model 5 ci with instalments Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on compound interest topic of quantitative aptitude
(a) Rs.32,400
(b) Rs.32,800
(c) Rs.32,000
(d) Rs.32,200
The correct answers to the above question in:
Answer: (b)
Using Rule 9(i),
Sum borrowed = Present worth of Rs.17640 due 1 year hence + Present worth of Rs.17640 due 2 years hence
= Rs.$(17640/{(1 + 5/100)} + 17640/{(1 + 5/100)^2})$
= Rs.$(17640 × 20/21 + 17640 × 20/21 × 20/21)$
= Rs.(16800 + 16000) = Rs.32800
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Read more ci with instalments Based Quantitative Aptitude Questions and Answers
Question : 1
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
a) 8,000
b) 8,280
c) 8,820
d) 8,410
Answer »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
${400x + 441x}/441$ = 16820
841x = 16820 × 441
$x = {16820 × 441}/841$ = Rs.8820
Question : 2
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
Question : 3
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
a) Rs.50000
b) Rs.40000
c) Rs.46000
d) Rs.46824
Answer »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$[(1 + r/100)^n - 1]$
Let principal (present worth) for first year be $P_1$ and that for two years be $P_2$.
16224 = $P_1(1 + 4/100)$
16224 = $P_1(1 + 1/25) = {26P_1}/25$
$P_1 = {16224 × 25}/26$ = Rs.15600
Again,
$16224 = P_2(1 + 4/100)^2$
16224 = $P_2(26/25)^2 = {676P_2}/625$
$P_2 = {16224 × 625}/676$ = 15000
Cash value of the scooter
= Rs.(16224 + 15600 + 15000) = Rs.46824
Question : 4
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.
a) Rs.6,156
b) Rs.6,651
c) Rs.6,516
d) Rs.6,615
Answer »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 : 5
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
compound interest Shortcuts and Techniques with Examples
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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 …
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