The difference between the simple interest and the compound interest on Rs 1,200 for 1 year at 10% per annum, when interest is reckoned half yearly, is equal to how many rupees?

Introduction:
This question compares simple interest and compound interest when interest is reckoned half yearly. It tests your ability to handle different compounding frequencies and then compute the numerical difference between the two types of interest for the same principal, rate, and time.

Given Data / Assumptions:

• Principal P = Rs 1,200
• Annual rate r = 10% per annum
• Time t = 1 year
• Simple interest is calculated yearly at 10%
• Compound interest is calculated with half yearly compounding at the same nominal rate

Concept / Approach:
Simple interest uses the formula:
SI = P * r * t / 100For half yearly compound interest, the rate per half year is r / 2 and the number of periods is 2 in one year. The amount is:
A = P * (1 + r_half/100)^2The compound interest is A - P. The required answer is CI - SI.

Step-by-Step Solution:
Step 1: Compute simple interest for 1 year at 10%.SI = 1,200 * 10 * 1 / 100SI = 1,200 * 0.10 = Rs 120Step 2: Compute compound interest with half yearly compounding.Rate per half year = 10 / 2 = 5% = 0.05Number of half years n = 2A = 1,200 * (1 + 0.05)^2(1.05)^2 = 1.1025A = 1,200 * 1.1025 = Rs 1,323CI = A - P = 1,323 - 1,200 = Rs 123Step 3: Find the difference between CI and SI.Difference = CI - SI = 123 - 120 = Rs 3

Verification / Alternative check:
The extra amount due to half yearly compounding, compared to yearly simple interest, should be small because the rate and time are not large. A difference of Rs 3 on Rs 1,200 is 0.25%, which is reasonable for the compounding effect over one year.

Why Other Options Are Wrong:

• Rs 2, Rs 4, Rs 5, Rs 6: These values do not match the exact computation based on the correct formulas. They may arise from incorrect exponent, wrong rate per period, or arithmetic mistakes.

Common Pitfalls:
Candidates may mistakenly apply 10% twice instead of splitting into 5% per half year, or they might forget to subtract principal to find CI. Also, some simply compare interest amounts without respecting the compounding periods, which leads to incorrect differences.

Final Answer:
The difference between compound interest and simple interest in this case is Rs 3.