What will be the compound interest (rounded to two decimal places) on Rs. 20,000 for 1.5 years at an annual rate of 8% compounded half-yearly?

1. A

   2567.52 रूपये

2. B

   2488.32 रूपये

3. C

   2497.28 रूपये

4. D

   2400 रूपये

Appeared in: CGHS SSC - 2018

Explanation

• The core concept is adjusting the annual rate and time for half-yearly compounding.
• The annual rate of 8% becomes 4% per half-year.
• The time of 1.5 years becomes 3 half-year periods.
• The formula for the final amount (A) is A = P(1 + r/100)n, where P is principal, r is the rate per period, and n is the number of periods.
• Calculation: A = 20000 * (1.04)3 = 22,497.28.
• Compound Interest (CI) = Amount - Principal = 22,497.28 - 20,000 = 2,497.28.

Why Other Options Were Wrong

• Option A: This value (Rs. 2567.52) is incorrect and likely results from a miscalculation, possibly using an incorrect rate or number of periods.
• Option B: This value (Rs. 2488.32) is incorrect. It might arise from an error in calculating (1.04)3 or another arithmetic mistake during the process.
• Option D: This value (Rs. 2,400) represents the Simple Interest (SI), not the Compound Interest.

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of compound interest with half-yearly compounding as background academic context rather than a clinical decision trigger.
• While not a clinical skill, quantitative aptitude is a key component of nursing entrance exams, testing logical reasoning and problem-solving abilities.
• Understanding concepts like percentages and interest can be useful for financial planning and management, which are important life skills for any professional.
• What if the interest was compounded quarterly? The rate would be 8%/4 = 2% per quarter, and the time would be 1.5 years * 4 = 6 quarters. The calculation would be CI = 20000 * (1.02)6 - 20000, resulting in a different, slightly higher interest amount.

How to Approach the Question

• First, identify all the given values: Principal (P), annual rate (R), and time (T).
• Note the compounding frequency (in this case, 'half-yearly'). This is the most critical step.
• Adjust the annual rate and time period based on the frequency. For half-yearly, divide the rate by 2 and multiply the time by 2.
• Apply the standard compound interest formula: A = P(1 + r/100)n.
• Calculate the final amount (A) and then subtract the principal (P) to find the compound interest (CI).
• Be careful to distinguish between compound interest and simple interest, which is a common distractor in options.

Concept Tested & Keywords

• Concept Tested: Calculation of compound interest with half-yearly compounding.
• Stem keywords: compound interest, Rs. 20,000, 1.5 years, 8%, compounded half-yearly
• Lead-in keywords: What will be
• Negative lead-in flag: false

Question ID

Q16-UfT1BFcSMpodZFZMMP

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