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Directions: Study the following questions carefully and answer them:
1
A sum of money doubles itself at compound interest in 5 years. In how many years will it become eight times?
» Explain it
D
P ( 1 +  R ) 5   = 2P  ⇒ 
  ( 1 +  R ) 5   =  2P   = 2           ...(i)
100   P
100  

Let P ( 1 +  R ) n  = 8P
100  

⇒ 
  ( 1 +  R ) n  = 8 = 23 = 
100  
{( 1 +  R ) 5 } 3           [using (i)]
100            

⇒  ( 1 +  R ) n   =  ( 1 +  R ) 15  ⇒ n = 15.
100   100  

Thus, the required time = 15 years.

Hence, option D is correct.

2
What annual payment will discharge a debt of Rs. 7620 due in 3 years at 50/3% per annum compound interest?
» Explain it
A
So,  x  +  x  +  x  = 7620
( 1 +  50 ) ( 1 +  50 ) 2 ( 1 +  50 ) 3
  3 × 100   3 × 100     3 × 100    

⇒  294x + 252x + 216x = 7620 × 343
 
⇒  x =  ( 7620 × 343 ) = 3430.
762

So, Amount of each installment = Rs. 3430.

Hence, option A is correct.

3
In a factory the production of cement rose 4840 tonnes from 4000 tonnes in two years. Find the rate of growth per annum.
» Explain it
A
4840 = 4000  ( 1 +  R ) 2
100  

121  =  ( 1 +  R ) 2
100 100  

( 11 ) 2  =  ( 1 +  R ) 2
10   100  

⇒  ( 1 +  10 )  =  ( 1 +  R )  ⇒ R = 10.
100 100

Hence, option A is correct.

4
Amit borrowed Rs. 20,000 from his friend at 15% per annum simple interest he lent it to Tarun at the same but rate compounded annually. Find his gain after 2 years.
» Explain it
C
Method I:

As we all know,

S.I. and C.I. for 1st year is the same.

for second year C.I. = R% of S.I. + S.I.

By this,
Gain of Amit = C.I. of 2 years - S.I. of 2 years.

⇒ S.I. (of 1st year) + (S.I. + R% of S.I.) - 2 S.I.

⇒ R% of S.I.

As S.I. for each year is the same

So, gain =  15  ×  20,000 × 15 × 1  ⇒ 15 × 15 × 2 ⇒ Rs. 450.
100 100
__________________________________________________________

Method II:

SI for 2 year at the rate of 15% = 15 × 2 = 30%

CI for 2 year at the rate of 15%, applying the net% effect for 2 years

= 15 + 15 +  15 × 15  = 32.25%
100

Amit's gain % = 32.25% – 30% = 2.25%

So, Total gain of Amit = 2.25% of 20,000 =  2.25 × 20,000  = 450
100

Hence, option C is correct.

5
Akash borrowed Rs. 72,000 from a bank to purchase one bike. If the rate of interest be 10% per annum compounded annually, what payment he will have to make after 2 years 4 months?
» Explain it
D
Method I:

Principal amount → Rs. 72,000

Rate → 10%

Time =  ( 2 +  1 ) years.
3

A = P ( 1 +  R ) 7/3
100  

A = 72000 ( 1 +  10 ) 7/3
100  

A = 72000 ( 11 ) 2  ×  ( 1 +  10 )
10   3×100

A = 72000 ( 121  ×  31 )
100 30

A = 90,024.
_______________________________________________

Method II:

CI for 2 yr 4 months at the rate of 10, applying the net% effect for first 2 years

= 10 + 10 +  10 × 10  = 21%
100

Rate of interest of 4 months = 4 × 10 ≈ 3.3%
12

For next 4 months = 21 + 3.3 +  21 × 3.3  = 24.99% ≈ 25%
100

Here, we can see that in 2yr 4 months the given compound rate of interest is approximate 25%.

Now, 125% of 72000 =  125 × 72000  = 90,000 ≈ 90,024
100

Hence, option D is correct.