
1.

If a sum of money compounded annually becomes 1.44 times of itself in 2 years, then the rate of interest per annum is

Answer: Option
D
Explanation:
P 
( 
1 + 
R 
) 
^{2} 
= 1.44P 
100 

⇒ 
( 
1 + 
R 
) 
^{2} 
= 1.44 = (1.2)^{2} 
100 

⇒ R = 0.2 × 100 = 20%


2.

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.

9 years

B.

27 years

C.

6 years

D.

3 years

Answer: Option
C
Explanation:
Let the sum be ₹ P.
∴ P 
( 
1 + 
R 
) 
^{3} 
= 3P 
100 

⇒ 
( 
1 + 
R 
) 
^{3} 
= 3 ...(i) 
100 

Let, P 
( 
1 + 
R 
) 
^{n} 
= 9P 
100 

⇒ 
( 
1 + 
R 
) 
^{n} 
= 9 = (3)^{2} = 
[( 
1 + 
R 
) 
^{3} 
] 
^{2} 
[using (i)] 
100 

100 


⇒ 
( 
1 + 
R 
) 
^{n} 
= 
( 
1 + 
R 
) 
^{6} 
100 

100 

∴ n = 6 years


3.

If the compound interest on a sum for 2 years at 12 
1 
% p.a. is ₹ 510, the simple interest on the same sum at the same rate 
2 
for the same period of time is

Answer: Option
D
Explanation:
CI = P 
( 
1 + 
R 
) 
^{n} 
– P 
100 

⇒ 510 = P 
( 
1 + 
25/2 
) 
^{2} 
– P 
100 

⇒ 510 = P 
( 
1 + 
25 
) 
^{2} 
– P 
200 

⇒ 510 = P 
( 
9 
) 
^{2} 
– P 
8 

⇒ 510 = 
81P 
– P = 
17P 
64 
64 
⇒ P = 
510 × 64 
= ₹ 1920 
17 
= 
1920 × 25/2 × 2 
= ₹ 480 
100 


4.

The compound interest on a certain sum of money for 2 years at 5% is ₹ 328, then the sum is

Answer: Option
C
Explanation:
Method I :
CI = ₹ 328; R = 5%; n = 2 years; P = ?
CI = P 
( 
1 + 
R 
) 
^{n} 
– P 
100 

⇒ 328 = P 
( 
1 + 
5 
) 
^{2} 
– P 
100 

⇒ 328 = P 
( 
21 
) 
^{2} 
– P 
20 

⇒ 328 = 
441P 
– P = 
41P 
400 
400 
⇒ P = 
328 × 400 
= ₹ 3200 
41 
__________________________________________
Method II :
To solve this question, we can apply the net% effect formula.
Net% effect = 
( 
x + y + 
xy 
) 
% 
100 
Here, x = y = 5% (because, rate of interest is same for both the years)
= 
( 
5 + 5 + 
5 × 5 
) 
% = 10.25% 
100 
Let the sum be ₹ x.
Therefore, CI = 10.25% of x
⇒ 328 = 10.25% of x
⇒ x = 
328 × 100 
= ₹ 3200 
10.25 


5.

The compound interest on ₹ 5,000 for 3 years at 10% p.a. will amount to

A.

₹ 1,654

B.

₹ 1,655

C.

₹ 1,600

D.

₹ 1,565

Answer: Option
B
Explanation:
Method I :
P = ₹ 5,000; R = 10%; n = 3 years
CI = P 
( 
1 + 
R 
) 
^{n} 
– P 
100 

= 5000 
( 
1 + 
10 
) 
^{3} 
– 5000 
100 

= 5000 
( 
11 
) 
^{3} 
– 5000 
10 

= 6655 – 5000 = ₹ 1,655
__________________________________________
Method II :
For the first two years, let's apply the net% effect.
Here, x = y = 10%
Net% effect = 
( 
x + y + 
xy 
) 
% 
100 
= 
( 
10 + 10 + 
10 × 10 
) 
% = 21% 
100 
Now, let's take this 21% as x and 10% as y for the calculation of third year.
= 
( 
21 + 10 + 
21 × 10 
) 
% = 33.1% 
100 
Therefore, CI = 33.1% of 5000
CI = 
33.1 
× 5000 = ₹ 1,655 
100 

