# Compound Interest- Aptitude Questions and Answers

 The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is 10 rs. What is the sum ? A) 5,000 B) 6,000 C) 6,250 D) 7,500 Correct Answer : 6,250 Explanation :Let the sum is 100 then S.I. = 100* 4* 2 / 100 = 8 C.I = 100 *(1 + 4/100)2 - 100 = 100*( 26/25) 2 - 100 = 204/25 Difference between C.I and S.I = 204/25 - 8 = 4/25 = .16 So, 0.16 : 10 : : 100 : P ∴ P = (10* 100) / 0.16 = 6250 The effective annual rate of interest corresponding to a nominal rate of 22% per annum payable half-yearly is? A) 44% B) 23.21% C) 46.42% D) 22% Correct Answer : 23.21% Explanation :Amount = P[1+(R/2)/100]2n , if interest is payable half-yearly Let the amount is 100 for one year So, effective amount = 100*(1 + 11/100)2 = 100*(1 + 11/100)*(1 + 11/100) = 111*1.11 = 123.21 Then, Effective rate = 123.21 -100 = 23.21% Raj borrowed Rs. 5000 at 10% per annum on simple interest and lent the same amount at 15% per annum on compound interest. At the end of 2 years, he would ? A) Gain Rs. 612.5 B) Gain Rs. 621.5 C) Loss Rs. 612.5 D) Loss Rs. 621.5 Correct Answer : Gain Rs. 612.5 Explanation :Simple interest paid by Raj At the end of 2 years simple interest =P*R*T /100 = 5000*10*2 /100 = 1000 Amount gained by Raj on lent it on compound interest Amount = P*(1+ R/100) T =5000(1 + 15/100)2 =5000(1.15)2 =6612.5 compound interest = 6612.5 - 5000 = 1612.5 Amount gain by Raj = 1612.5 - 1000 = 612.5 The difference between the compound interest and the simple interest earned at the end of the third year on a sum of money at a rate of 10% per annum is Rs 77.5. What is the sum? A) Rs 3500 B) Rs 2500 C) Rs 3000 D) Rs 2000 Correct Answer : Rs 2500 Explanation :Let Principle Amount =P, Time T = 3 and Rate R = 10% Simple Interest, SI = PTR/100 = 3*10*P/100 = 0.3P Compound Interest, CI = A-P = P[1+(R/100)]T - P = P[1+(10/100)]3 - P = P[1.1]3 - P = 1.331P - P = 0.331P Now, CI - SI = 77.5 => 0.331P - 0.3P = 77.5 => 0.031P = 77.5 Principle Amount, P = 77500/31 = Rs 2500