A bill of $1500 has a Banker's Discount of $45. What is the rate of interest for

A bill of $1500 has a Banker's Discount of $45. What is the rate of interest for 6 months?

A bill of $1500 has a Banker's Discount of $45. What is the rate of interest for 6 months?

Correct Answer: 6%

Step 1: Identify the values given in the problem. The bill amount (Principal) is $1500 and the Banker's Discount (BD) is $45.
Step 2: Understand that the time period is 6 months. In terms of years, this is 6/12 = 0.5 years.
Step 3: Use the formula for the rate of interest: Rate = (BD x 100) / (Principal x Time).
Step 4: Substitute the values into the formula: Rate = (45 x 100) / (1500 x 0.5).
Step 5: Calculate the denominator: 1500 x 0.5 = 750.
Step 6: Now calculate the rate: Rate = (45 x 100) / 750.
Step 7: Calculate 45 x 100 = 4500.
Step 8: Now divide 4500 by 750 to find the rate: 4500 / 750 = 6.
Step 9: Therefore, the rate of interest for 6 months is 6%.

Banker's Discount – The difference between the face value of a bill and the present value, calculated using the interest rate over a specific time period.
Rate of Interest Calculation – The formula to calculate the rate of interest based on the banker's discount, principal amount, and time period.
Time Conversion – Understanding how to convert time into the correct format (years) for interest calculations.