Question

The difference between Simple Interest and Compound Interest on Rs. 500 for 1 year at 10% per annum, reckoned half yearly is

• A. Rs. 1
• B. Rs. 1.25
• C. Rs. 1.5
• D. Rs. 2

Answer 1

The Correct Option is B

The correct option is (B): Rs. 1.25.

Answer 2

We need the difference between simple interest and compound interest on Rs. 500 for 1 year at 10% per annum, with compounding done half yearly. We can check each option by directly computing both interests and their difference.

1. Option (A): Rs. 1: The simple interest on Rs. 500 at 10% for 1 year is Rs. 50. For a difference of only Rs. 1, the compound interest would need to be Rs. 51, but computing CI compounded half yearly gives Rs. 51.25, not Rs. 51, so this is slightly off.
2. Option (B): Rs. 1.25: Simple interest is Rs. 50. Compound interest, compounded half yearly at 5% per half year for 2 half years, is 500 x (1.05)^2 - 500 = 551.25 - 500 = Rs. 51.25. The difference is 51.25 - 50 = Rs. 1.25, matching exactly.
3. Option (C): Rs. 1.5: This would require the compound interest to be Rs. 51.5, but the actual compound interest works out to Rs. 51.25, so this overstates the difference.
4. Option (D): Rs. 2: This would require the compound interest to be Rs. 52, well above the actual Rs. 51.25, so this is too large a difference.

Working out both interests precisely gives a difference of Rs. 1.25.

Therefore, the correct answer is Rs. 1.25.

Answer 3

The question asks for the gap between simple interest and compound interest on Rs. 500 for 1 year at 10% per annum, where the compounding happens every half year. Rather than computing both interest amounts in full, this method isolates where that gap actually comes from: the simple interest for each half year is fixed at Rs. 500 x 5% = Rs. 25, and the only extra amount compound interest earns beyond two such half-yearly amounts is the interest that first half year's Rs. 25 itself earns during the second half year. We can test each option against this one quantity.

1. Option (A): Rs. 1: For the gap to be exactly Rs. 1, the Rs. 25 earned in the first half year would have to earn only Rs. 1 in the second half year, which works out to a rate of \( \frac{1}{25} \times 100 = 4\% \) on that amount. The half-yearly rate given in the question is 5%, not 4%, so Rs. 1 does not fit.
2. Option (B): Rs. 1.25: Here the Rs. 25 earned in the first half year earns interest on itself for the second half year at the same 5% half-yearly rate: \( 25 \times \frac{5}{100} = 1.25 \). This is exactly the extra amount compounding half yearly adds beyond straightforward simple interest, so Rs. 1.25 fits precisely.
3. Option (C): Rs. 1.5: This would require the Rs. 25 to earn interest at \( \frac{1.5}{25} \times 100 = 6\% \) in the second half year, which is higher than the 5% half-yearly rate actually given, so this does not fit.
4. Option (D): Rs. 2: This would need the Rs. 25 to earn interest at \( \frac{2}{25} \times 100 = 8\% \), far above the 5% half-yearly rate stated in the question, so this option is ruled out as well.

Only Rs. 1.25 matches the interest that the first half year's own interest earns during the second half year at the given 5% half-yearly rate, which is exactly where the difference between simple and compound interest comes from in this case.

Therefore, the correct answer is Rs. 1.25.