If the Banker's Discount on a bill of Rs. 8000 due in 6 months at 12% per annum

If the Banker's Discount on a bill of Rs. 8000 due in 6 months at 12% per annum is Rs. 480, what is the true discount?

If the Banker's Discount on a bill of Rs. 8000 due in 6 months at 12% per annum is Rs. 480, what is the true discount?

Correct Answer: Rs. 240

Step 1: Understand the terms. The Banker's Discount is the discount given by the bank on a bill before it is due.
Step 2: Identify the given values. The Banker's Discount is Rs. 480, and the time until the bill is due is 6 months.
Step 3: Convert the time into years. Since 6 months is half a year, we can write it as 6/12.
Step 4: Use the formula for True Discount. The formula is: True Discount = Banker's Discount * (Time / (Time + 1)).
Step 5: Substitute the values into the formula. True Discount = 480 * (6/12).
Step 6: Simplify the fraction. 6/12 equals 0.5.
Step 7: Calculate the True Discount. True Discount = 480 * 0.5 = Rs. 240.

Banker's Discount – The amount deducted by the bank from the face value of a bill to determine the present value, based on the interest rate and time until maturity.
True Discount – The actual discount on a bill that reflects the present value of the future payment, calculated using the Banker's Discount and the time factor.
Time Factor – The ratio of the time until the bill is due to the total time period, which is used to adjust the Banker's Discount to find the True Discount.