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Direction : Study the following questions carefully and choose the right answer.
1
Shantanu borrowed Rs. 2.5 lakh from a bank to purchase one car. If the rate of interest be 6% per annum compounded annually, what payment he will have to make after 2 years 6 months?
» Explain it
D
CI for 2 years 6 months at the rate of 6, applying the net% effect for first 2 years

= 6 + 6 +  6 × 6  = 12.36%
100

Rate of interest for 6 months =  6  × 6 = 3%
12

For next 6 months = 12.36 + 3 +  12.36 × 3  = 15.36 + 0.37%  = 15.73%
100

Here, we can see that in 2 years 6 months the given compound rate of interest is approximate 15.73%.

Now, 115.73% of 250000 =  115.73 × 250000  = 289,325. 
100

Hence, option D is correct.
2
A certain amount of money is lent out at compound interest at the rate of 20% per annum for two years, compounded annually. It would give Rs. 482 more if the amount is compounded half yearly. Find the principle.
» Explain it
E
Approach I:  To solve this question, we can apply the net % effect formula

x + y +  xy %
100
Compounded annually at rate 20% per annum for 2 years, we get
= 20 + 20 +  20 × 20  = 44%
100

Similarly, compounded half yearly at rate 10%, we get
= 10 + 10 +  10 × 10  = 21%
100

And, 21 + 10 +  21 × 10  = 33.1%
100

And, 33.1 + 10 +  33.1 × 10  = 46.41%
100

Now as per the question,

Difference between compound interest yearly and half yearly = 46.41 – 44 = 2.41%

Given, 2.41% ≡ 482
100% ≡ x
⇒ x =  482 × 100  = 20,000
2.41

Approach II:

When compounded annually, the amount received at the end of the period is

A = P [ 1 +  r ] n
100  

When compounded half yearly, the amount received at the end of the period is
A = P [ 1 +  r/2 ] 2n
100  

Let the principle be P.

Interest on this amount when compounded annually at the rate of 20% per annum = P [(1.20)2 − 1]
Interest on this amount when compounded half yearly = P [(1.10)4 − 1]

The difference between the two is Rs. 482

∴   P [(1.10)4 − 1] – P [(1.20)2 −1] = 482

∴   P [1.4641 – 1.44] = 482

∴   P = Rs. 20,000

Hence, option E is correct.
 
3
A man gave 50% of his savings of Rs 67,280 to his wife and divided the remaining sum between his two sons A and B of 14 and 12 years of age respectively. He divided it in such a way that each of his sons, when they attain the age of 18 years, would receive the same amount at 5% compound interest per annum. The share of B was
» Explain it
D
Total Income = 67,280

After giving 50% salary to his wife the man is left with an amount = 33,640

Let's assume the man gave Rs. x to A. Therefore B will get Rs. (33640 – x).

  33640  
14 years A   12 years B
x (33640 – x)

Now, as per the question A & B will be getting an equal amount with CI at 5% rate per year at the 18th year.
 
⇒  x ( 1 +  5 ) 4   = (33640 – x) [ 1+  5 ] 6
100   100  


⇒   
x
(33640 – x)
  =  
( 1 +  5 ) 6
100  
 
( 1 +  5 ) 4
100  

⇒    x    =    ( 21  ×  21 )
(33640 – x) 20 20

⇒ 400 x = 33640 × 441 – 441x

⇒ 841x = 33640 × 441
 
x =  33640 × 441  = 40 × 441 = 17640/-
841

Therefore, at the time of divison of money, B would have got a sum = (33640 – 17640) = Rs. 16000 

Hence, option D is correct.
4
Aditya and Bhushan invested 10000 each in scheme A and scheme B respectively for 3 years. Scheme A offers Simple interest @ 12% per annum and scheme B offers compound interest @ 10%. After 3 years, who will have larger amount and by how much? 
» Explain it
C
Lets first calculate the total rate % that Aditya will have after 3 years:

As per the question Aditya invested at rate of 12% pa simple interst

So, for 3 years tenure he will get = 12 × 3 = 36%

And the amount that Bhushan invested at rate of 10% pa compound interest

By net% effect formula, we can calculate the total perecntage for 3 years tenure = 33.1% (sub details)

So, the difference between SI and CI = 36% – 33.1% = 2.9% (SI is more)

Here Aditya will get, 2.9% of 10000 = 290

So Aditya will have Rs. 290 more than Bhushan.

---------------------------------------------------------------------------------
Sub-details:-

Net% effect = x + y =  xy %
100

For the first 2 years: Here, x = y = 10%
 
= 10 + 10 =  10 × 10  = 21%
100

And for the next year: Here x = 21% and y = 10%
= 21 + 10 =  21 × 10  = 33.1%
100

Hence, option C is correct.

5
A sum of Rs. 9960 was borrowed at 15/2% per annum compound interest and paid back in two years in two equal annual installments. What was the amount of each installment?
» Explain it
B
Let the each instalment be x.

x  +    x      = 9960
( 1 +  15 ) ( 1 +  15 ) 2
2 × 100   2 × 100    

x  +    x      = 9960
( 1 +  3 ) ( 1 +  3 ) 2
40   40    

⇒   40 x  +  1600 x  = 9960
43 1849

⇒   1720 x + 1600 x  = 9960
1849
⇒  3320 x = 9960 × 1849 ⇒  x = Rs. 5547

Hence, option B is correct.