Calculate the periodic rate required to reach a specific financial goal or growth target.
End of Period (0)
Beginning of Period (1)
Calculated Implied Rate per Period:
0.00%
Understanding the Excel RATE Function
The RATE function in Excel is a powerful financial tool used to calculate the interest rate or growth rate per period for an annuity. Unlike simple algebraic equations, the rate is calculated through an iterative process (Newton-Raphson method) because the variable for the rate exists in multiple parts of the time-value-of-money formula.
How to Interpret Inputs
When using this calculator, it is vital to follow the standard accounting sign convention (cash flow direction):
nper: The total number of payment periods (e.g., if you have a 5-year loan paid monthly, nper is 60).
pmt: The fixed payment made each period. Use a negative number if you are paying out, or a positive number if you are receiving funds.
pv: The present value, or the total amount that a series of future payments is worth now.
fv: The future value, or the cash balance you want to attain after the last payment is made. If omitted, it is assumed to be 0.
type: Indicates when payments are due. 0 (default) is for the end of the period, and 1 is for the beginning.
Common Calculation Example
Scenario
NPER
PMT
PV
FV
Calculated Rate
Personal Loan
48
-250
10000
0
0.77% (Monthly)
Investment Growth
10
-1000
0
15000
8.14% (Annual)
Why does the calculator return an error?
The RATE function works by iterating. If the successive results do not converge within 20 iterations to a precision of 0.0000001, it returns an error. This often happens if the combination of PV, FV, and PMT is mathematically impossible or if the initial "Guess" is too far from the actual result.
function calculateExcelRate() {
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) || 0;
var type = parseInt(document.getElementById('type').value);
var guess = parseFloat(document.getElementById('guess').value) || 0.1;
var resultContainer = document.getElementById('result-container');
var rateResultDiv = document.getElementById('rate-result');
var annualNote = document.getElementById('annual-rate-note');
if (isNaN(nper) || isNaN(pmt) || isNaN(pv)) {
alert("Please fill in Nper, Pmt, and Pv fields.");
return;
}
var rate = guess;
var epsMax = 1e-10;
var iterMax = 100;
var iteration = 0;
var found = false;
while (iteration < iterMax) {
var f, df;
if (Math.abs(rate) < epsMax) {
f = pv + pmt * nper + fv;
df = pmt * nper * (nper – 1) / 2;
} else {
var term = Math.pow(1 + rate, nper);
var termMinus1 = term – 1;
f = pv * term + pmt * (1 + rate * type) * (termMinus1 / rate) + fv;
df = nper * pv * Math.pow(1 + rate, nper – 1) +
pmt * (1 + rate * type) * ( (nper * Math.pow(1 + rate, nper – 1) / rate) – (termMinus1 / (rate * rate)) ) +
pmt * type * (termMinus1 / rate);
}
var nextRate = rate – f / df;
if (Math.abs(nextRate – rate) < epsMax) {
rate = nextRate;
found = true;
break;
}
rate = nextRate;
iteration++;
}
resultContainer.style.display = 'block';
if (found && !isNaN(rate) && isFinite(rate)) {
var percentRate = (rate * 100).toFixed(4);
rateResultDiv.innerText = percentRate + "%";
annualNote.innerText = "If your periods are monthly, the nominal annual rate is " + (rate * 12 * 100).toFixed(2) + "%.";
} else {
rateResultDiv.innerText = "#NUM!";
annualNote.innerText = "The calculator could not converge on a solution. Try adjusting your 'Guess' or check your input signs (PMT vs PV).";
}
}