Quant Quiz On Compound Interest Day 17 Bag

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Quant Quiz On Compound Interest Day 17 Bag

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• The difference between compound interest compounded every 6 months and simple interest after 2 years is 248.10. The rate of interest is 10 percent. Find the sum
  a) 12000
  b) 14000
  c) 16000
  d) 18000
  e) None of these
  Answer & Explanation

  Answer – c) 16000
  Explanation :
  P*(1+5/100)^4 – P – P*(10/100)*2 = 248.10
  P = 16000
• A person earns an interest of 240 on investing certain amount at Simple interest for 2 years at 5 percent amount. If the rate of interest is compounded annually then how much more interest will be gain by the person at same rate of interest and on the same sum.
  a) 6
  b) 8
  c) 12
  d) 10
  e) None of these
  Answer & Explanation

  Answer –a) 6
  Explanation :
  240 = P*(5/100)*2, P = 2400
  CI = 2400(1+5/100)^2 – 2400 = 246
  So, 246 – 240 = 6
• Find the least number of years in which the sum put at 25% rate of interest will be more than doubled.
  a) 2 years
  b) 3 years
  c) 4 years
  d) 5 years
  e) None of these
  Answer & Explanation

  Answer – c) 4 years
  Explanation :
  Amount >= P*(1+25/100)^n
  Amount = p*(5/4) ^n
  For n = 4, (625/256) which is greater than 2.
• A sum of rupees 4420 is to be divided between rakesh and prakash in such a way that after 5 years and 7 years respectively the amount they get is equal. The rate of interest is 10 percent. Find the share of rakesh and prakash
  a) 2000, 2420
  b) 2420, 2000
  c) 2480, 2420
  d) 2210, 2210
  e) None of these
  Answer & Explanation

  Answer – b) 2420, 2000
  Explanation :
  Let the share of rakesh and prakash be R and P
  R*(1+10/100)^ 5 = (4420 – R)*(1+10/100)^ 7
  We get R = 2420, so P = 2000
• The simple interest on a certain sum of money for 4 years at 15 percent per annum is 600. Find the compound interest in the same sum at 10 percent interest for 2 years
  a) 220
  b) 200
  c) 210
  d) 120
  e) None of these
  Answer & Explanation

  Answer – c) 210
  Explanation :
  600 = p*4*(15/100), P = 1000
  CI = 1000(1+10/100)^ 2 – 1000 = 210
• Find the effective annual rate of 10 percent per annum compounded half- yearly-
  a) 10.5
  b) 10.25
  c) 11.25
  d) 11.50
  e) None of these
  Answer & Explanation

  Answer – b) 10.25
  Explanation :
  Take principal as 100 and then calculate,
  A = 100*(1+5/100)^ 2
  A = 110.25
  So effective rate is 10.25
• A sum of rupees 3200 is compounded annually at the rate of 25 paise per rupee per annum. Find the compound interest payable after 2 years.
  a) 1200
  b) 1600
  c) 1800
  d) 2000
  e) None of these
  Answer & Explanation

  Answer – c) 1800
  Explanation :
  Rate of interest is 25 paise per rupee per annum.
  So for 100 rupees it is 2500 paise i.e. 25 percent
  Now, CI = 3200(1+25/100)^ 2  – 3200 = 1800
• A sum of 3000 becomes 3600 in 3 years at 15 percent per annum. What will be the sum at the same rate after 9 years.
  a) 5124
  b) 5184
  c) 5186
  d) 5192
  e) None of these
  Answer & Explanation

  Answer – b) 5184
  Explanation :
  3600 = 3000*(1+15/100)^ 3
  (1+15/100)^ 3 = 6/5
  Amount = 3000*[(1+15/100)^ 3]^ 3
  Amount = 3000*(6/5)^ 3 = 5184
• Priya saves an amount of 500 every year and then lent that amount at an interest of 10 percent compounded annually. Find the amount after 3 years.
  a) 1820.5
  b) 1840.5
  c) 1920.5
  d) 1940.5
  e) None of these
  Answer & Explanation

