Question : The difference between compound interest (compounding annually) and simple interest on a sum at the rate of 30% per annum for 2 years is INR 3,600. What is the sum?
Option 1: INR 75,000
Option 2: INR 40,000
Option 3: INR 50,000
Option 4: INR 60,000
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Correct Answer: INR 40,000
Solution : Difference between compound interest (compounding annually) and simple interest = INR 3600 Rate, $R$ = 30% Term = 2 years Let $P$ be the principal sum. Difference between compound interest (compounding annually) and simple interest for 2 years $=P×(\frac{R}{100})^2$ $⇒ 3600 = P×(\frac{30}{100})^2$ $⇒ 3600 = P×\frac{9}{100}$ $\therefore P = \frac{360000}{9}=40000$ Hence, the correct answer is INR 40,000.
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