Question 70

The difference between the compound interest and the simple interest on an amount of ₹1,500 for 2 years, at a given rate of interest per annum, is ₹60. What is the rate of interest per annum, if in the case of compound interest, the interest is compounded annually?

Solution

Difference between CI and SI for 2 years when principal amount and rate are the same = $$principal\times(\frac{rate}{100})^2$$

$$60=1500\times(\frac{rate}{100})^2$$

$$1=25\times(\frac{rate}{100})^2$$

$$\frac{1}{25}=\frac{rate^2}{10000}$$

$$\frac{1}{1}=\frac{rate^2}{400}$$

$$rate^2 = 400$$

$$rate^2 = 20^2$$
rate of interest = 20%

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