Compound Interest(Quantitative Aptitude > Interest ) Questions and answers for exam Preparation

Quantitative Aptitude > Interest

COMPOUND INTEREST MCQs

Total Questions : 262 | Page 4 of 27 pages

Question 31. At a certain rate per annum, the simple interest on a sum of money for one year is Rs.260 and the compound interest on the same sum for two years is Rs.540.80. The rate of interest per annum is

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Answer: Option C. -> 8%
Answer: (c)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 32. If the compound interest on a certain sum for 2 years at 4% p.a. is Rs.102, the simple interest at the same rate of interest for two years would be

Rs.100
Rs.200
Rs.150
Rs.50

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Answer: Option A. -> Rs.100
Answer: (a)If the sum be P, thenC.I. = P$[(1 + R/100)^T - 1]$102 = $[(1 + 4/100)^2 - 1]$102 = P$[(26/25)^2 - 1]$102 = P$(676/625 - 1)$102 = P$({676 - 625}/625)$102 = P × $51/625$P = ${102 × 625}/51$ = Rs.1250S.I. = ${1250 × 2 × 4}/100$ = Rs.100

Question 33. A sum becomes Rs.2,916 in 2 years at 8% per annum compound interest. The simple interest at 9% per annum for 3 years on the same amount will be

Rs.625
Rs.600
Rs.650
Rs.675

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Answer: Option D. -> Rs.675
Answer: (d)Using Rule 1,A = P$(1 + R/100)^T$2916 = $x(1 + 8/100)^2$2916 = $x(27/25)^2$$x = {2916 × 25 × 25}/{27 × 27}$ = Rs.2500S.I. = ${P × R × T}/100$= ${2500 × 9 × 3}/100$ = Rs.675

Question 34. If the compound interest on a sum for 2 years at 12$1/2$% per annum is Rs.510, the simple interest on the same sum at the same rate for the same period of time is :

Rs.460
Rs.400
Rs.450
Rs.480

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Answer: Option D. -> Rs.480
Answer: (d)C.I. = P$[(1 + R/100)^T - 1]$510 = P$[(1 + 25/200)^2 - 1]$510 = P$(81/64 - 1)$P = ${510 × 64}/17$ = 1920S.I. = ${1920 × 2 × 25}/{100 × 2}$ = Rs.480Using Rule 10,Here, C.I. = Rs.510, R = 12$1/2$%, S.I. = ?C.I. = S.I.$(1 + R/200)$$510 = S.I.(1 + 25/400)$S.I. = ${510 × 400}/425$ = Rs.480

Question 35. If the compound interest on a sum for 2 years at 12$1/2$ p.a is Rs.510, the simple interest on the same sum at the same rate for the same period of time is

Rs.480
Rs.400
Rs.460
Rs.450

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Answer: Option A. -> Rs.480
Answer: (a)Principal = Rs.P (let)C.I. = P$[(1 + R/100)^T - 1]$510 = P$[(1 + 25/200)^2 - 1]$510 = P$[(1 + 1/8)^2 - 1]$510 = P$[(9/8)^2 - 1]$510 = P$(81/64 - 1)$510 = P$({81 - 64}/64)$510 = ${17P}/64$P = ${510 × 64}/17$ = Rs.1920S.I. = $\text"Principal × Time × Rate"/100$= ${1920 × 2 × 25}/{100 × 2}$ = Rs.480Using Rule 10,Here, C.I. = Rs.510, R = 12$1/2$%, S.I. = ?C.I. = S.I.$(1 + R/200)$510 = S.I.$(1 + 25/400)$510 = S.I.$(425/400)$S.I. = ${510 × 400}/425$ = Rs.480

Question 36. The compound interest on a certain sum of money at 5% per annum for 2 years is Rs.246. The simple interest on the same sum for 3 years at 6% per annum is

Rs.432
Rs.435
Rs.430
Rs.450

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Answer: Option A. -> Rs.432
Answer: (a)Using Rule 1,C.I. = P$[(1 + R/100)^T - 1]$246 = P$[(1 + 5/100)^2 - 1]$246 = P$[(21/20)^2 - 1]$246 = P$({441 - 400}/400)$246 = ${41P}/400$P = ${246 × 400}/41$ = Rs.2400SI = $\text"Principal × Time × Rate"/100$= ${2400 × 3 × 6}/100$ = Rs.432

Question 37. 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

Rs.400
Rs.350
Rs.380
Rs.375

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Answer: Option A. -> Rs.400
Answer: (a)If the principal be P thenC.I. = P$[(1 + R/100)^T - 1]$420 = P$[(1 + 10/100)^2 - 1]$420 = P$({121 - 100}/100)$420 = ${P × 21}/100$P = ${420 × 100}/21$ = Rs.2000S.I. = ${PRT}/100 = {2000 × 10 × 2}/100$ = Rs.400Using Rule 10,Here, C.I. = Rs.420, R = 10%, S.I. = ?C.I. = S.I.$(1 + R/200)$420 = S.I.$(1 + 10/200)$420 = S.I.$(210/200)$S.I. = ${420 × 200}/210$ = Rs.400

Question 38. The compound interest on Rs.10,000 in 2 years at 4% per annum, the interest being compounded half-yearly, is :

Rs.828. 82
Rs.636.80
Rs.912. 86
Rs.824.32

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Answer: Option D. -> Rs.824.32
Answer: (d)Using Rule 1,A = 10,000$(1 + 2/100)^4$=10,000$(51/50)^4$ =10824.3216Interest = 10,824.3216 - 10,000= Rs.824.32

Question 39. A man borrows Rs.21000 at 10% compound interest. How much he has to pay annually at the end of each year, to settle his loan in two years ?

Rs.12300
Rs.12000
Rs.12200
Rs.12100

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Answer: Option D. -> Rs.12100
Answer: (d)If each instalment be x, then Present worth of first instalment= $x/{1 + 10/100} = {10x}/11$= Present worth of second instalment= $x/(1 + 10/100)^2 = 100/121x$$10/11x + 100/121x$ = 21000${110x + 100x}/121 = 21000$210x = 21000 × 121$x = {21000 × 121}/210$ = Rs.12100 Using Rule 9,If a sum 'P' is borrowed at r% annual compound interest which is to be paid in 'n' equal annual installments including interest, then(i) For n = 2, Each annual installment= $p/{(100/{100 + r}) + (100/{100 + r})^2$(ii) For n = 3, Each annual installment= $p/{(100/{100 + r}) + (100/{100 + r})^2 + (100/{100 + r})^3$

Question 40. At what rate per cent per annum will Rs.2304 amount to Rs.2500 in 2 years at compound interest ?

4$1/3$%
4$1/2$%
4$1/6$%
4$1/5$%

Discuss Question

Answer: Option C. -> 4$1/6$%
Answer: (c)Using Rule 1,Let the rate per cent per annum be r. Then,2500 = 2304$(1 + r/100)^2$$(1 + r/100)^2 = 2500/2304 = (50/48)^2$$1 + r/100 = 50/48 = 25/24$$r/100 = 25/24 - 1 = 1/24$r = $100/24 = 25/6 = 4{1}/6$%