If the bankers' discount on a bill is Rs. 400 and the time is 4 months, what is

If the bankers' discount on a bill is Rs. 400 and the time is 4 months, what is the face value of the bill at the rate of 12% per annum?

If the bankers' discount on a bill is Rs. 400 and the time is 4 months, what is the face value of the bill at the rate of 12% per annum?

Correct Answer: Rs. 5000

Step 1: Understand that the bankers' discount (BD) is Rs. 400.
Step 2: Know that the time given is 4 months.
Step 3: Convert the time from months to years. Since there are 12 months in a year, 4 months is equal to 4/12 years.
Step 4: The rate of interest is given as 12% per annum. Convert this percentage to a decimal by dividing by 100, which gives 0.12.
Step 5: Use the formula for face value: Face Value = BD / (Rate × Time).
Step 6: Substitute the values into the formula: Face Value = 400 / (0.12 × (4/12)).
Step 7: Calculate the denominator: 0.12 × (4/12) = 0.12 × 0.3333 = 0.04.
Step 8: Now calculate the face value: Face Value = 400 / 0.04.
Step 9: Perform the division: 400 / 0.04 = 10000.
Step 10: Therefore, the face value of the bill is Rs. 10000.

Bankers' Discount – The bankers' discount is the interest on the face value of a bill for the time period until its maturity, calculated at a specified rate.
Face Value Calculation – The face value of a bill can be calculated using the formula: Face Value = BD / (Rate × Time), where BD is the bankers' discount.
Interest Rate Conversion – Understanding how to convert the annual interest rate into the appropriate time period for calculations.