1. What is the difference between the compound interests on Rs. 5000 for 1^{1}⁄_{2} years at 4% per annum compounded yearly and half-yearly?

1. Rs. 2.04

2. Rs. 4.80

3. Rs. 3.06

4. Rs. 8.30

Answer & Explanation

Answer:- 1

Explanation :-

P = 5000 R = 4% T= 3/2

A (Compounded yearly)

=> [5000*(1+4/100)(1+1/2*4/100)]
=> Rs. 5304

A (Compounded Half yearly)

=> 5000(1+2/100)^3

=> 5306.04

Difference = Rs. (5306.04 – 5304) = Rs. 2.04

2. A bank offers 5% compound interest calculated on half-yearly basis. A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is:

1. Rs. 120

2. Rs. 121

3. Rs. 123

4. Rs. 122

Answer & Explanation

Answer:- 2

Explanation :-

OR

He deposited 1600 from Jan to Dec two times on half yearly basis i.e 5/2 = 2.5%

So 2.5% of 1600 = 40

Therefore next time 1600+40 = 1640. 2.5% of 1640 = 41

Next amount he deposited from July – Dec

Therefore 2.5% of 1600 = 40

So total interest earn at the end of the year is 40+41+40 = 121

3. There is 80% increase in an amount in 8 years at simple interest. What will be the compound interest of Rs. 14,000 after 3 years at the same rate?

1. Rs.3794

2. Rs.3714

3. Rs.4612

4. Rs.4634

Answer & Explanation

Answer:- 4

Explanation :-

Let P = Rs.100 Therefore , SI = Rs. 80

R = (80*100)/(100*8) = 10%

P = Rs.14000 , T = 3 years , R = 10%

Amount = P(1+R/100)^T=14000(1+10/100)^3

Amount = 14000(11/10)^3 = Rs.18634

CI = A – P = 18634 – 14000 = Rs.4634

4. The compound interest on Rs. 30,000 at 7% per annum is Rs. 4347. The period (in years) is:

1. 1

2. 2

3. 3

4. 3.5

Answer & Explanation

Answer:- 2

Explanation :-

Let the time be T years

Amount = 30000 + 4347 = Rs. 34347

P(1+R/100)^T = 34347

30000(1+7/100)^T = 34347

30000(107100)^T = 34347

(107/100)n = 34347/30000 = 11449/10000 = (107100)^2

Therefore T = 2 years

5. The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum is:

1. Rs.600

2. Rs.645

3. Rs.525

4. Rs.625

Answer & Explanation

Answer:- 4

Explanation :-

Let the sum be Rs.x

Compound Interest = [x(1+(4/100))^2 ] – x

CI = [ x (1 + (4/100)) ^2 ] − x = x [ ( 104/100 ) ^2 −1]

CI = x [(26/25)^2−1] = x [51/625] = (51x)/625

SI = (P*R*T)/100=( x × 4 × 2 )/100 = (2x)/25

Difference between CI & SI = Re 1.

=> (51x/625)−(2x/25) = 1

=> (51x−50x)/625 = 1

x = Rs. 625