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

$\frac{PR^2}{(100)^2}$

Compound intereat = P[ 1 + \(\frac{R}{100}\)]² - P

Simple interest = \(\frac{P x R x 2}{100}\)

Difference between simple interest and compound interest for 2 years

= P[ 1 + \(\frac{R}{100}\)]² - P  - \(\frac{P x R x 2}{100}\)

= P[ \(\frac{100 +R}{100}\)]² - P  - \(\frac{P x R x 2}{100}\)

= P[ \(\frac{(100 +R)² - (100)²}{(100)²}\)]  - \(\frac{P x R x 2}{100}\)

= P[ \(\frac{(100 +R)² - (100)²}{(100)²}\)]  - \(\frac{P x R x 2}{100}\)

= P[ \(\frac{(R² + 200R}{(100)²}\)]  - \(\frac{P x R x 2}{100}\)

=  \(\frac{(PR)²}{(100)²}\) + \(\frac{(200PR}{(100)²}\))   - \(\frac{P x R x 2}{100}\)

=  \(\frac{(PR)²}{(100)²}\) + \(\frac{(2 x P xR}{100}\))   - \(\frac{P x R x 2}{100}\)

=  \(\frac{(PR)²}{(100)²}\)