Bankers Calculator

Banker's Discount & Gain Calculator

Calculate discounts using the Banker's Rule (360-day basis)

Calculation Summary

Banker's Discount (BD) –

True Discount (TD) –

Banker's Gain (BG) –

Present Worth (PW) –

Understanding the Banker's Calculator

In commercial finance, the "Banker's Rule" is a convention that uses 360 days in a year rather than 365. This method, often referred to as "Ordinary Interest," simplifies calculations for short-term commercial paper and bills of exchange. This calculator helps determine the discrepancy between the simple interest charged on the face value versus the true interest charged on the present worth.

Key Definitions

• Face Value: The total amount of the bill or note due at maturity.
• Banker's Discount (BD): The simple interest calculated on the Face Value for the period from the date of discounting to the date of maturity.
• True Discount (TD): The actual interest that would be charged on the Present Worth to reach the Face Value over the given time.
• Present Worth (PW): The current value of the bill today, which, when interest is added, equals the Face Value.
• Banker's Gain (BG): The difference between the Banker's Discount and the True Discount (BD – TD).

The Formulas Used

Time (T) = Days / 360
Banker's Discount (BD) = (Face Value × Rate × T) / 100
Present Worth (PW) = (Face Value × 100) / (100 + (Rate × T))
True Discount (TD) = Face Value – PW
Banker's Gain (BG) = BD – TD

Practical Example

Suppose a merchant has a bill of exchange with a Face Value of 5,000 due in 72 days. If a bank discounts the bill at an Annual Rate of 10%:

1. Time: 72 / 360 = 0.2 years.
2. Banker's Discount: 5,000 × 0.10 × 0.2 = 100.00.
3. Present Worth: 5,000 / (1 + (0.10 × 0.2)) = 4,901.96.
4. True Discount: 5,000 – 4,901.96 = 98.04.
5. Banker's Gain: 100.00 – 98.04 = 1.96.

The bank earns an extra 1.96 because they calculate the 10% interest on the full 5,000 rather than on the money they actually advanced to the merchant.

function calculateBankersLogic() { var faceValue = parseFloat(document.getElementById('faceValue').value); var rate = parseFloat(document.getElementById('discountRate').value); var days = parseFloat(document.getElementById('timeDays').value); if (isNaN(faceValue) || isNaN(rate) || isNaN(days) || faceValue <= 0 || rate <= 0 || days <= 0) { alert("Please enter valid positive numbers for all fields."); return; } // Banker's Rule uses 360 days var t = days / 360; // Banker's Discount (BD) = (F * R * T) / 100 var bd = (faceValue * rate * t) / 100; // Present Worth (PW) = F / (1 + (RT/100)) var pw = faceValue / (1 + (rate * t) / 100); // True Discount (TD) = F – PW var td = faceValue – pw; // Banker's Gain (BG) = BD – TD var bg = bd – td; // Display Results document.getElementById('resBD').innerText = bd.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resTD').innerText = td.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resBG').innerText = bg.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('resPW').innerText = pw.toLocaleString(undefined, {minimumFractionDigits: 2, maximumFractionDigits: 2}); document.getElementById('bankerResults').style.display = 'block'; }