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function calculateDiscountRate() {
var maturityInput = document.getElementById("maturityValue");
var proceedsInput = document.getElementById("proceedsAmount");
var daysInput = document.getElementById("termDays");
var basisInput = document.getElementById("yearBasis");
var M = parseFloat(maturityInput.value);
var P = parseFloat(proceedsInput.value);
var days = parseFloat(daysInput.value);
var basis = parseFloat(basisInput.value);
var errorDiv = document.getElementById("errorMsg");
var resultDiv = document.getElementById("resultBox");
// Input Validation
if (isNaN(M) || isNaN(P) || isNaN(days) || M <= 0 || P <= 0 || days = M) {
errorDiv.style.display = "block";
resultDiv.style.display = "none";
errorDiv.innerHTML = "Proceeds must be less than Maturity Value to calculate a discount rate.";
return;
}
errorDiv.style.display = "none";
resultDiv.style.display = "block";
// Logic: Discount Amount (D) = Maturity (M) – Proceeds (P)
var D = M – P;
// Logic: Time in years (t)
var t = days / basis;
// Logic: Annual Discount Rate (d) = D / (M * t)
var rateDecimal = D / (M * t);
var ratePercent = rateDecimal * 100;
// Display Results
document.getElementById("displayDiscountAmount").innerHTML = "$" + D.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2});
document.getElementById("displayTimeYears").innerHTML = t.toFixed(4) + " years";
document.getElementById("displayRate").innerHTML = ratePercent.toFixed(4) + "%";
}
Understanding the Annual Simple Discount Rate
The Annual Simple Discount Rate Calculator is designed to help financial students, bankers, and borrowers determine the effective discount rate applied to a promissory note or Treasury bill. Unlike standard interest-bearing loans where interest is added to the principal at the end, a discount note deducts the interest (called the "discount") upfront from the face value.
In this scenario, the borrower receives less than the face value (the "Proceeds") but must repay the full face value (the "Maturity Value") at the end of the term. The difference represents the cost of borrowing.
How the Calculation Works
To find the annual simple discount rate, we must determine the relationship between the discount amount, the maturity value, and the time period involved.
Formula:
d = (M – P) / (M × t)
Where:
d = Annual Simple Discount Rate
M = Maturity Value (Face Value)
P = Proceeds (Amount Received)
t = Time in years (Days / 360 or 365)
Step-by-Step Example
Imagine a business signs a promissory note with a Maturity Value of $10,000. The bank offers the loan based on a discount model, giving the business $9,600 in cash (Proceeds) today. The term of the note is 90 days, using the ordinary interest method (360-day year).
- Calculate the Discount Amount: $10,000 – $9,600 = $400.
- Convert Time to Years: 90 days / 360 = 0.25 years.
- Calculate Rate: $400 / ($10,000 × 0.25) = $400 / $2,500 = 0.16.
- Result: The Annual Simple Discount Rate is 16%.
Simple Discount vs. Simple Interest
It is crucial not to confuse the discount rate with the interest rate.
- Simple Interest: Calculated based on the Principal (the amount received).
- Simple Discount: Calculated based on the Maturity Value (the amount to be repaid).
Because the Maturity Value is always higher than the Proceeds, the Simple Discount Rate will mathematically appear lower than the equivalent Simple Interest Rate for the same cash flow, although the actual cost in dollars is the same.
Why Use 360 vs. 365 Days?
In finance, calculating time fractions of a year varies by convention:
- Ordinary Interest (Banker's Rule): Uses a 360-day year. This is common in commercial banking and legacy corporate treasury calculations. It slightly inflates the lender's yield.
- Exact Interest: Uses a 365-day year (or 366 for leap years). This is often used by government treasuries and for consumer fairness in some jurisdictions.
This calculator allows you to toggle between these bases to ensure your calculation matches the terms of your specific financial instrument.