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Simple Interest and Compound Interest Questions and Answer Quiz 5 for SBI Clerk, NRA CET, IBPS RRB Clerk and RBI Assistant Exams with Detailed Solution

Directions: Kindly read the questions carefully and answer the questions given below.
1
What would be the compound interest obtained on an amount of Rs. 4,800 at the rate of 5 p.c.p.a after 3 years?
» Explain it
B
P = 4800, T = 3 years, R = 5%

By the net% effect we would calculate the effective compound rate of interest for 3 years = 15.76% (Refer to sub-details)

Therefore, CI = 15.76% of 4800

CI =  15.76 × 4800  = ₹ 756.5
100
_________________________________________________________________

Sub-details:

Calculation of effective compound rate of interest for 3 years will be as follows.

For the first 2 years, let's apply the net% effect.

Here, x = y = 5%


Net% effect = x + y =  xy  
100

= 5 + 5 +  5 × 5  = 10 + 0.25 = 10.25%
100

Now let's take this 10.25% as x and 5% as y for the calculation of 3rd year.

= 10.25 + 5 +  10.25 × 5  = 15.25 + .51 = 15.76%
100

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Traditional Method:

CI = 4800 [( 1 +  5 ) 3  – 1 ]
100  

= 4800 [ 21 × 21 × 21 – 20 × 20 × 20 ]
20 × 20 × 20

= 4800 ×  ( 9261 – 8000 )   ⇒  4800 ×  1261  = ₹ 756.6.
20 × 20 × 20 8000

Hence, option B is correct.

2
The difference between compound interest and simple interest at the same rate of interest R percent per annum on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the value of R?
» Explain it
A
Smart Approach:

To solve this question, we can apply a short trick approach

Sum =   Difference × 1002
r2

Given,

Sum (Amount) = 15000,  Difference = 96,  r = ?

By the short trick approach, we get

15000 =  96 × 1002   ⇒ r2 =  96 × 1002   ⇒ r2 = 64   ⇒   r = 8%
r2 15000

Traditional Approach:

As per the information, we get the eqn.

CI for 2 years – SI for 2 years = 96

[ 15000 ×  ( 1 +  R ) 2  – 15000 ]  –  ( 15000 × R × 2 ) = 96
100   100

⇒ 15000 [( 1 +  R ) 2  – 1 –  2R ]  = 96
100   100

⇒ 15000 [ (100 + R2) – 10000 – 200 R ] = 96
10000

⇒  R2 =  96 × 2  = 64  ⇒  R = 8.
3

   Rate = 8%

Hence, option A is correct.

3
There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest on Rs. 12000 after 3 years at the same rate of interest?
» Explain it
C
Since increase in interest in 6 years = 60%

Therefore, increase in interest in 1 year = 10% (Rate of interest)

Now, P = 12000, T = 3 years & R = 10% p.a.

By the net% effect we would calculate the effective compound rate of interest for 3 years = 33.1% (Refer to sub-details)

Therefore, CI = 33.1% of 12000

CI =  33.1 × 12000  = ₹ 3972.
100
_________________________________________________________________

Sub-details:

Calculation of effective compound rate of interest for 3 years will be as follows.

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 3rd year.

= 21 + 10 +  21 × 10  = 33.1%
100

Hence, option C is correct.

4
An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest at the rate of 10%, the effective rate interest becomes 
» Explain it
A
Yearly rate of interest  = 10%

Rate of interest charged on half yearly basis = 5%

It's given that the financier charges interest on half yearly basis. Hence, he actually charges Compound Interst and not Simple Interest.

Therefore, applying the net% effect formula for effective rate of compound interest for 2 half years (1 year = 2 half years), we get

Net% effect = x + y +  xy  
100

x = y = 5%

Net% effect = 5 + 5 +  5 × 5  = 10 + 0.25 = 10.25%
100

Hence, option A is correct.

5
The certain sum will amount to Rs 12,100 in 2 years at 10% per annum of compound interest, interest being compounded annually. The sum is
» Explain it
A
To solve this question, we can apply a net% effect formula

Net% effect = x + y +  xy %
100

x = y = 10%

= 10 + 10 +  10 × 10  = 21%
100


Now, Amount (P + CI)  = (100 + 21)% = 121%   ≡    ₹ 12100

 ∴  Principal  = 100%   ≡    ₹ x

By the cross multiplication, we get

x =  12100 × 100  = ₹ 10000.
121

__________________________________________________________

Traditional Method:

Given,

Amount = 12,100;   r = 10%,   t = 2 yrs

Amount =  P [ 1 +  r ] t
100  

12100 =  P [ 1 +  10 ] 2
100  

⇒  12100 =  P [ 11 ] 2   ⇒  12100 = P ×  11  ×  11
10   10 10

⇒   P = ₹ 10,000.

Hence, option A is correct.