Find the difference between simple interest and the annual compound interest on Rs 9,600 for 2 years at the rate of 5% per annum.

Answer: Rs 24

Solution:

Given,

Principal (P) = Rs 9,600

Time (T) = 2 years

Rate (R) = 5%

To find: Difference between simple interest and annual compound interest (SI - CI) = ?

We know,

$Simple Interest (SI) = \dfrac{PTR}{100}$

$SI = \dfrac{9600×2×5}{100}$

$SI = \dfrac{9600}{10}$

$\therefore SI = Rs 960$

Also,

$Compound Interest (CI) = P \left [ \left ( 1 + \dfrac{R}{100} \right )^T - 1 \right ]$

$CI = P \left [ \left ( 1 + \dfrac{5}{100} \right )^2 - 1 \right ]$

$CI = P \left [ \left (  \dfrac{100+5}{100} \right )^2 - 1 \right ]$

$CI = P \left [ \left (  \dfrac{105}{100} \right )^2 - 1 \right ]$

$CI = P \left [ \left (  \dfrac{21}{20} \right )^2 - 1 \right ]$

$CI = P \left [ \dfrac{441}{400} - 1 \right ]$

$CI = P \left [ \dfrac{441 -400}{400}  \right ]$

$CI = P \left [ \dfrac{41}{400} \right ]$

$CI = 9600 × \dfrac{41}{400}$

$CI = 24 × 41$

$CI = Rs 984$

Now,

$SI - CI = Rs 960 - Rs 984 = -Rs 24$

Hence, the required difference between the simple interest and annual compound interest is negative Rs 24.