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?
Answer & explanation
Correct answer: option 3
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[ \(\frac{(R² + 200R}{(100)²}\)] - \(\frac{P x R x 2}{100}\)
= \(\frac{(PR)²}{(100)²}\) + \(\frac{(200PR}{(100)²}\)) - \(\frac{P x R x 2}{100}\)
= \(\frac{(PR)²}{(100)²}\) + \(\frac{(2 x P xR}{100}\)) - \(\frac{P x R x 2}{100}\)
= \(\frac{(PR)²}{(100)²}\)