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Compound Interest Questions and Answer Quiz 8 for IBPS PO, SBI Clerk Mains, IBPS RRB PO, IBPS RRB Clerk, CET and RBI Assistant Mains Exams with Detailed Solution

Directions: Read the following questions carefully and answer them:
1
₹ 6100 was partly invested in Scheme A at 10% pa compound interest (compounded annually) for 2 years and partly in Scheme B at 10% pa simple interest for 4 years. Both the schemes earn equal interests. How much was invested in Scheme A ?
» Explain it
C
Let the amount invested in Scheme A is ₹ x.

Then, the amount invested in Scheme B be ₹ (6100 – x)

Now, according to the question,

x ( 1 +  10 ) 2  – x  =  (6100 – x) × 10 × 4
100   100

⇒  x ( 121  – 1 )  =  (6100 – x) × 40
100 100

⇒   21x  =  (6100 – x) × 40
100 100

⇒  21x = 6100 × 40 – 40x

⇒  61x = 6100 × 40

⇒  x =  6100 × 40   =  ₹ 4000
61

∴  The amount invested in Scheme A is ₹ 4000.

Hence, option C is correct.

2
A sum of ₹ 198 deposited at CI doubles itself after 4 years. After 20 years it will become
» Explain it
A
P ( 1 +  R ) 4  = 2P
100  

⇒   ( 1 +  R ) 4  = 2     ...(i)
100  

After 20 years,

( 1 +  R ) 20  =  [ ( 1 +  R ) 4 ] 5  = 25 = 32
100   100    

Thus, the amount becomes 32 times.

So, amount = 198 × 32  =  ₹ 6336

Hence, option A is correct.

3
Lata had ₹ 40000. She invested some amount in scheme A at CI at 15% and the remaining amount in scheme B at SI at 10%. If she got the same interest from both the investments at the end of one year. How much in ₹ did she invest in scheme B?
» Explain it
B
Let the amount invested in Scheme A is ₹ x.
 
Then, the amount invested in Scheme B therefore will be ₹ (40000 – x)
 
We know that for the 1st year both Simple Interest and Compound Interest on a sum remains the same. Now, according to the question, 
 
⇒ 15% of x = 10% of (40000 – x) 
 
⇒ 15x = 400000 – 10x 
 
⇒ 25x = 400000
 
⇒ x = 16000 
 
  Amount invested in scheme B = 40000 – 16000 = 24000.

Hence, option B is correct.
 
4
An amount of ₹ 110000 is invested at compound interest payable annually. If the rate of interest is 11% pa, what will be the total interest after two years ?
» Explain it
B
Method I :

P = ₹ 110000; R = 11%; n = 2 years

CI = P ( 1 +  R ) n  – P
100  

CI = 110000 ( 1 +  11 ) 2  – 110000
100  

= 110000 ( 111 ) 2  – 110000
100  

= 135531 – 110000  =  ₹ 25531

_________________________________________


Method II :

To solve this question, we can apply the net% effect formula

Net% effect =  ( x + y +  xy ) %
100

Here, x = y = 11%         (because rate of interest is same for both the years)

By the net% effect, we get effective rate of interest

( 11 + 11 +  11 × 11 ) % = 23.21%  
100

Therefore,  23.21% of 110000  =  ₹ 25531

Hence, option B is correct.

5
Find the compound interest on ₹ 12000 for 2 years, the rate of interest being 3% per annum.
» Explain it
D
Method I :

P = ₹ 12000; R = 3%; n = 2 years

CI =  P ( 1 +  R ) n  – P
100  

CI = 12000 ( 1 +  3 ) 2  – 12000
100  

= 12000 ×  103  ×  103  – 12000
100 100

= 12730.8 – 12000  =  ₹ 730.8

_____________________________________________


Method II :

To solve this question, we can apply the net% effect formula

Net% effect =  ( x + y +  xy ) %
100

Here, x = y = 3%            (because rate of interest is same for both the years)

By the net% effect, we get effective rate of interest

( 3 + 3 +  3 × 3 ) % = 6.09%  
100

Therefore, 6.09% of 110000  =  ₹ 730.8

Hence, option D is correct.