model 2 at ci sum becomes ‘n’ times after ‘t’ years 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 : 11 [SSC CGL Tier-I 2010]
A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in
a) 60 years
b) 45 years
c) 54 years
d) 48 years
Answer »Answer: (b)
A = P$(1 + R/100)^T$
2 = 1$(1 + R/100)^15$
Cubing on both sides, we have
8 = 1$(1 + R/100)^45$
Required time = 45 years
Using Rule 5,
Here, m = 2, t = 15 years
It becomes 8 times = $2^3$ times
in t × n years= 15 × 3 = 45 years
Question : 12 [SSC MTS 2013]
A sum of money becomes 1.331 times in 3 years as compound interest. The rate of interest is
a) 50%
b) 8%
c) 10%
d) 7.5%
Answer »Answer: (c)
If principal = Rs.1000, amount = Rs.1331
A = P$(1 + R/100)^T$
$1331/1000 = (1 + R/100)^3$
$(11/10)^3 = (1 + R/100)^3$
$1 + R/100 = 11/10$
$R/100 = 1/10$
R = $1/10 × 100$ = 10%
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 = 1.331, t = 3 years
R% = $(n^{1/t} - 1) × 100%$
= $[(1.331)^{1/3} - 1] × 100%$
= [1.1 - 1] × 100%
= 0.1 × 100% ⇒ R% = 10%
Question : 13 [SSC CGL Tier-II 2012]
A sum of money at compound interest amounts to thrice itself in 3 years. In how many years will it be 9 times itself ?
a) 3 years
b) 9 years
c) 6 years
d) 27 years
Answer »Answer: (c)
A = P$(1 + R/100)^T$
Let P = Rs.1, then A = Rs.3
3 = 1$(1 + R/100)^3$
On squaring both sides,
9 = 1$(1 + R/100)^6$
Time = 6 years
Using Rule 11,
Here, $x = 3, n_1 = 3, y = 9, n_2$ = ?
Using, $x^{1/n_1} = y^{1/n_2}$
$(3)^{1/3} = (9)^{1/n_2}$
$3^{1/3} = (3^2)^{1/n_2}$
$3^{1/3} = 3^{2/n_2}$
$1/3 = 2/n_2 ⇒ n_2$ = 6 years
Question : 14 [SSC CHSL 2013]
If the amount is 3$3/8$ times the sum after 3 years at compound interest compounded annually, then the rate of interest per annum is
a) 33$1/3$%
b) 25%
c) 16$2/3$%
d) 50%
Answer »Answer: (d)
A = P$(1 + R/100)^T$
$27/8x = x(1 + R/100)^3$
$(3/2)^3 = (1 + R/100)^3$
$1 + R/100 = 3/2$
$R/100 = 3/2 - 1 = 1/2$
R = $1/2$ × 100 ⇒ R = 50%
Using Rule 8,
n= $27/8$, t = 3 years
R% = $(n^{1/t} - 1) × 100%$
= $((27/8)^{1/3} - 1) × 100%$
= $[(3/2) - 1]$ × 100% ⇒ R% = 50%
Question : 15 [SSC Investigator 2010]
At what rate percent per annum of compound interest, will a sum of money become four times of itself in two years ?
a) 20%
b) 100%
c) 50%
d) 75%
Answer »Answer: (b)
A = P$(1 + R/100)^T$
4 = $(1 + R/100)^2$
1 + $R/100$ = 2
$R/100$ = 1 ⇒ R = 100%
Using Rule 8,
Here, n = 4, t = 2 years
R% = $(n^{1/t} - 1)$ × 100%
= $((4)^{1/2} - 1)$ × 100% = 100%
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model 2 at ci sum becomes ‘n’ times after ‘t’ years Shortcuts »
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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 …
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