If the Banker's Discount on a bill of Rs. 20000 due in 6 months at 10% is Rs. 10

If the Banker's Discount on a bill of Rs. 20000 due in 6 months at 10% is Rs. 1000, what is the true discount?

If the Banker's Discount on a bill of Rs. 20000 due in 6 months at 10% is Rs. 1000, what is the true discount?

Correct Answer: Rs. 666.67

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. 1000, and the time until the bill is due is 6 months, which is 0.5 years.
Step 3: Use the formula for True Discount. The formula is: True Discount = Banker's Discount × (Time / (Time + 1)).
Step 4: Substitute the values into the formula. Here, Time is 0.5 years, so we calculate: True Discount = 1000 × (0.5 / (0.5 + 1)).
Step 5: Calculate the denominator. (0.5 + 1) = 1.5.
Step 6: Calculate the fraction. 0.5 / 1.5 = 1/3 or approximately 0.3333.
Step 7: Multiply the Banker's Discount by the fraction. True Discount = 1000 × 0.3333 = Rs. 666.67.

Banker's Discount – The discount calculated on the face value of a bill based on the time until maturity and the interest rate.
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.