Question:
The difference between Simple Interest and Compound Interest on Rs. 500 for 1 year at 10% per annum, reckoned half yearly is
The difference between Simple Interest and Compound Interest on Rs. 500 for 1 year at 10% per annum, reckoned half yearly is
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For compound interest, ensure that the rate is halved and the time is doubled for half-yearly compounding.
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
The formula for Simple Interest (SI) is:
\[
SI = \frac{P \times R \times T}{100}
\]
For Rs. 500 at 10% per annum for 1 year:
\[
SI = \frac{500 \times 10 \times 1}{100} = 50
\]
The formula for Compound Interest (CI) when interest is compounded half yearly is:
\[
CI = P \left(1 + \frac{R}{2 \times 100}\right)^{2T} - P
\]
For Rs. 500 at 10% per annum for 1 year:
\[
CI = 500 \left(1 + \frac{10}{2 \times 100}\right)^{2} - 500 = 500 \left(1 + 0.05\right)^2 - 500
\]
\[
CI = 500 \times 1.1025 - 500 = 551.25 - 500 = 51.25
\]
The difference between CI and SI is:
\[
51.25 - 50 = 1.25
\]
Thus, the difference is Rs. 1.25.
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Approach Solution -2
We need the difference between simple interest and compound interest on Rs. 500 for 1 year at 10 percent per annum, compounded half yearly. We can check each option against the actual computed difference.
- Rs. 1: The simple interest is \( \frac{500 \times 10 \times 1}{100}=50 \). If the difference were Rs. 1, the compound interest would need to be Rs. 51. The actual half yearly compound amount is \( 500\left(1+\frac{5}{100}\right)^2=551.25 \), giving compound interest of 51.25, not 51.
- Rs. 1.25: The half yearly compound amount is \( 500 \times 1.05^2=551.25 \), giving compound interest of 51.25. The simple interest is 50, so the difference is \( 51.25-50=1.25 \), matching exactly.
- Rs. 1.5: This would require a compound interest of Rs. 51.5, but the actual computed compound interest is Rs. 51.25, so this is too high.
- Rs. 2: This would require a compound interest of Rs. 52, well above the actual computed Rs. 51.25, so this is too high.
The half yearly compound amount gives a compound interest of Rs. 51.25 against a simple interest of Rs. 50, a difference of exactly Rs. 1.25.
Therefore, the correct answer is Rs. 1.25.
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Approach Solution -3
Under half-yearly compounding, the simple interest earned in the first half-year, Rs. \( 500 \times 10\% \times 0.5=25 \), is itself credited to the account and starts earning interest during the second half-year, at the same half-yearly rate of 5 percent. This is exactly the extra amount that compounding adds beyond simple interest. We can check each option against this extra amount.
- Rs. 1: The interest earned on the first half-year's Rs. 25 is \( 25 \times 5\%=1.25 \), not Rs. 1.
- Rs. 1.25: The interest earned on the first half-year's Rs. 25 is \( 25 \times 5\%=1.25 \), matching this option exactly.
- Rs. 1.5: The computed extra interest is Rs. 1.25, not Rs. 1.5.
- Rs. 2: The computed extra interest is Rs. 1.25, well short of Rs. 2.
The difference between compound and simple interest here is exactly the interest the first half-year's Rs. 25 earns during the second half-year, which is Rs. 1.25.
Therefore, the correct answer is Rs. 1.25.
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