If the principal amount is $$ P $$ and the rate of interest is $$ R\% $$ per annum, then what is the difference between simple interest and compound interest for 2 years?

Question

Accepted Answer

The simple interest (SI) for 2 years is calculated as:  
$$
SI = \frac{P \cdot R \cdot 2}{100}
$$

The compound interest (CI) for 2 years is given by:  
$$
CI = P \left(1 + \frac{R}{100}\right)^2 - P
$$

Expanding $$ CI $$:  
$$
CI = P \left(1 + \frac{R}{100} + \frac{R^2}{(100)^2}\right) - P
$$  
$$
CI = P \cdot \frac{R}{100} + P \cdot \frac{R^2}{(100)^2}
$$

The difference between CI and SI is:  
$$
Difference = CI - SI
$$  
Substituting values:  
$$
Difference = P \cdot \frac{R^2}{(100)^2}
$$

Simplifying further, the difference becomes:  
$$
Difference = \frac{PR^2}{(100)^3}
$$

Answer

Answer

Answer