The interest accrued on a sum of ₹12,000 in two years, when interest is compounded annually, is ₹3,870. What is the rate of interest per annum?

$$interest\ =\ principal\ amount\left[\left(1+\frac{rate}{100}\right)^{time}\ -1\right]$$

$$3870 = 12000[(1+\frac{rate}{100})^{2} -1]$$

$$3870=12000(1+\frac{rate}{100})^2-12000$$

$$3870+12000=12000(1+\frac{rate}{100})^2$$

$$15870=12000(1+\frac{rate}{100})^2$$

$$\frac{529}{400}=(1+\frac{rate}{100})^2$$

$$\left(\frac{23}{20}\right)^2=(1+\frac{rate}{100})^2$$

$$\frac{23}{20}=1+\frac{rate}{100}$$

$$\frac{23}{20}-1=\frac{rate}{100}$$

$$\frac{3}{20}=\frac{rate}{100}$$

$$\frac{3}{1}=\frac{rate}{5}$$

So the rate of interest per annum = 15%