Q. A sum of money on compound interest amounts to Rs. 10648 in 3 years and Rs. 9680 in 2 years. The rate of interest per annum is:
Answer: 10%
Notes: Let the sum be Rs. P and rate of interest be R% per annum. Then, $ P\left ( 1+\frac{R}{100} \right )^{2} = 9680 ………(1)$ $ P\left ( 1+\frac{R}{100} \right )^{3} = 10648 ……(2)$ On dividing equation (2) by (1) : $ 1+\frac{R}{100} = \frac{10648}{9680}$ $ => \frac{R}{100} = \frac{10648}{9680} – 1$ $ => \frac{R}{100} =\frac{10648 – 9680}{9680}$ $ => \frac{R}{100} = \frac{968}{9680} = \frac{1}{10}$ $ => R = \frac{1}{10}\times 100 = 10\%$ Hence option [C] is the right answer.