Interpolated rate calculation is a mathematical method used to estimate a value (usually a rate or yield) that falls between two known data points. This is most commonly applied in finance to determine the yield of a security whose maturity date does not exactly match the maturities of benchmark securities.
The Linear Interpolation Formula
This calculator uses the linear interpolation formula:
Y = Y1 + [(X – X1) * (Y2 – Y1)] / (X2 – X1)
X: The target date or value you want the rate for.
X1: The lower known date/point.
Y1: The rate at the lower known point.
X2: The upper known date/point.
Y2: The rate at the upper known point.
Practical Example
Suppose you are analyzing bonds. You know the yield for a 2-year bond is 2.00% and the yield for a 5-year bond is 3.50%. You want to find the estimated yield for a bond with a 3.5-year maturity.
In the fixed-income market, benchmarks like Treasury yields are only available for specific tenors (e.g., 2, 3, 5, 7, 10, and 30 years). If a corporate bond has 6.5 years left until maturity, traders use interpolation between the 5-year and 7-year Treasury rates to determine a fair "benchmark" rate for pricing that specific bond.
function calculateInterpolation() {
var x1 = parseFloat(document.getElementById('x1_val').value);
var y1 = parseFloat(document.getElementById('y1_val').value);
var x2 = parseFloat(document.getElementById('x2_val').value);
var y2 = parseFloat(document.getElementById('y2_val').value);
var xt = parseFloat(document.getElementById('xt_val').value);
var errorBox = document.getElementById('error-msg');
var resultContainer = document.getElementById('interpolation-result-container');
var resultDisplay = document.getElementById('interpolation-result');
// Reset visibility
errorBox.style.display = 'none';
resultContainer.style.display = 'none';
// Validation
if (isNaN(x1) || isNaN(y1) || isNaN(x2) || isNaN(y2) || isNaN(xt)) {
errorBox.innerText = "Please enter all values to perform the calculation.";
errorBox.style.display = 'block';
return;
}
if (x1 === x2) {
errorBox.innerText = "Error: Lower and Upper points (X1 and X2) cannot be the same. This causes division by zero.";
errorBox.style.display = 'block';
return;
}
// Math Logic
// Formula: y = y1 + (x – x1) * (y2 – y1) / (x2 – x1)
var result = y1 + ((xt – x1) * (y2 – y1) / (x2 – x1));
// Display result
resultDisplay.innerText = result.toFixed(4) + "%";
resultContainer.style.display = 'block';
}