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,
$latex P\left ( 1+\frac{R}{100} \right )^{2} = 9680 .........(1)&s=1$
$latex P\left ( 1+\frac{R}{100} \right )^{3} = 10648 ......(2)&s=1$
On dividing equation (2) by (1) :
$latex 1+\frac{R}{100} = \frac{10648}{9680}&s=2$
$latex => \frac{R}{100} = \frac{10648}{9680} - 1&s=2$
$latex => \frac{R}{100} =\frac{10648 - 9680}{9680}&s=2$
$latex => \frac{R}{100} = \frac{968}{9680} = \frac{1}{10}&s=2$
$latex => R = \frac{1}{10}\times 100 = 10\%&s=1$
Hence option [C] is the right ansewr.
