The simple interest at 10% p.a. on a deposit for 2 years is Rs. 4,000. If the interest is compounded on an annual basis, how much more will be the amount ofinterest ?
Given: The simple interest at 10% p.a. on a deposit for 2 years is Rs. 4,000. Formula used: simple interest = (principal × rate × time)/100 compound interest (CI) = A – P = P[(1 + R/100)n – 1]; where A = amount, P = principal, R = rate p.a., n = time period Concept Used: compound interest is also successive percentage increase. rate = 10 + 10 + (10 × 10)/100 = 21% Solution: Let the principal is Rs. P .∴ 4000 = (P × 10 × 2)/100 ⇒ principal = Rs. 20,000 ⇒ compound interest = 20,000 × 21/100 ⇒ compound interest = Rs. 4200 ⇒ increased interest = Rs. (4200 - 4000) = Rs. 200 So, compound interest rupees is 200 more than simple interest. Smart Method Difference in rate of CI and SI for 2 years = R2/100 = 102/100 = 1% Rate of SI for 2 years = 10 × 2 = 20% According to question,