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A man invested Rs. X at 15% simple interest and Rs. 2X at 8% compound interest, compounded annually, for two years respectively. The difference between the simple interest and compound interest received after two years is Rs. 820. Find the value of X.

1. Rs. 25000
2. Rs. 30600
3. Rs. 28600
4. Rs. 22200

Correct answer: Rs. 25000

Solution

Simple interest on X at 15% for 2 years is $\frac{15\times X\times 2}{100}=0.30X$. Compound interest on 2X at 8% for 2 years is $2X[(1.08)^2-1]=2X(0.1664)=0.3328X$. Their difference is $0.0328X=820$, giving $X=25000$.

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