 # S.I. & C.I. (15)

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%

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(R/100)^106.09
100(R/100)^106.09
100(R/100106.09
100 106.09
R=106.09100 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

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

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)/
=> 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

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 = (11/10)^21
But Given That CI = Rs. 525
=> (11/10)525
=> P[ (121/100) − 1525
=> P (21/100) 525
=>P = 2500
SI on Rs.2500 for 4 years at 5% = (PRT)/100 = (2500×5×4)/100
=> 25×5×25×20 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