1. The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:

1. 6.07%

2. 6.08%

3. 6.06%

4. 6.09%

Answer:- 4

Explanation :-

Let principal , be Rs.100

Amount after 1 year on Rs.100 at 6% per annum when interest is compounded half-yearly

=> P [1+(R/200)]^2T = 100[1+(6/200) ) ]^(2×1)

=> 100(1+3/100)^2 => 100(103/100)^2

=> (100×103×103) / (100×100)

=> 103×103/100 = Rs. 106.09

Rate of interest on which Rs.100 becomes Rs.106.09 after 1 year

when the interest is compounded annually

Let R be the rate of interest

P(1 + R/100)^T = 106.09

100(1 + R/100)^1 = 106.09

100(1 + R/100) = 106.09

100 + R = 106.09

R=106.09−100 = 6.09%

2. Arun invested an amount of Rs. 20000 in a fixed deposit scheme for 2 years at compound interest rate 4 p.c.p.a. How much amount will Arun get on maturity of the fixed deposit?

1. 20342

2. 21632

3. 22324

4. 24120

Answer & Explanation

Answer:- 2

Explanation :-

Amount after 2 years = P(1+R/100)^T

= 20000(1+4/100)^2

= 20000(104/100)^2

= (20000×104×104) / (100×100)

= 2×104×104 = Rs. 21632

3. Simple interest on a certain sum of money for 4 years at 5% per annum is half the compound interest on Rs. 3000 for 2 years at 10% per annum. The sum placed on simple interest is:

1. Rs.1575

2. Rs. 2200

3. Rs. 1200

4. Rs. 1625

Answer & Explanation

Answer:- 1

Explanation :-

Amount after 2 year on Rs.3000 at 10% .a. (compounded annually)

P(1+R/100)^T

=> 3000(1+10100)^2

=> 3000(110/100)^2

=> 3000×110×110)/(100×100) = 3×11×110 = 3630

CI = 3630 – 3000 = Rs.630

As SI on a certain sum of money for 4 years at 5% per annum is half of the CI

SI = 630/2 = Rs.315

P=(100×SI)/RT = (100×315)/(5×4) = (20×315)/4

=> 5×315 = Rs. 1575

4. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is:

1. Rs. 500

2. Rs. 400

3. Rs. 450

4. Rs. 600

Answer & Explanation

Answer:- 1

Explanation :-

Lets suppose the sum be Rs. P.

CI after 2 years at 10% p.a. (compounded annually) = [P(1+R/100)^T] – P

CI = [ P(1+10/100)^2 ] – P = [ P(110/100)^2 ] – P = P [ (11/10)^2−1]

But Given That CI = Rs. 525

=> P [ (11/10)2 −1 ] = 525

=> P[ (121/100) − 1] = 525

=> P (21/100) = 525

=>P = 2500

SI on Rs.2500 for 4 years at 5% = (PRT)/100 = (2500×5×4)/100

=> 25×5×4 = 25×20 = Rs. 500

5. The difference between simple interest and compound on Rs. 2400 for one year at 10% per annum reckoned half-yearly is:

1. Rs. 4

2. Rs. 6

3. Rs. 3

4. Rs. 2

Answer & Explanation

Answer:- 2

Explanation :-

Amount = P(1+(R/200)^2T = 2400[1+(10/200)]^(2×1)

Amount = 2400(1+5/100)^2 = 2400(105/100)2

Amount = (2400×105×105)/(100×100) = Rs. 2646

CI = 2646 – 2400 = Rs. 246

Simple Interest on Rs.2400 at 10% per annum for 1 year = (PRT)/100

SI = (2400×10×1)/100 = Rs. 240

CI -SI = 246 – 240 = Rs.6