# Compound Interest- Aptitude Questions and Answers

 The difference between compound and simple interests on a certain sum for 2 years at 5% per annum is Rs.40. The sum is? A) Rs.16,000 B) Rs.15,000 C) Rs.12,000 D) Rs.10,000 Correct Answer :Rs.16,000 Explanation :Let the sum be rs X then, CI = X*( 1 + 5/100 )2 - X = X*(441 / 400 - 1) = X*41 / 400 SI = X*5*2 / 100 = X / 10 As is given, CI - SI = 40 X* ( 41 / 400 - 1 / 10) = 40 X* (41 - 40) / 400 = 40 X = 16000 If Rs. 7500 are borrowed at compound interest at the rate of 4% per annum, then after 2 years the amount to be paid is ? A) Rs. 8082 B) Rs. 7800 C) Rs. 8100 D) Rs. 8112 Correct Answer :Rs. 8112 Explanation :Amount = P(1+R/100)n , if interest is payable annually Amount =7500*(1 + 4/100)2 = 7500 * 26/25 * 26/25 = 8112 The compound interest on Rs 2800 for 11/2 years at 10% per annum is ? A) Rs. 441.35 B) Rs. 436.75 C) Rs. 434 D) Rs. 420 Correct Answer :Rs. 434 Explanation :Let Principal = P, Rate = R% per annum, Time = n years. When time is fraction of a year, say 43/4 years, then amount= P(1+R/100)4 x (1+(3R/4)/100) So, Amount = 2800 * (1 + 10/100) * (1 + (1*10/2) / 100) = 2800 * (1 + 10/100) * (1 +5/100) = 2800 * 11/10 * 21/20 = 3234 Required C.I. = (3234 - 2800) = 434 A money lender lends Rs 2000 for 6 months at 20% per annum whereas the interest is compounded quarterly. After the given period he will get the amount of ? A) Rs. 2205 B) Rs. 2200 C) Rs. 2160 D) Rs. 2040 Correct Answer :Rs. 2205 Explanation :Let Principal = P, Rate = R% per annum, Time = n years. Amount = P(1 + (R/4)/100 )4n , if interest is payable quarterly Hence,required amount = 2000* (1 + (20/4) / 100 )4*1/2 = 2000*(1 + 5/100)2 = 2000*(21 / 20)2 = 2205 The compound interest on a certain sum of money for 2 years at 10% per annum is Rs 420. The simple interest on the same sum at the same rate and for the same time will be ? A) Rs. 350 B) Rs. 375 C) Rs. 380 D) Rs. 400 Correct Answer :Rs. 400 Explanation :Let the principle is P. As is given, compound interest= P*(1 +10/100)2 - P = 420 P*(11/10)2 - P = 420 P*(121/100) - P = 420 P*(121-100)/100 = 420 P = 2000 So, simple interest.= P*R*T / 100 = 2000* 2* 10 / 100 = 400 The difference between the simple and the compound interest compounded every six months at the rate of 10 percent per annum at the end of two years is Rs 124.05. What is the sum ? A) Rs. 10000 B) Rs. 6000 C) Rs. 12000 D) Rs. 8000 Correct Answer :Rs. 8000 Explanation :Let Principal = P, Rate = R% per annum, Time = n years. Compound Interest, CI = P* [ 1 + (R/2)/100 ]2n - P , if compound interest is half-yearly Simple Interest, SI = P*R*T / 100 Then,CI - SI = ( P*(1 + 5/100)4 - P ) - ( P* 10* 2 / 100 ) = 124.05 P*(21/20)4 - P - P/ 5 = 124.05 P*(194481 - 160000 - 32000 ) / 160000 = 124.05 P = 19848000 / 2481 P = 8000 In what time will Rs 90600 amounts to Rs 109626 at 10% compound Interest? A) 2 years B) 3 years C) 5 years D) 4 years Correct Answer :2 years Explanation :Amount = P(1+R/100)n , if compound interest is payable annually Then, 109626 = 90600*(1 + 10/100)n 109626 / 90600 = (11/10)n (121/100) = (11/10)n (11/10)2 = (11/10)n n = 2 years Compound interest on a certain sum of money at 20% per annum for 2 years is Rs 5995. What is the simple interest on the same money at 8% per annum for 6 years ? A) Rs. 5989 B) Rs. 6789 C) Rs. 6540 D) Rs. 7844 Correct Answer :Rs. 6540 Explanation :Let Principal = P, Rate = R% per annum, Time = n years. Compound Interest, CI=P(1+R/100)n - P Then, 5995 = P*(1 + 20/100)2 - P 5995 =P*(36/25 - 1) 5995 = P* 11/25 P = 5995*25 / 11 P = 13625 Hence Simple Interest, SI = P*R*T / 100 = 13625 * 8 * 6 / 100 = 6540 On a simple interest rate of 20% annually, a trader gets 6000 rupees in 3 years. How much he gets more if the lent was on compound interest ? A) 1200 B) 480 C) 4000 D) 400 Correct Answer :480 Explanation :Let Principal = P, Rate = R% per annum, Time = n years. Simple Interest , SI = P*R*T /100 Amount = P + Simple Interest =P + (P*R*T/100) = 6000 P + P*20*3 /100 = 6000 P = 6000*5/8 = 3750 Thus, Simple Interest in 3 years, SI = 6000 - 3750 = 2250 Compound Interest, CI=P*(1 + R/100)n - P CI = 3750*(1 + 20/100)3 - 3750 =3750*[ (6/5)3 -1 ] =3750*( 91/125 ) =2730 Hence, trader will be get more if the lent was on CI = CI - SI = 2730 - 2250 = 480 The difference between the compound interest and the simple interest on a certain sum at 5% per annum for 2 years is Rs 1.50 . The sum is ? A) 600 B) 500 C) 400 D) 300 Correct Answer :600 Explanation :Let the sum is 100 then S.I. = 100* 5* 2 / 100 = 10 C.I = 100 *(1 + 5/100)2 - 100 = 41/4 Difference between C.I and S.I = 41/4 - 10 = 0.25 So, 0.25 : 1.50 : : 100 : P ∴ P = (1.50 * 100) / 0.25 = 600 If the compound interest on a certain sum for 2 years at 12.5% per annum is 170, the simple interest will be? A) 200 B) 150 C) 160 D) 170 Correct Answer :160 Explanation :Let the principle is P So compound interest = P * ( 1 + 12.5/100)2 - P = 170 P* (112.5/100) *(112.5/100) - P = 170 P* (12656.25 - 10000) / 10000 = 170 ∴ P = 1700000 / 2656.25 Simple interest SI = P* T* R /100 = (1700000 / 2656.25)* 2* 12.5 / 100 = 160 Albert invested an amount of Rs 8000 in a fixed deposit scheme for 2 years at compound interest rate 5% annum . How much amount will Albert get on maturity of the fixed deposit ? A) Rs. 8600 B) Rs. 8620 C) Rs. 8820 D) Rs. 8840 Correct Answer :Rs. 8820 Explanation :Amount= 8000*(1 + 5/100)² = 8000* 21/20* 21/20 = 8820