model 2 at ci sum becomes ‘n’ times after ‘t’ years 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) 10 years
(b) 15 years
(c) 18 years
(d) 12 years
The correct answers to the above question in:
Answer: (c)
Let the sum be x. Then,
$2x = x(1 + r/100)^6$
2 = $(1 + r/100)^6$
Cubing both sides,
8 =$((1 + r/100)^6)^3$
8 = $(1 + r/100)^18$
$8x = x(1 + r/100)^18$
The sum will be 8 times in 18 years.
i.e., Time = 18 years
Using Rule 5,
Here, m = 2, t = 6 years
It will becomes 8 times of itself
= $2^3$ times of it self
in t × n years = 6 × 3 = 18 years
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Read more ci becomes n times after t years Based Quantitative Aptitude Questions and Answers
Question : 1
If the amount is 2.25 times of the sum after 2 years at compound interest (compound annually), the rate of interest per annum is :
a) 50%
b) 25%
c) 45%
d) 30%
Answer »Answer: (a)
Suppose P = Rs.100
and amount A = Rs.225
A = P$(1 + r/100)^t$
or 225 = $100(1 + r/100)^2$
or $225/100 = [1 + r/100]^2$
or 1 + $r/100 = 15/10$
or ${100 + r}/100 = 15/10$
or 100 + r = 150
or r = 50%
Using Rule 8,If a sum becomes 'n' times of itself in 't' years on compound interest, then R% = $[n^{1/t} - 1] × 100%$
Here, n = 2.25, t = 2 years
R% = $(n{1/t} - 1) × 100%$
R% = $[(2.25)^{1/2} - 1]$ × 100%
= [1.5 - 1] × 100%
= 0.5 × 100% = 50%
Question : 2
A sum of Rs.12,000, deposited at compound interest becomes double after 5 years. How much will it be after 20 years ?
a) Rs.1,92,000
b) Rs.1,44,000
c) Rs.1,50,000
d) Rs.1,20,000
Answer »Answer: (a)
A = P$(1 + R/100)^T$
24000 = 12000$(1 + R/100)^5$
2 = $(1 + R/100)^5$
$2^4 = (1 + R/100)^20$
i.e. The sum amounts to Rs.192000 after 20 years.
Using Rule 11,A certain sum at C.I. becomes x times in $n_1$ year and y times in $n_2$ years then $x^{1/n_1} = y^{1/n_2}$
Here, x = 2, $n_1 = 5, y = ?, n_2$ = 20
$x^{1/n_1} = y^{1/n}$
$2^{1/5} = y^{1/20}$
$y = (2^{1/5})^20$
$y = 2^4 ⇒ y$ = 16 times
Sum = 16 × 12000 = Rs.1,92,000
Question : 3
A sum of money becomes double in 3 years at compound interest compounded annually. At the same rate, in how many years will it become four times of itself ?
a) 7.5 years
b) 4 years
c) 6.4 years
d) 6 years
Answer »Answer: (d)
A = P$(1 + R/100)^T$
Let P. Rs., A = Rs.2
2 = 1$(1 + R/100)^3$
On squaring both sides.
4 = 1$(1 + R/100)^6$
Time = 6 years
Using Rule 11,
Here, $x = 2, n_1 = 3, y = 4, n_2$ = ?
$x^{1/n_1} = y^{1/n_2}$
$2^{1/3} = 4^{1/n_2}$
$2^{1/3} = (2^2)^{1/n_2}$
$2^{1/3} = 2^{2/n_2}$
$1/3 = 2/n_2$
$n_2$ = 6 Years
Question : 4
If a sum of money compounded annually becomes 1.44 times of itself in 2 years, then the rate of interest per annum is
a) 20%
b) 25%
c) 21%
d) 22%
Answer »Answer: (a)
A = P$(1 + R/100)^T$
1.44P = P$(1 + R/100)^2$
$(1.2)^2 = (1 + R/100)^2$
$1 + R/100$ = 1.2
R = 0.2 × 100 = 20%
Using Rule 8,
Here, n = 1.44, t = 2 years
R% = $(n^{1/6} - 1) × 100%$
= $[(1.44)^{1/2} - 1] × 100%$
= [(1.2) - 1] × 100%
= 0.2 × 100% ⇒ R% = 20%
Question : 5
A sum of money placed at compound interest doubles itself in 4 years. In how many years will it amount to four times itself ?
a) 16 years
b) 12 years
c) 8 years
d) 13 years
Answer »Answer: (c)
A = P$(1 + R/100)^T$
Let P be Rs.1, then A = Rs.2
2 = 1$(1 + R/100)^4$
$2^2 = (1 + R/100)^8$
Time = 8 years
Using Rule 11,
Here, $x = 2, n_1 = 4, y = 4, n_2$ = ?
Using $x^{1/n_1} = y^{1/n_2}$
$(2)^{1/4} = (4)^{1/n_2}$
$(2)^{1/4} = (2^2)^{1/n_2}$
$2^{1/4} = 2^{1/n_2}$
$1/4 = 2/n_2$
$n_2$ = 8 years
Question : 6
A sum of money placed at compound interest doubles itself in 5 years. In how many years, it would amount to eight times of itself at the same rate of interest ?
a) 20 years
b) 10 years
c) 7 years
d) 15 years
Answer »Answer: (d)
Let the Principal be P and rate of interest be r%.
2 P = P$(1 + r/100)^2$
2 = $(1 + r/100)^5$ ...(i)
On cubing both sides,
8 = $(1 + r/100)^15$
Time = 15 years
Using Rule 5,
Here, m = 2, t = 5 years
It becomes 8 times = $2^3$ times
in t × n = 5 × 3 = 15 years
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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