Find the banker's discount at a bill of 12750 due four months hence when rate of interest is 6% per annum.

Options

A. 1) 250
B. 2) 120
C. 3) 255
D. 4) 300

Answer

To find the banker's discount on a bill of ₹12,750 due four months hence at a rate of interest of 6% per annum, we can follow these steps:

### Step 1: Understand the formula for Banker's Discount
The Banker's Discount (BD) can be calculated using the formula:
\[ \text{BD} = \text{Principal} \times \text{Rate} \times \text{Time} \]
Where:
- Principal is the amount of the bill
- Rate is the rate of interest per annum
- Time is the time in years

### Step 2: Convert the time period into years
Since the bill is due in four months, we need to convert this time into years:
\[ \text{Time} = \frac{4 \text{ months}}{12 \text{ months/year}} = \frac{1}{3} \text{ years} \]

### Step 3: Substitute the values into the formula
Now we can substitute the values into the formula:
- Principal = ₹12,750
- Rate = 6% per annum = 0.06
- Time = \(\frac{1}{3}\) years

So, the Banker's Discount (BD) is:
\[ \text{BD} = 12,750 \times 0.06 \times \frac{1}{3} \]

### Step 4: Calculate the Banker's Discount
Now we perform the calculation:
1. Calculate \(0.06 \times \frac{1}{3}\):
\[ 0.06 \times \frac{1}{3} = 0.02 \]

2. Now multiply this by the principal:
\[ \text{BD} = 12,750 \times 0.02 = 255 \]

### Final Answer
The Banker's Discount on the bill is ₹255.

---