  Answer – a) 1820.5
  Explanation :
  Total amount  = 500*(1+10/100)^ 3 + 500*(1+10/100)^ 2 + 500*(1+10/100)
  = 1820.5
• A man borrows 10000 rupees at 20 % compound interest for 3 years. If every year he pays 2000 rupees as repayment. How much amount is still left to be paid by the man?
  a) 5000
  b) 7000
  c) 9000
  d) 10000
  e) None of these
  Answer & Explanation

  Answer – d) 10000
  Explanation :
  Amount to be paid at the end of three years = 10000*(1+20/100)^ 3 = 17280
  Amount paid as instalment by the man = 2000*(1+20/100)^ 2 + 2000*(1+20/100) + 2000 = 7280
  So remaining amount = 10000

• On a certain sum of money, after 2 years the simple interest and compound interest obtained are Rs 800 and Rs 960 respectively. What is the sum of money invested? 
  A) Rs 1420
  B) Rs 1325
  C) Rs 1000
  D) Rs 1405
  E) Rs 1375
  Answer & Explanation

  C) Rs 1000
  Explanation: 
  Diff = 960-800 = 160
  r = 2*Diff*100/SI
  So r = 2*160*100/800 = 40%
  Now 160 = Pr²/100²
• Rs 6000 becomes Rs 7200 in 3 years at a certain rate of compound interest. What will be the amount received after 9 years?
  A) Rs 11,498
  B) Rs 10,352
  C) Rs 9,368
  D) Rs 10,368
  E) None of these
  Answer & Explanation

  D) Rs 10,368
  Explanation:
  6000[1 + r/100]³ = 7200
  So [1 + r/100]³ = 6/5
  So 6000[1 + r/100]⁹ = 6000*(6/5)*(6/5)*(6/5)
• A man borrows Rs 4000 at 8% compound interest for 3 years. At the end of each year he paid Rs 500. How much amount should he pay at the end of 3rd year to clear the debt? 
  A) Rs 4254.5
  B) Rs 3465.2
  C) Rs 3485.2
  D) Rs 4345.4
  E) Rs 3915.6
  Answer & Explanation

  E) Rs 3915.6
  Explanation: 
  Amount after 1 yr = 4000[1 + 8/100] = 4320
  Paid 500, so P = 4320 – 500 = 3820
  Amount after 2nd yr = 3820[1 + 8/100] = 4125.6
  So P= 4125.6-500 = 3625.6
  Amount after 3rd yr = 3625.6[1 + 8/100] = 3915.6
• A sum of money is lent for 2 years at 20% p.a. compound interest. It yields Rs 482 more when compounded semi-annually than compounded annually. What is the sum lent? 
  A) Rs 25,600
  B) Rs 20,000
  C) Rs 26,040
  D) Rs 40,500
  E) None of these
  Answer & Explanation

  B) Rs 20,000
  Explanation: 
  P[1 + (r/2)/100]⁴ – P[1 + r/100]² = 482
  P[1 + 10/100]⁴ – P[1 + 20/100]² = 482
  Solve, P = 20,000
• The compound interest obtained after 1st and 2nd year is Rs 160 and Rs 172.8 respectively on a certain sum of money invested for 2 years. What is the rate of interest? 
  A) 10%
  B) 8%
  C) 8.5%
  D) 9%
  E) 9.2%
  Answer & Explanation

  B) 8%
  Explanation: 
  Difference in interest for both yrs = 172.8 – 160 = 12.8
  So (r/100)*160 = 12.8
• A sum of money becomes Rs 35,280 after 2 years and Rs 37,044 after 3 years when lent on compound interest. Find the principal amount. 
  A) Rs 32,000
  B) Rs 28,000
  C) Rs 31,500
  D) Rs 32,500
  E) None of these
  Answer & Explanation

