Question:medium

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

Updated On: Jul 15, 2026
  • Rs. 1
  • Rs. 1.25
  • Rs. 1.5
  • Rs. 2
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The Correct Option is B

Approach Solution - 1

Step 1: Understanding the Question.
We need the difference between simple interest and compound interest on Rs. 500 for 1 year at 10% per annum, where the compound interest is calculated half yearly.

Step 2: Key Formula or Approach.
Simple interest uses \( SI = \frac{P \times R \times T}{100} \). For compound interest calculated half yearly, we halve the annual rate and double the number of periods, then use \( A = P \left(1 + \frac{r}{100}\right)^n \).

Step 3: Detailed Explanation.
Simple interest:
\[ SI = \frac{500 \times 10 \times 1}{100} = 50 \]
For compound interest, the half yearly rate is 5%, and there are 2 half year periods in 1 year:
\[ A = 500 \left(1 + \frac{5}{100}\right)^2 = 500 \times (1.05)^2 = 500 \times 1.1025 = 551.25 \]
\[ CI = 551.25 - 500 = 51.25 \]
Difference between CI and SI:
\[ 51.25 - 50 = 1.25 \]

Step 4: Final Answer.
The difference between simple interest and compound interest is Rs. 1.25. \[ \boxed{Rs.\ 1.25} \]
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Approach Solution -2

This looks at the same Rs. 500, 1 year, 10% per annum question through the algebra of compounding twice in a year rather than computing rupee amounts directly. If \( r \) is the half-yearly rate as a decimal, simple interest over two half years equals \( 2r \) times the principal, while compound interest equals \( \left[(1+r)^2 - 1\right] \) times the principal. Expanding \( (1+r)^2 = 1 + 2r + r^2 \), the compound interest becomes \( (2r + r^2) \) times the principal, so the difference between compound and simple interest is always exactly \( r^2 \) times the principal, regardless of the rupee figures involved. We can check each option against this identity.

  1. Option (A): Rs. 1: With \( P = 500 \) and half-yearly rate \( r = 0.05 \), the identity gives a difference of \( 500 \times (0.05)^2 = 500 \times 0.0025 = 1.25 \), not Rs. 1, so this option does not satisfy the identity.
  2. Option (B): Rs. 1.25: This matches \( 500 \times (0.05)^2 = 1.25 \) exactly, confirming the identity holds for this value.
  3. Option (C): Rs. 1.5: For this to hold, \( r^2 \) would need to equal \( \frac{1.5}{500} = 0.003 \), giving \( r \approx 0.0548 \), which does not correspond to the given 5% half-yearly rate, so this option fails the identity.
  4. Option (D): Rs. 2: This would require \( r^2 = \frac{2}{500} = 0.004 \), giving \( r \approx 0.0632 \), again inconsistent with the actual 5% half-yearly rate, so this option is also ruled out.

The algebraic identity \( P r^2 \) pins the difference at Rs. 1.25 for a principal of Rs. 500 compounded half yearly at a 5% half-yearly rate.

Therefore, the correct answer is Rs. 1.25.

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