If the Banker's Discount on a bill of Rs. 22000 due in 5 months at 6% is Rs. 550

If the Banker's Discount on a bill of Rs. 22000 due in 5 months at 6% is Rs. 550, what is the true discount?

If the Banker's Discount on a bill of Rs. 22000 due in 5 months at 6% is Rs. 550, what is the true discount?

Correct Answer: Rs. 229.17

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. 550, the bill amount is Rs. 22000, and the time until the bill is due is 5 months.
Step 3: Convert the time from months to years. Since there are 12 months in a year, 5 months is equal to 5/12 years.
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 = 550 × (5/12).
Step 6: Calculate the True Discount. First, calculate (5/12) which is approximately 0.4167. Then multiply 550 by 0.4167 to get approximately Rs. 229.17.
Step 7: Conclude that the True Discount is Rs. 229.17.

Banker's Discount – The difference between the face value of a bill and its present value, calculated using the interest rate and time until maturity.
True Discount – The actual discount on a bill, which is the difference between the face value and the present value, taking into account the time value of money.
Time Factor – The importance of the time period in calculating discounts, as it affects the present value of the bill.