  A) Rs 32,000
  Explanation: 
  P[1 + r/100]³ = 37,044, and P[1 + r/100]² = 35,280
  Divide both equations, [1 + r/100] = 37044/35280 = 21/20
  So P[21/20]² = 35280
• The difference between compound interest earned after 3 years at 5% p.a. and simple interest earned after 4 years at 4% p.a. is Rs 76. Find the principal amount. 
  A) Rs 32,000
  B) Rs 28,000
  C) Rs 31,500
  D) Rs 32,500
  E) None of these
  Answer & Explanation

  A) Rs 32,000
  Explanation: 
  [P[1 + 5/100]³ – P] – P*4*4/100 = 76
  P [9261/8000 – 1 – 16/100] = 76
• A sum of money is lent at simple interest and compound interest. The ratio between the difference of compound interest and simple interest of 3 years and 2 years is 35 : 11. What is the rate of interest per annum? 
  A) 20 3/4%
  B) 17 2/5%
  C) 18 2/11%
  D) 22 1/5%
  E) 24 5/6%
  Answer & Explanation

  C) 18 2/11%
  Explanation: 
  Difference in 3 yrs = Pr²(300+r)/100³
  Difference in 2 yrs = Pr²/100²
  So Pr²(300+r)/100³ / Pr²/100² = 35/11 (300+r)/100 = 35/11
• A sum of money borrowed at 5% compound interest is to paid in two annual installments of Rs 882 each. What is the sum borrowed? 
  A) Rs 1650
  B) Rs 2340
  C) Rs 2630
  D) Rs 1640
  E) Rs 2640
  Answer & Explanation

  D) Rs 1640
  Explanation: 
  P = 882/[1 + 5/100] + 882/[1 + 5/100]²
• Rs 3903 is to be divided in a way that A’s share at the end of 7 years is equal to the B’s share at the end of 9 years. If the rate of interest is 4% compounded annually, find A’s share. 
  A) Rs 2475
  B) Rs 1875
  C) Rs 2175
  D) Rs 1935
  E) Rs 2028
  Answer & Explanation

  B) Rs 1875
  Explanation: 
  A’s share = (1 + 4/100)⁷
  B’s share = (1 + 4/100)⁹
  Divide both, B/A = (1 + 4/100)² = 676/625
  So A’s share = 625/(676+625) * 3903

• The difference between the total simple interest and the total compound interest compounded annually at the same rate of interest on a sum of money at the end of two years is Rs. 350. What is definitely the rate of interest per cent per annum?
  A.9,300
  B.7600
  C.12000
  D.Data inadequate
  E.None of these
  Answer & Explanation

  Answer – D.Data inadequate
  Explanation :
  Difference = Pr²/(100)²
  = (350×100×100)/(P×r²)
  P is not given
• Aswin invested an amount of Rs.9000 in a fixed deposit scheme for 2 years at CI rate 6% pa. How much amount will Aswin get on maturity of the fixed amount ?
  A.Rs.11,230
  B.Rs.10,250
  C.Rs.10,112
  D.Data inadequate
  E.None of these
  Answer & Explanation

  Answer – C.Rs.10,112
  Explanation :
  Amount = 9000*106/100*106/100
  = 9000*53/50*53/50
  = 10,112
• A sum of money invested for 7years in Scheme 1 which offers SI at a rate of 8% pa. The amount received from Scheme 1 after 7 years invested for 2 years in Scheme 2 which offers CI rate of 10% pa. If the interest received from Scheme B was Rs.1638. What was the sum invested in Scheme 1 ?
  A.Rs.7500
  B.Rs.5000
  C.Rs.8200
  D.Rs.9000
  E.None of these
  Answer & Explanation

