model 5 ci with instalments Practice Questions Answers Test with Solutions & More Shortcuts
compound interest PRACTICE TEST [6 - EXERCISES]
model 1 basic compound interest using formula
model 2 at ci sum becomes ‘n’ times after ‘t’ years
model 3 combination of si & ci
model 4 difference in ci & si
model 5 ci with instalments
model 6 comparing sum in different years
Question : 1 [SSC CGL Prelim 2000]
A builder borrows Rs.2550 to be paid back with compound interest at the rate of 4% per annum by the end of 2 years in two equal yearly instalments. How much will each instalment be ?
a) Rs.1283
b) Rs.1352
c) Rs.1275
d) Rs.1377
Answer »Answer: (b)
A = Rs.2550
R = 4% per annum
n = 2 years
Let each of the two equal instalments be x
Present worth = $\text"Instalment"/(1 + r/100)^n$
$P_1 = x/(1 + 4/100)^1 = x/{1 + 1/25} = x/{26/25}$
or $P_1 = 25/26x$
Similarly,
$P_2 = (25/26)^2x = 625/676x$
$P_1 + P_2$ = A
$25/26x + 625/676x$ = 2550
${(650 + 625)x}/676 = 2550$
$1275/676x = 2550$
x = 2550 $× 676/1275$ ⇒ x = Rs.1352
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= $p/{(100/{100 + r}) + (100/{100 + r})^2 + (100/{100 + r})^3$
Here, P = Rs.2550, n = 2, r = 4%
Each instalment
= $p/{(100/{100 + r}) + (100/{100 + r})^2$
= $2550/{(100/{100 + 4}) + (100/{100 + 4})^2$
= $2550/{100/104 + (100/104)^2}$
= $2550/{100/104(1 + 100/104)}$
= $2550/{100/104 (204/104)}$
= ${2550 × 104 × 104}/20400 $= Rs.1352
Question : 2 [SSC CGL Prelim 2008]
Kamal took Rs.6800 as a loan which along with interest is to be repaid in two equal annual instalments. If the rate of interest is 12$1/2$%, compounded annually, then the value of each instalment is
a) Rs.4000
b) Rs.8100
c) Rs.4050
d) Rs.4150
Answer »Answer: (c)
Let the annual instalment be x
A = P$(1 + R/T)^T$
$x = P_1(1 + 25/200)$
$x = P_1 × 9/8$
$P_1 = 8/9x$
Similarly, $P_2 = 64/81x$
$P_1 + P_2$ = 6800
$8/9x + 64/81x$ = 6800
${72x + 64x}/81 = 6800$
${136x}/81 = 6800$
$x = {6800 × 81}/136$ = Rs.4050
Using Rule 9(i),
Here, P = Rs.6800, R = $25/2$%, n = 2
Each instalment
= $p/{(100/{100 + r}) + (100/{100 + r})^2$
= $6800/{(100/{100 +{25/2}}) + (100/{100 + {25/2}})^2$
= $6800/{200/225 + (200/225)^2}$
= $6800/{200/225(1 + {200/225})}$
= ${6800 × 225 × 225}/{200 × 425}$ = Rs.4050
Question : 3 [SSC CHSL 2014]
A sum of Rs.210 was taken as a loan. This is to be paid back in two equal instalments. If the rate of interest be 10% compounded annually, then the value of each instalment is
a) Rs.225
b) Rs.127
c) Rs.210
d) Rs.121
Answer »Answer: (d)
Using Rule 9(i),
Let the value of each instalment be Rs.x
Principal = Present worth of Rs.x due 1 year hence, present worth of Rs. x due 2 years hence
210 = $x/(1 + R/100) + x/(1 + R/100)^2$
210 = $x/(1 + 10/100) + x/(1 + 10/100)^2$
210 = $x/{1 + 1/10} + x/(1 + 1/10)^2$
210 = $x/{11/10} + x/(11/10)^2$
210 = ${10x}/11 + {100x}/121$
210 = ${110x + 100x}/121$
210 × 121 = 210 x
$x = {210 × 121}/210$ = Rs.121
Question : 4 [SSC CHSL 2015]
Mr. Dutta desired to deposit his retirement benefit of Rs. 3 lakhs partly to a post office and partly to a bank at 10% and 6% interests respectively. If his monthly interest income was Rs. 2000, then the difference of his deposits in the post office and in the bank was :
a) Rs.1,00,000
b) Rs.50,000
c) Nil
d) Rs.40,000
Answer »Answer: (c)
Using Rule 1,
Let the amount deposited in Post Office be Rs.x lakhs.
