If the Banker's Discount on a bill of Rs. 8000 due in 1 year at 12% is Rs. 960,

If the Banker's Discount on a bill of Rs. 8000 due in 1 year at 12% is Rs. 960, what is the true discount?

If the Banker's Discount on a bill of Rs. 8000 due in 1 year at 12% is Rs. 960, what is the true discount?

Correct Answer: Rs. 480

Step 1: Understand the terms. The Banker's Discount is the discount given by the bank on a bill, and the True Discount is the actual discount considering the time until the bill is due.
Step 2: Identify the values given in the question. The Banker's Discount is Rs. 960, and the time until the bill is due is 1 year.
Step 3: Use the formula for True Discount: True Discount = Banker's Discount × (Time / (Time + 1)).
Step 4: Substitute the values into the formula. Here, Time is 1 year, so we have: True Discount = 960 × (1 / (1 + 1)).
Step 5: Calculate the fraction: (1 / (1 + 1)) = (1 / 2) = 0.5.
Step 6: Multiply the Banker's Discount by the fraction: True Discount = 960 × 0.5 = Rs. 480.
Step 7: Conclude that the True Discount is Rs. 480.

Banker's Discount – The discount calculated on the face value of a bill based on the interest rate and time until maturity.
True Discount – The actual discount on the present value of a bill, which accounts for the time value of money.
Time Value of Money – The principle that money available now is worth more than the same amount in the future due to its potential earning capacity.