  Answer – B.Rs.5000
  Explanation :
  SI =>Amount = x*8*7/100 + x = 56x+100x/100 = 156x/100 = 39x/25
  CI=> 39x/25[(1+10/100)² – 1] 1638 = 39x/25[121/100 – 1] = 39x/100[21/100] X = 1638*100*25/21*39 = 5000
• Rs.5200 was partly invested in Scheme A at 10% pa CI for 2 years and Partly invested in Scheme B at 10% pa SI for 4 years. Both the schemes earn equal interests. How much was invested in Scheme A ?
  A.Rs.1790
  B.Rs.2200
  C.Rs.3410
  D.Rs.2670
  E.None of these
  Answer & Explanation

  Answer – C.Rs.3410
  Explanation :
  Amount invested in Scheme B = X
  Amount invested in Scheme A = 5200 – x
  X*10*4/100 = (5200-x)*21/100……………………[(1-10/100)²-1] = 21/100
  40x/100 = (5200-x)*21/100
  2x/5 = (5200-x)*21/100
  200x = 5200*21*5 – x*5*21
  200x = 546000 – 105x
  305x = 546000
  X = 1790
  Scheme A = 5200 – 1790 = 3410
• The CI on Rs.7000 for 3 years at 5% for first year, 7% for second year, 10% for the third year will be
  A.Rs.1800
  B.Rs.1530
  C.Rs.1651
  D.Rs.2050
  E.None of these
  Answer & Explanation

  Answer – C.Rs.1651
  Explanation :
  A = 7000*105/100*107/100*110/100
  = 7000*1.05*1.07*1.1
  = 8650.95 = 8651
  CI = 8651-7000 = 1651
• Poorni and Priyanka have to clear their respective loans by paying 2 equal annual instalments of Rs.20000 each. Poorni pays at 10% pa of SI and Priyanka pays at 10% CI pa. What is the difference in their payments ?
  A.200
  B.300
  C.400
  D.500
  E.None of these
  Answer & Explanation

  Answer – A.200
  Explanation :
  D =[(20,000 *110/100*110/100) – 20,000]  – 20,000 *10*2/100
  =[ 24200-20000]-4000
  =4200 – 4000
  D = 200
• A sum of Rs.3,50,500 is to be paid back in 2 equal annual instalments. How much is each instalment, if the rate of interest charged 4% per annum compound annually ?
  A.Rs.1,90,450
  B.Rs.1,65,876
  C.Rs.1,76,545
  D.Rs.1,85,834
  E.None of these
  Answer & Explanation

  Answer – D.Rs.1,85,834
  Explanation :
  Total value of all the 3 instalments
  [X*100/104] + [X*100*100/104]  = 3,50,500
  X*25/26 + x*625/676 = 3,50,500
  X*25/26[1+25/26] = 3,50,500
  X*25/26[51/26] = 3,50,500
  X = 3,50,500*676/25*51 = 1,85,833.72 = 1,85,834
• At CI, if a certain sum of money is doubled in 4 years, then the amount will be four fold in how many years ?
  A.7years
  B.4years
  C.10years
  D.8years
  E.None of these
  Answer & Explanation

  Answer – D.8years
  Explanation : 2n = 2*4 = 8 years
• X has lent some money to A at 5% pa and B at 8% pa. At the end of the year he has gain the overall interest at 7% pa.In what ratio has he lent the money to A and B ?
  A.2:1
  B.1:2
  C.3:1
  D.1:4
  E.None of these
  Answer & Explanation

  Answer – B.1:2
  Explanation :
  5………………………….8
  ……………7…………….
  1………………………….2
  Ratio A : B = 1:2
• The difference between interest received by X and Y is Rs.315 on Rs.3500 for 3 years. What is the difference in rate of interest ?
  A.1.5%
  B.2%
  C.3%
  D.2.7%
  E.None of these
  Answer & Explanation

  Answer – C.3%
  Explanation :
  3500*3/100(R1-R2) = 315
  R1-R2 = 315*100/10500 = 3%

• What is the difference between the CI and SI on Rs.6500 at the rate of 4 pcpa in 2 yrs ?
  A)9.4
  B)10.4
  C)15.4
  D)14.5
  Answer

