Question 57

The difference between the compound interest and simple interest on a sum of ₹2,500 for 2 years is ₹100. Find the rare of interest per annum, if the nominal rate of interest per annum is the same for both simple and compound interest, and in the case of compound interest, the interest is compounded annually.

Solution

difference between CI and SI for two years = $$principal\left(\frac{rate}{100}\right)^2$$

$$100=2500\left(\frac{rate}{100}\right)^2$$

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

$$\left(\frac{1}{5}\right)^2=\left(\frac{rate}{100}\right)^2$$

$$\frac{1}{5}=\frac{rate}{100}$$

rate of interest = 20%

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