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Quantitative Aptitude > Interest

COMPOUND INTEREST MCQs

Total Questions : 262 | Page 5 of 27 pages
Question 41. In how many years will Rs.2,000 amounts to Rs.2,420 at 10% per annum compound interest?
  1.    1$1/2$ years
  2.    3 years
  3.    2 years
  4.    2$1/2$ years
 Discuss Question
Answer: Option C. -> 2 years
Answer: (c)Using Rule 1,According to question,2420 = 2000$(1 + 10/100)^t$$2420/2000 = (11/10)^t$or $(11/10)^t = 121/100$or, $(11/10)^t = (11/10)^2$t = 2 years
Question 42. A certain sum, invested at 4% per annum compound interest, compounded half yearly, amounts to Rs.7,803 at the end of one year. The sum is
  1.    Rs.7,700
  2.    Rs.7,000
  3.    Rs.7,500
  4.    Rs.7,200
 Discuss Question
Answer: Option C. -> Rs.7,500
Answer: (c)Using Rule 1,Let the sum be P.As, the interest is compounded half-yearly,R = 2%, T = 2 half yearsA = P$(1 + R/100)^T$7803 = P$(1 + 2/100)2$7803 = $(1 + 1/50)^2$7803 = P$× 51/50 × 51/50$P = ${7803 × 50 × 50}/{51 × 51}$ = Rs.7500
Question 43. At what percent per annum will Rs.3000/- amounts to Rs.3993/- in 3 years if the interest is compounded annually?
  1.    13%
  2.    9%
  3.    11%
  4.    10%
 Discuss Question
Answer: Option D. -> 10%
Answer: (d)Using Rule 1,If A = Amount, P = Principal, r = Rate of Compound Interest (C.I.), n = no. of years then,A=P$(1 + r/100)^n$, C.I. = A - PC.I. = P$[(1 + r/100)^n - 1]$
Question 44. A certain sum of money yields Rs.1261 as compound interest for 3 years at 5% per annum. The sum is
  1.    Rs.8000
  2.    Rs.9000
  3.    Rs.7500
  4.    Rs.8400
 Discuss Question
Answer: Option A. -> Rs.8000
Answer: (a)Let the principal be Rs.x. Now,C.I. = P$[(1 + R/100)^T - 1]$1261 = $x[(1 + 5/100)^3 - 1]$1261 = $x(9261/8000 - 1)$1261 = $x({9261 - 8000}/8000)$= ${1261x}/8000$$x = {1261 × 8000}/1261$ = Rs.8000
Question 45. The principal, which will amount to Rs.270.40 in 2 years at the rate of 4% per annum compound interest, is
  1.    Rs.220
  2.    Rs.200
  3.    Rs.250
  4.    Rs.225
 Discuss Question
Answer: Option C. -> Rs.250
Answer: (c)Using Rule 1,Let the principal be Rs.P.270.40 = P $(1 + 4/100)^2$270.40 = P $(1 + 0.04)^2$P = ${270.40}/{1.04 × 1.04}$ = Rs.250
Question 46. A man saves Rs.2000 at the end of each year and invests the money at 5% compound interest. At the end of 3 years he will have :
  1.    Rs.2205
  2.    Rs.4305
  3.    Rs.4205
  4.    Rs.6305
 Discuss Question
Answer: Option D. -> Rs.6305
Answer: (d)Using Rule 1,Amount = $2000(1 + 5/100)^2 + 2000(1 + 5/100)$= 2000 × $(21/20)^2 + 2000(21/20)$= 2000 × $21/20 × 41/20$ = Rs.4305Required amount= 4305 + 2000 = Rs.6305
Question 47. In what time will Rs.10,000 amount to Rs.13310 at 20% per annum compounded half yearly?
  1.    3 years
  2.    1$1/2$ years
  3.    2$1/2$ years
  4.    2 years
 Discuss Question
Answer: Option B. -> 1$1/2$ years
Answer: (b)Using Rule 1,If A = Amount, P = Principal, r = Rate of Compound Interest (C.I.), n = no. of years then,A=P$(1 + r/100)^n$, C.I. = A - PC.I. = P$[(1 + r/100)^n - 1]$
Question 48. A loan of Rs.12,300 at 5% per annum compound interest, is to be repaid in two equal annual instalments at the end of every year. Find the amount of each instalment.
  1.    Rs.6,156
  2.    Rs.6,651
  3.    Rs.6,516
  4.    Rs.6,615
 Discuss Question
Answer: Option D. -> Rs.6,615
Answer: (d)Using Rule 9(i),Let each instalment be x.$x/(1 + 5/100) + x/(1 + 5/100)^2 = 12300$${20x}/21 + (20/21)^2x = 12300$${20x}/21(1 + 20/21)$ = 12300${20x}/21 × 41/21 × x = 12300$$x = {12300 × 21 × 21}/{20 × 41}$ ⇒ x = 6615
Question 49. A man buys a scooter on making a cash down payment of Rs.16224 and promises to pay two more yearly instalments of equivalent amount in next two years. If the rate of interest is 4% per annum, compounded yearly, the cash value of the scooter, is
  1.    Rs.50000
  2.    Rs.40000
  3.    Rs.46000
  4.    Rs.46824
 Discuss Question
Answer: Option D. -> Rs.46824
Answer: (d)Using Rule 1,If A = Amount, P = Principal, r = Rate of Compound Interest (C.I.), n = no. of years then,A=P$(1 + r/100)^n$, C.I. = A - PC.I. = P$[(1 + r/100)^n - 1]$
Question 50. Rs. 16,820 is divided between two brothers of age 27 years and 25 years. They invested their money at 5% per annum compound interest in such a way that both will receive equal money at the age of 40 years. The share (in Rs.) of elder brother is
  1.    8,000
  2.    8,280
  3.    8,820
  4.    8,410
 Discuss Question
Answer: Option C. -> 8,820
Answer: (c)Using Rule 1,Share of elder brother = Rs.x (let)Share of younger brother = Rs.(16820 - x)A = P$(1 + R/100)^T$According to the question,$x(1 + 5/100)^{13} = (16820 - x)(1 + 5/100)^{15}$$x = (16820 - x)(1 + 1/20)^2$$x = (16820 - x)(21/20)^2$$(20/21)^2x = 16820 - x$${400x}/441 + x$ = 16820${400x + 441x}/441$ = 16820841x = 16820 × 441$x = {16820 × 441}/841$ = Rs.8820

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