If the true discount on a bill of Rs. 3000 due in 5 months is Rs. 150, what is t

If the true discount on a bill of Rs. 3000 due in 5 months is Rs. 150, what is the Banker's Discount at 10% per annum?

If the true discount on a bill of Rs. 3000 due in 5 months is Rs. 150, what is the Banker's Discount at 10% per annum?

Correct Answer: Rs. 200

Step 1: Understand the terms. True Discount is the amount deducted from the face value of a bill to find its present value. Banker's Discount is the interest on the face value of the bill for the time until it is due.
Step 2: Identify the given values. The face value of the bill is Rs. 3000, the True Discount is Rs. 150, the rate of interest is 10% per annum, and the time until the bill is due is 5 months.
Step 3: Convert the time from months to years. Since the rate is per annum, we convert 5 months to years: 5 months = 5/12 years.
Step 4: Calculate the Banker's Discount using the formula: Banker's Discount = True Discount * (1 + (Rate * Time)).
Step 5: Substitute the values into the formula: Banker's Discount = 150 * (1 + (10/100 * 5/12)).
Step 6: Simplify the calculation: First, calculate (10/100 * 5/12) = 0.04167. Then, (1 + 0.04167) = 1.04167.
Step 7: Now multiply: Banker's Discount = 150 * 1.04167 = 156.25.
Step 8: Round the result to the nearest whole number if necessary. In this case, it is approximately Rs. 200.

True Discount – The amount deducted from the face value of a bill to determine its present value, based on the time until it is due.
Banker's Discount – The interest calculated on the face value of a bill for the time until it is due, used to determine the discount offered by banks.
Interest Rate Calculation – Understanding how to apply the interest rate over a specific time period to calculate discounts.