Find the banker's discount at a bill of 25500 due 2 months hence, when rate of interest is 3% per annum.

Answer

To find the banker's discount on a bill of Rs. 25,500 due in 2 months with an interest rate of 3% per annum, we can follow these steps:

### Step 1: Understand the formula for Banker's Discount
The formula for calculating the banker's discount (BD) is given by:
\[ BD = \frac{A \times r \times t}{100} \]
where:
- \( A \) = value of the bill
- \( r \) = rate of interest per annum
- \( t \) = time in years

### Step 2: Identify the values
From the question:
- The value of the bill \( A = 25,500 \)
- The rate of interest \( r = 3\% \)
- The time until the bill is due is 2 months.

### Step 3: Convert time into years
Since the rate is given per annum, we need to convert the time from months to years:
\[ t = \frac{2 \text{ months}}{12 \text{ months/year}} = \frac{1}{6} \text{ years} \]

### Step 4: Substitute the values into the formula
Now, we can substitute the values into the formula:
\[ BD = \frac{25500 \times 3 \times \frac{1}{6}}{100} \]

### Step 5: Simplify the expression
First, calculate \( 25500 \times 3 \):
\[ 25500 \times 3 = 76500 \]
Now substitute this back into the equation:
\[ BD = \frac{76500 \times \frac{1}{6}}{100} \]
Next, calculate \( 76500 \times \frac{1}{6} \):
\[ 76500 \div 6 = 12750 \]
Now, substitute this back into the equation:
\[ BD = \frac{12750}{100} \]

### Step 6: Final calculation
Now, divide \( 12750 \) by \( 100 \):
\[ BD = 127.5 \]

### Conclusion
The banker's discount on the bill is Rs. 127.5.

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