Payment made each period. Use negative for outgoing cash.
The total amount that a series of future payments is worth now (e.g., loan amount).
The cash balance you want to attain after the last payment. Default is 0.
0 – End of the period (Regular Annuity)
1 – Beginning of the period (Annuity Due)
Rate per Period:
Annual Rate (Period Rate × 12):
(Assuming periods are months)
Annual Rate (Period Rate × 1):
(Assuming periods are years)
What is the Excel RATE Function?
The Excel RATE Function Calculator is a financial tool designed to calculate the interest rate per period of an annuity. In Microsoft Excel, the function syntax is =RATE(nper, pmt, pv, [fv], [type], [guess]). This online tool replicates that logic in your browser, allowing you to solve for the yield or interest rate when you know the loan term, payment amount, and present value.
Understanding the Inputs
To use this calculator effectively, it is crucial to understand the standard financial arguments:
Nper (Number of Periods): The total number of payments. For a 5-year loan paid monthly, this would be 5 × 12 = 60.
Pmt (Payment): The fixed payment made each period. Important: Financial calculations require following sign conventions. If you receive money (loan), it's positive. If you pay money, it should be negative.
Pv (Present Value): The current value of the loan or investment. For a loan, this is the principal amount.
Fv (Future Value): The value remaining after the last payment is made. For loans, this is usually 0 (the loan is paid off). For investments, this is the target savings goal.
Type: Indicates when payments are due. '0' means at the end of the period (common for mortgages), and '1' means at the beginning (common for leases).
Formulas and Calculation Logic
Unlike simple arithmetic formulas, the RATE function solves an equation iteratively. There is often no direct algebraic solution for the rate ($r$) in the annuity formula:
This calculator uses the Newton-Raphson method, a numerical root-finding algorithm, to approximate the rate that balances the equation to zero.
Example Calculation
Suppose you take a loan of $10,000 (Pv) and agree to pay $200 (Pmt) per month for 60 months (Nper). What is the monthly interest rate?
Nper: 60
Pmt: -200 (Negative because it's cash outflow)
Pv: 10,000 (Positive because it's cash inflow)
Fv: 0
Type: 0
Entering these values will return a monthly rate of approximately 0.618%. To get the Annual Percentage Rate (APR), you multiply this by 12, resulting in roughly 7.42%.
Common Errors in Rate Calculation
The most common error users encounter is the #NUM! error in Excel or a "Calculation failed" message. This usually happens when:
Sign Confusion: You entered both PV and PMT as positive numbers. One represents money coming in, and the other represents money going out. They must have opposite signs.
Unrealistic Numbers: The payments are too small to ever pay off the principal, or the mathematical solution is imaginary.
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"@type": "Question",
"name": "Why does the RATE function return a #NUM! error?",
"acceptedAnswer": {
"@type": "Answer",
"text": "The #NUM! error (or non-convergence) usually occurs when cash flow signs are incorrect. Ensure that cash inflows (money received) are positive and cash outflows (payments made) are negative. For example, in a loan scenario, PV should be positive and PMT should be negative."
}
}, {
"@type": "Question",
"name": "How do I convert the period rate to an annual interest rate?",
"acceptedAnswer": {
"@type": "Answer",
"text": "The RATE function returns the rate per period. If your NPER is in months, the result is a monthly rate. To get the annual rate, multiply the result by 12. If NPER is in quarters, multiply by 4."
}
}, {
"@type": "Question",
"name": "What is the difference between Type 0 and Type 1?",
"acceptedAnswer": {
"@type": "Answer",
"text": "Type 0 assumes payments are made at the end of the period (common for mortgages and loans). Type 1 assumes payments are made at the beginning of the period (common for rent and leases)."
