Directions: Study the following questions carefully and answer them:
Important for :
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.