A bill of Rs. 8000 is due in 2 months. If the bankers' discount is Rs. 160, what

A bill of Rs. 8000 is due in 2 months. If the bankers' discount is Rs. 160, what is the rate of interest?

A bill of Rs. 8000 is due in 2 months. If the bankers' discount is Rs. 160, what is the rate of interest?

Correct Answer: 12%

Step 1: Identify the given values. The bill amount (Principal) is Rs. 8000, the bankers' discount (BD) is Rs. 160, and the time until the bill is due is 2 months.
Step 2: Convert the time from months to years. Since the time is 2 months, we convert it to years: 2 months = 2/12 = 1/6 years.
Step 3: Use the formula for the rate of interest. The formula is Rate = (BD × 100) / (Principal × Time).
Step 4: Substitute the values into the formula. Rate = (160 × 100) / (8000 × 1/6).
Step 5: Calculate the denominator. First, calculate 8000 × (1/6) = 8000 / 6 = 1333.33.
Step 6: Now calculate the rate. Rate = (160 × 100) / 1333.33.
Step 7: Calculate the final value. Rate = 16000 / 1333.33 = 12%.
Step 8: Conclude that the rate of interest is 12%.

Bankers' Discount – The bankers' discount is the interest on the face value of a bill for the time it has to run until maturity.
Rate of Interest Calculation – The formula for calculating the rate of interest based on bankers' discount, principal, and time.
Time Conversion – Understanding how to convert time into the correct format (years) for interest calculations.