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Quantitative Aptitude > Interest

COMPOUND INTEREST MCQs

Total Questions : 262 | Page 2 of 27 pages
Question 11. At what rate per annum will Rs.32000 yield a compound interest of Rs.5044 in 9 months interest being compounded quarterly ?
  1.    80%
  2.    20%
  3.    50%
  4.    32%
 Discuss Question
Answer: Option B. -> 20%
Answer: (b)Using Rule 1,Let the rate of CI be R per cent per annum.CI = P$[(1 + R/100)^T - 1]$5044 = 32000$[(1 + R/400)^3 - 1]$[Since, Interest is compounded quarterly]$5044/32000 = (1 + R/400)^3 - 1$$(1 + R/400)^3 - 1 = 1261/8000$$(1 + R/400)^3 = 1 + 1261/8000$$(1 + R/400)^3 = 9261/8000 = (21/20)^3$1 + $R/400 = 21/20$$R/400 = 21/20 - 1 = 1/20$R = $400/20$ = 20
Question 12. The compound interest on Rs.16,000 for 9 months at 20% per annum, interest being compounded quarterly, is
  1.    Rs.2,518
  2.    Rs.2,520
  3.    Rs.2,522
  4.    Rs.2,524
 Discuss Question
Answer: Option C. -> Rs.2,522
Answer: (c)Using Rule 1,The interest is compounded quarterly.R = $20/4$ = 5%Time = 3 quartersC.I. = P$[(1 + R/100)^T - 1]$= 16000$[(1 + 5/100)^3 - 1]$= $16000[(21/20)^3 - 1]$= $16000({9261 - 8000}/8000)$= $16000 × 1261/8000$ = Rs.2522
Question 13. A sum of Rs.8000 will amount to Rs.8820 in 2 years if the interest is calculated every year. The rate of compound interest is
  1.    5%
  2.    6%
  3.    3%
  4.    7%
 Discuss Question
Answer: Option A. -> 5%
Answer: (a)Using Rule 1,If the rate of C.I. be r% per annum, thenA = P$(1 + R/100)^T$8820 = 8000$(1 + r/100)^2$$8820/8000 = (1 + r/100)^2$$441/400 = (21/20)^2 = (1 + r/100)^2$$1 + r/100 = 21/20$$r/100 = 21/20 - 1 = 1/20$r = $1/20$ × 100r = 5% per annum
Question 14. In what time will Rs.1000 becomes Rs.1331 at 10% per annum compounded annually ?
  1.    3$1/2$ years
  2.    3 years
  3.    2 years
  4.    2$1/2$ years
 Discuss Question
Answer: Option B. -> 3 years
Answer: (b)Using Rule 1,Let the required time be n years.Then,1331 = 1000$(1 + 10/100)^n$[$P_1 = P(1+ r/100)^n$]$1331/1000 = ({10 + 1}/10)^n$$(11/10)^n = (11/10)^3$n = 3
Question 15. A sum of money on compound interest amounts to Rs.10648 in 3 years and Rs.9680 in 2 years. The rate of interest per annum is :
  1.    20%
  2.    5%
  3.    15%
  4.    10%
 Discuss Question
Answer: Option D. -> 10%
Answer: (d)Using Rule 1,Let the sum be P and rate of interest be R% per annum. Then,$P(1 + R/100)^2 = 9680$ ...(i)$P(1 + R/100)^3 = 10648$ ...(ii)On dividing equation (ii) by (i)$1 + R/100 = 10648/9680$$R/100 = 10648/9680$ -1= ${10648 - 9680}/9680$$R/100 = 968/9680 = 1/10$R = $1/10 × 100$ = 10%
Question 16. In what time Rs.8,000 will amount to Rs.9,261 at 10% per annum compound interest, when the interest is compounded half yearly ?
  1.    2 years
  2.    3$1/2$ years
  3.    2$1/2$ years
  4.    1$1/2$ years
 Discuss Question
Answer: Option D. -> 1$1/2$ years
Answer: (d)Using Rule 1 and 2,Interest is compounded half yearly.Rate of interest = 5%Time = $n/2$ years (let)or n half-yearsA = P$(1 + R/100)^T$9261 = 8000$(1 + 5/100)^n$$9261/8000 = (21/20)^n$$(21/20)^3 = (21/20)^n$n = 3 half years= $3/2$ years = $1{1}/2$ years
Question 17. An amount of Rs.6,000 lent at 5% per annum compound interest for 2 years will become
  1.    Rs.6,615
  2.    Rs.600
  3.    Rs.6,610
  4.    Rs.6,600
 Discuss Question
Answer: Option A. -> Rs.6,615
Answer: (a)Using Rule 1,A = P$(1 + R/100)^T$= 6000$(1 + 5/100)^2$= 6000 × $21/20 × 21/20$ = Rs.6615
Question 18. The sum of money that yields a compound interest of Rs.420 during the second year at 5% p.a is
  1.    Rs.21,000
  2.    Rs.4,000
  3.    Rs.8,000
  4.    Rs.42,000
 Discuss Question
Answer: Option C. -> Rs.8,000
Answer: (c)Using Rule 1,CI = P$[(1 + R/100)^T –1] - {PR}/100$420 = P$[(1 + 5/100)^2 - 1] - {P × 5}/100$420 = P$[(21/20)^2 - 1] - {5P}/100$420 = ${41P}/400 - {5P}/100 = {21P}/400$P = ${420 × 400}/21$ = Rs.8000
Question 19. A principal of Rs.10,000, after 2 years compounded annually, the rate of interest being 10% per annum during the first year and 12% per annum during the second year (in rupees) will amount to :
  1.    Rs.11,320
  2.    Rs.12,000
  3.    Rs.12,500
  4.    Rs.12,320
 Discuss Question
Answer: Option D. -> Rs.12,320
Answer: (d)Using Rule 3,A = P$(1 + r_1/100)(1 + r_2/100)$= 10000$(1 + 10/100)(1 + 12/100)$= 10000 × $11/10 × 28/25$ = Rs.12320
Question 20. The compound interest on Rs.2000 in 2 years if the rate of interest is 4% per annum for the first year and 3% per annum for the second year, will be
  1.    Rs.143.40
  2.    Rs.142.40
  3.    Rs.141.40
  4.    Rs.140.40
 Discuss Question
Answer: Option B. -> Rs.142.40
Answer: (b)Using Rule 3,Amount = $2000(1 + 4/100)(1 + 3/100)$= 2000 ×1.04 ×1.03 = Rs.2142.40CI = Rs.(2142.40 - 2000) = Rs.142.40

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