A sum of money invested at compound interest amounts to Rs. 9,600 in 2 years and to Rs.10,800 in 3 years. Find the rate of interest per annum.

Correct option is C

Given:

Amount after 2 years = ₹9600
Amount after 3 years = ₹1,0800
Formula Used:

Amount after n years = $$P(1 + \frac{r}{100})^n$$​​

Solution:

Use the compound interest formula to relate amounts at 3 years and 2 years

$$\frac{\text{Amount after 3 years}}{\text{Amount after 2 years}} = \frac{P \left(1 + \frac{r}{100}\right)^3}{P \left(1 + \frac{r}{100}\right)^2} = 1 + \frac{r}{100}$$​
​Substitute given values: 

$$\frac{10800}{9600} = 1 + \frac{r}{100} \\\ \\1.125 = 1 + \frac{r}{100} \\\ \\\frac{r}{100} = 0.125 \\\ \\r = 12.5\%$$​​