Question : The difference between the compound interest and the simple interest on an amount of INR 1,500 for 2 years, at a given rate of interest per annum, is INR 60. What is the rate of interest per annum, if in the case of compound interest, the interest is compounded annually?
Option 1: 20%
Option 2: 15%
Option 3: 25%
Option 4: 12.5%
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Correct Answer: 20%
Solution : Given, Principal Amount = INR 1500 Time = 2 years The difference between CI and SI = INR 60 Compound Interest – Simple Interest = Principal × $(\frac{R}{100})^2$, where $R$ is the rate of interest. ⇒ CI – SI $= 1500 × (\frac{R}{100})(\frac{R}{100})$ ⇒ $(\frac{R}{100})^2 = \frac{60}{1500}$ ⇒ $(\frac{R}{100})^2=\frac{1}{25}$ ⇒ $R^2 = \frac{1}{25}$ × 100 × 100 ⇒ $R^2 = 400$ ⇒ $R = \sqrt{400}$ ⇒ $R = 20$% Hence, the correct answer is 20%.
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