A man gets a simple interest on Rs. 1000 on a certain principal at the rate of 5 p.c.p.a. in 4 years. What compound interest will the man get on twice the principal in 2 years at the same rate ?

Answer: Option E

\begin{aligned} & {\text{Principal}} \\ & {\text{ = Rs}}{\text{.}}\left( {\frac{{100 \times 1000}}{{5 \times 4}}} \right) \\ & = {\text{Rs}}{\text{. 5}}000 \\ & {\text{Now, P = Rs}}{\text{.}}\,10000, \\ & {\text{T = 2 years,}} \\ & {\text{R = 5% }} \\ & {\text{Amount}} \\ & {\text{ = Rs}}{\text{.}}\left[ {10000 \times {{\left( {1 + \frac{5}{{100}}} \right)}^2}} \right] \\ & = {\text{Rs}}{\text{.}}\left( {10000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}}} \right) \\ & = {\text{Rs}}. 11025 \\ & \therefore {\text{C}}{\text{.I}}{\text{. = }}\left( {11025 - 10000} \right) \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}. 1025 \\\end{aligned}

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Details Explanation

Understanding Simple Interest:
Simple interest is calculated only on the principal amount (the initial amount of money).
The formula for simple interest is: Simple Interest = (Principal × Rate × Time) / 100
Solving for the Principal:
In this problem, we know the simple interest (Rs. 1000), the rate (5% per year), and the time (4 years). We can use the simple interest formula to find the principal:
1000 = (Principal × 5 × 4) / 100
Solving for Principal, we get: Principal = Rs. 5000
Understanding Compound Interest:
Compound interest is calculated on the principal amount plus accumulated interest from previous periods. It grows faster than simple interest.
The formula for compound interest is a bit more complex, but we can break it down step-by-step.
Calculating Compound Interest:
The question asks for the compound interest on twice the principal (2 × Rs. 5000 = Rs. 10000) for 2 years at 5% interest.
Year 1: Interest = (10000 × 5 × 1) / 100 = Rs. 500
Amount at the end of Year 1 = 10000 + 500 = Rs. 10500
Year 2: Interest = (10500 × 5 × 1) / 100 = Rs. 525
Total compound interest over 2 years = 500 + 525 = Rs. 1025
Therefore, the correct answer is B: Rs. 1025 (Note: There's a discrepancy in the provided options. The calculation leads to Rs. 1025, which is not listed.)