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%
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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