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function calculateExcelRate() {
// Get inputs strictly matching IDs
var nperInput = document.getElementById("nper").value;
var pmtInput = document.getElementById("pmt").value;
var pvInput = document.getElementById("pv").value;
var fvInput = document.getElementById("fv").value;
var typeInput = document.getElementById("type").value;
var resultBox = document.getElementById("result-box");
var errorMsg = document.getElementById("error-message");
var rateResult = document.getElementById("rate-result");
var annualRate12 = document.getElementById("annual-rate-12");
var annualRate1 = document.getElementById("annual-rate-1");
// Reset display
resultBox.style.display = "none";
errorMsg.style.display = "none";
errorMsg.innerHTML = "";
// Parse and Validate
var nper = parseFloat(nperInput);
var pmt = parseFloat(pmtInput);
var pv = parseFloat(pvInput);
var fv = fvInput === "" ? 0 : parseFloat(fvInput);
var type = typeInput === "" ? 0 : parseInt(typeInput);
// Basic Validation
if (isNaN(nper) || isNaN(pmt) || isNaN(pv)) {
errorMsg.innerHTML = "Please enter valid numeric values for Nper, Pmt, and Pv.";
errorMsg.style.display = "block";
return;
}
if (nper <= 0) {
errorMsg.innerHTML = "Number of periods (Nper) must be greater than 0.";
errorMsg.style.display = "block";
return;
}
// Implementation of Excel's RATE function using Newton-Raphson method
// Formula: PV * (1+r)^n + PMT * (1+r*type) * ( (1+r)^n – 1 ) / r + FV = 0
var rate = 0.1; // Initial guess (10%)
var y, y0, y1, x0, x1;
var f = 0;
var i = 0;
var maxIter = 128; // Increased iterations for accuracy
var epsilon = 1e-7; // Precision
// Check for simple case where rate is 0
if (Math.abs(pmt * nper + pv + fv) < epsilon) {
rate = 0;
} else {
// Iteration loop
for (i = 0; i < maxIter; i++) {
if (Math.abs(rate) < epsilon) {
// Rate is essentially zero, use L'Hopital's rule or approximation
y = pv * (1 + nper * rate) + pmt * (1 + rate * type) * nper + fv;
} else {
// General formula
// f(r) = PV(1+r)^n + PMT(1+r*type)((1+r)^n – 1)/r + FV = 0
// Rewritten for stability usually involves calculating Present Value of flows at rate r and subtracting initial PV?
// Let's use the net present value function logic which sums to zero.
// f(r) = PV + PMT * (1 – (1+r)^-n)/r * (1 + r*type) + FV * (1+r)^-n
// We need to find r where f(r) = 0.
var pow = Math.pow(1 + rate, nper);
// Function Value
// Derived from: PV * pow + PMT * (1 + rate * type) * (pow – 1) / rate + FV = 0
// Note: This matches the Future Value equation logic set to 0.
var fValue = pv * pow + pmt * (1 + rate * type) * (pow – 1) / rate + fv;
// Derivative
// d/dr of PV*pow + PMT/rate*(1+r*type)*(pow-1) + FV
// This is complex. Let's use Secant Method or simple Newton with numeric derivative if analytical is too heavy.
// Let's use Newton-Raphson with analytical derivative for better convergence.
// var P = (1+r)^n
// F(r) = PV*P + PMT*((P-1)/r + (P-1)*type) + FV
// Actually, standard iteration code for RATE often looks like this:
// Re-calculating using a standard financial library approach:
var t1 = Math.pow(1 + rate, nper);
var t2 = Math.pow(1 + rate, nper – 1);
// f(r)
var fObj = pv * t1 + pmt * (1 + rate * type) * (t1 – 1) / rate + fv;
// f'(r)
var term1 = pv * nper * t2;
var term2_num = pmt * (1 + rate * type) * (nper * t2 * rate – (t1 – 1));
var term2_den = rate * rate;
var term2 = term2_num / term2_den;
var term3 = pmt * type * (t1 – 1) / rate; // Component from product rule on (1+r*type)
// Actually let's use a simpler numeric derivative method (Secant) if analytical is prone to implementation errors without a library.
// But user requires logic.
// Let's rely on a specific approximation step:
// New Rate = Old Rate – f(r) / f'(r)
var fDerivative = (nper * pv * t2) +
(pmt * (1 + rate * type) * ((nper * t2) / rate – (t1 – 1) / (rate * rate))) +
(pmt * type * (t1 – 1) / rate);
var newRate = rate – fValue / fDerivative;
if (Math.abs(newRate – rate) = maxIter || isNaN(rate) || !isFinite(rate)) {
errorMsg.innerHTML = "Could not calculate a stable rate. Please check your inputs. Ensure PV and PMT have opposite signs.";
errorMsg.style.display = "block";
} else {
// Display results
var percent = (rate * 100).toFixed(4);
var annual12 = (rate * 12 * 100).toFixed(4);
var annual1 = (rate * 100).toFixed(4);
rateResult.innerHTML = percent + "%";
annualRate12.innerHTML = annual12 + "%";
annualRate1.innerHTML = annual1 + "%";
resultBox.style.display = "block";
}
}