Amount deposited in bank = Rs.(3 - x) lakhs
According to the question,
${x × 10 × 1}/{100 × 12} + {(3 - x) × 6 × 1}/{100 × 12}$
= $2000/100000 = 1/50$
10x + 18 - 6x
= $1/50$ × 1200 = 24
4x = 24 - 18 = 6
x = $6/4$ = Rs.$3/2$ lakhs
∴ Required difference = 0
Question : 5 [SSC CHSL 2015]
The income of a company increases 20% per year. If the income is Rs. 26,64,000 in the year 2012, then its income in the year 2010 was :
a) Rs.21,20,000
b) Rs.28,55,000
c) Rs.28,20,000
d) Rs.18,50,000
Answer »Answer: (d)
Using Rule 1,
Let the income of company in 2010 be Rs.P
According to the question,
A = P$(1 + R/100)^T$
2664000 = P$(1 + 20/100)^2$
2664000 = P$(1 + 1/5)^2$
2664000 = P × $(6/5)^2$
P = ${2664000 × 5 × 5}/{6 × 6}$ = Rs.1850000
IMPORTANT quantitative aptitude EXERCISES
-
500+ Basic Compound Interest MCQs Aptitude Practice Test »
-
Top 499+ Compound Interest MCQs For BANK SSC UPSC Railway »
-
New 455+ Compound Interest Problems Solution for BANK SSC »
-
Top 399+ Compound Interest Questions for UPSC TNPSC Exams »
-
Top 599+ Compound Interest Practice MCQs For SBI IBPS RBI »
-
Top 489+ Compound Interest Practice Sums For All SSC Exam »
model 5 ci with instalments Shortcuts »
Click to Read...model 5 ci with instalments Online Quiz
Click to Start..compound interest Shortcuts and Techniques with Examples
-
model 1 basic compound interest using formula
Defination & Shortcuts … -
model 2 at ci sum becomes ‘n’ times after ‘t’ years
Defination & Shortcuts … -
model 3 combination of si & ci
Defination & Shortcuts … -
model 4 difference in ci & si
Defination & Shortcuts … -
model 5 ci with instalments
Defination & Shortcuts … -
model 6 comparing sum in different years
Defination & Shortcuts …
quantitative aptitude CATEGORIES
RECENT BLOGS
Recently Added Subject & Categories For All Competitive Exams
New 100+ Compound Interest MCQ with Answers PDF for IBPS
Compound Interest verbal ability questions and answers solutions with PDF for IBPS RRB PO. Aptitude Objective MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Mixture and Alligation MCQ Questions PDF for IBPS
Most importantly Mixture and Alligation multiple choice questions and answers with PDF for IBPS RRB PO. Aptitude MCQ Practice Exercises all Bank Exams
Continue Reading »
IBPS Profit and Loss Questions Solved Problems with PDF
Most important Profit and Loss multiple choice questions and answers with PDF for IBPS RRB PO. 100+ Aptitude MCQ Practice Exercises all competitive exams
Continue Reading »
100+ Average Aptitude Questions Answers solutions MCQ PDF
New Average multiple choice questions and answers with PDF for IBPS RRB PO. 100+ Quantitative Aptitude MCQ Practice Exercises all competitive exams
Continue Reading »