Bankers Discount
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Banker's Discount
The Banker's Discount (BD) is the interest calculated on a bill of exchange or a promissory note by a banker. It is the difference between the nominal value (face value) of the bill and the amount the banker actually pays for it before its maturity date.
Formula for Banker's Discount
The formula to calculate the Banker's Discount is:
$$ \text{BD} = \text{FV} \times \frac{r \times t}{100} $$
Where:
- \(\text{BD} = \text{Banker's Discount}\)
- \(\text{FV} = \text{Face Value of the bill}\)
- \(r = \text{Rate of interest per annum}\)
- \(t = \text{Time in years}\)
Example Calculation
Suppose a bill with a face value of $10,000 is discounted at a rate of 8% per annum, 3 months before its maturity date. To calculate the Banker's Discount:
- Convert the time into years: \[ t = \frac{3}{12} = 0.25 \text{ years} \]
- Substitute the values into the formula: \[ \text{BD} = 10,000 \times \frac{8 \times 0.25}{100} \]
- Calculate the Banker's Discount: \[ \text{BD} = 10,000 \times \frac{2}{100} = 10,000 \times 0.02 = 200 \]
Therefore, the Banker's Discount is $200.