A sum of $4000 is borrowed for 2 years at a Banker's Discount of $800. What is t

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Question: A sum of $4000 is borrowed for 2 years at a Banker\'s Discount of $800. What is the effective interest rate?

Options:

Correct Answer: 6%

Solution:

Effective interest rate = (Banker\'s Discount / Principal) × (1 / Time) × 100 = (800 / 4000) × (1 / 2) × 100 = 4%.

A sum of $4000 is borrowed for 2 years at a Banker's Discount of $800. What is the effective interest rate?

A sum of $4000 is borrowed for 2 years at a Banker's Discount of $800. What is the effective interest rate?

Step 1: Identify the principal amount borrowed, which is $4000.
Step 2: Identify the Banker's Discount, which is $800.
Step 3: Identify the time period for which the money is borrowed, which is 2 years.
Step 4: Use the formula for effective interest rate: Effective interest rate = (Banker's Discount / Principal) × (1 / Time) × 100.
Step 5: Substitute the values into the formula: Effective interest rate = (800 / 4000) × (1 / 2) × 100.
Step 6: Calculate the fraction: 800 / 4000 = 0.2.
Step 7: Calculate the time fraction: 1 / 2 = 0.5.
Step 8: Multiply the results: 0.2 × 0.5 = 0.1.
Step 9: Convert to percentage: 0.1 × 100 = 10%.
Step 10: The effective interest rate is 10%.

Banker's Discount – A method of calculating interest where the discount is taken from the principal before the loan is issued.
Effective Interest Rate – The actual interest rate that reflects the true cost of borrowing, taking into account the time period.
Time Factor in Interest Calculation – Understanding how the duration of the loan affects the calculation of interest rates.