Question : The difference between the compound interest and the simple interest on a certain sum of money at 10% per annum for 2 years is INR 200. What is the sum of money, if in the case of compound interest, interest is compounded annually?
Option 1: INR 25,000
Option 2: INR 15,000
Option 3: INR 12,000
Option 4: INR 20,000
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Correct Answer: INR 20,000
Solution : Given: The difference between the compound interest and the simple interest on a certain sum of money at 10% per annum for 2 years is INR 200. Use the formula, $CI–SI=P(\frac{R}{100})^T$ where $SI$, $CI$, $R$, $T$ are the simple interest, compound interest, rate, and time. According to the question, $200=P(\frac{10}{100})^2$ ⇒ $200=P(\frac{1}{10})^2$ ⇒ $200=P\times\frac{1}{100}$ ⇒ $P=$ INR 20,000 Hence, the correct answer is INR 20,000.
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