If the Banker's Discount on a bill of Rs. 8000 due in 3 months at 12% per annum

If the Banker's Discount on a bill of Rs. 8000 due in 3 months at 12% per annum is Rs. 80, what is the effective interest rate?

If the Banker's Discount on a bill of Rs. 8000 due in 3 months at 12% per annum is Rs. 80, what is the effective interest rate?

Step 1: Identify the given values. The face value of the bill is Rs. 8000, the Banker's Discount is Rs. 80, the time is 3 months, and the rate of interest is 12% per annum.
Step 2: Convert the time from months to years. Since the time is 3 months, we convert it to years by dividing by 12. So, 3 months = 3/12 = 0.25 years.
Step 3: Use the formula for effective interest rate. The formula is: Effective Interest = (Banker's Discount / Face Value) * (Rate / Time).
Step 4: Substitute the values into the formula. We have: Effective Interest = (80 / 8000) * (12 / 0.25).
Step 5: Calculate the fraction (80 / 8000). This simplifies to 0.01.
Step 6: Calculate the fraction (12 / 0.25). This simplifies to 48.
Step 7: Multiply the results from Step 5 and Step 6. So, 0.01 * 48 = 0.48.
Step 8: Convert the result into a percentage. 0.48 as a percentage is 48%.
Step 9: The effective interest rate is 4%.

Banker's Discount – The difference between the face value of a bill and its present value, calculated based on the interest rate and time until maturity.
Effective Interest Rate – The actual interest rate that reflects the true cost of borrowing, taking into account the time period and the discount applied.
Time Value of Money – The principle that money available now is worth more than the same amount in the future due to its potential earning capacity.