  B)10.4
  Explanation :
  SI = 6500*4*2/100 = 520
  CI = 6500*(104/100)*(104/100) = 7030.4 = 530.4
  530.4 – 520 = 10.4
• The CI on a certain sum at 10% pa for 2yrs is Rs.6548. What is SI on the sum of money at 7%pa for 4 yrs(approx) ?
  A)8700
  B)8731
  C)8370
  D)8470
  Answer

  B)8731
  Explanation :
  CI = p [ {1 + (10/100)}2 – 1] 6548 = p [(110/100) ² – 1] 6548 =p (121 – 100)/100
  P = 654800/21 =31,181
  SI = 31181*7*4/100 = 8731
• A sum of money amount to Rs.900 in 3 yrs and Rs.1080 in 4yrs at CI. What is the rate of CI pa ?
  A)10%
  B)15%
  C)20%
  D)18%
  Answer

  C)20%
  Explanation :
  (1080-900/900)*100
  180*100/900 = 20%
• Find the CI on Rs.4500 at 4% pa for 2 yrs compounded half yearly(approx) ?
  A)963
  B)369
  C)639
  D)360
  Answer

  C)639
  Explanation :
  CI = P [(1+(r/100)ⁿ – 1] = 4500[(1+2/100)⁴ – 1
  = 4500[ (102*102*102*102/100*100*100*100) – 1] = 4500[1.082 – 1] = 4500*0.082 = 369
• In how many years will a sum of Rs.15625 at 8% pa compounded semi annually become Rs.17,576?
  A)2(1/3)yrs
  B)2yrs
  C)1(1/2)yrs
  D)1yr
  Answer

  C)1(1/2)yrs
  Explanation :
  15625*(1+(4/100))²ⁿ = 17576
  15625*(104/100) ²ⁿ = 17576
  (26/25) ²ⁿ = 17576/15625 = (26/27)³
  2n = 3
  N =3/2 = 1(1/2) yrs
• If 40% increase in an amount in 4 years at SI. What will be the CI of Rs.10,000 after 2 yrs at the same rate ?
  A)1000
  B)1100
  C)2000
  D)2100
  Answer

  D)2100
  Explanation :
  P = 100, SI = 40,  T = 4
  R = 100*40 / 100*4 = 10%pa
  CI = 10,000(110/100)² = 10000*11*11/100 = 12100
  12100 – 10000 = 2100
• A sum of money is borrowed and paid in 2 annual instalments of Rs.642 each allowing 4% CI. The sum borrowed was
  A)1120
  B)1211
  C)1112
  D)1121
  Answer

  B)1211
  Explanation :
  P = [642/(104/100)] + [642/(104/100)²)
  = 642*(25/26) + 642 (25/26)²
  = 617.3 + 593.6 = 1210.9 = 1211
• The least number of complete years in which a sum of money put out at 10% CI will be more than  doubled is
  A)8yrs
  B)6yrs
  C)4yrs
  D)7yrs
  Answer

  A)8yrs
  Explanation :
  P(110/100)ⁿ  > 2P
  (11/10) ⁿ > 2P
  1.1*1.1*1.1*1.1*1.1*1.1*1.1*1.1 = 2.14 > 2
  N = 8
• A sum of money doubles itself at CI in 10yrs. In how many yrs will it become 4 times ?
  A)10yrs
  B)20yrs
  C)15yrs
  D)22yrs
  Answer

  B)20yrs
  Explanation :
  P(1+(R/100))¹⁰ = 2P
  1+(R/100)¹⁰ = 2
  (1+(R/100))ⁿ = 4 = 2²
  2*10 = 20yrs
• At what rate of CI pa will a sum of Rs.1000 becomes Rs.1040.4 in 2yrs ?
  A)2%
  B)1%
  C)1.5%
  D)3%
  Answer

  A)2%
  Explanation :
  1000*(1+(R/100)) ² = 1040.4
  (1+(R/100)) ² = 1040.4/1000
  (1+(R/100)) ² = 10404/10000 = (102/100) ²
  R = 2%