1 + r_plus, nper);
y_plus = pv * base_plus + pmt * (1 + r_plus * type) * (base_plus – 1) / r_plus + fv;
}
y_derivative = (y_plus – y) / h;
var new_rate = rate – y / y_derivative;
if (Math.abs(new_rate – rate) < precision) {
found = true;
rate = new_rate;
break;
}
rate = new_rate;
}
// 4. Output Results
if (found && !isNaN(rate) && isFinite(rate)) {
alertBox.style.display = 'none';
resultBox.style.display = 'block';
// Formatting
var ratePercent = rate * 100;
var annualRate = rate * 12 * 100; // Assume monthly periods for standard annualization
var apy = (Math.pow(1 + rate, 12) – 1) * 100;
document.getElementById('res_rate_period').innerHTML = ratePercent.toFixed(4) + "%";
document.getElementById('res_rate_annual_12').innerHTML = annualRate.toFixed(4) + "%";
document.getElementById('res_apy').innerHTML = apy.toFixed(4) + "%";
} else {
resultBox.style.display = 'none';
alertBox.style.display = 'block';
alertBox.innerHTML = "Calculation failed to converge. Please check your signs (PV and PMT usually have opposite signs).";
}
}