# S.I. & C.I. (14)

1. The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?
1. 9%
2. 12%
3. 8%
4. 6%

Explanation :-

Let  the Rate of Interest be R%
Compound Interest (CI) = [15000(1+R/100)^2]15000 15000[(1+R/100)^21]
Simple Interest (SI) = PRT/100=(15000×R×2)/100 300R
Difference between CI & SI = {15000[(1+R/100)^21] } − 300R 96
15000[1+(2R/100) (R/100)^21− 300R 96
15000 [(2R/100) (R/100)^2− 300R 96
300+ [15000(R/100)^2] − 300R 96
[15000(R/100)^2 ] 96
15000[ (R^2)/10000] 96
3[(R^2)/2] 96
R^64
8

2. If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 60, what is the compound interest on the same at the same rate and for the same time?
1. Rs. 63.5
2. Rs. 62
3. Rs. 61.5
4. Rs. 64

Explanation :-

P = (100×SI)/(RT) 100 × 60× Rs. 600
CI = P(1+R/100)^T = 600(1+5/100)^2 = 600[ (105/100) ] ^ 2
CI = (600×105×105)/(100×100) = Rs. 661.5
Compound Interest = 661.5 – 600 = Rs. 61.5

3. The difference between simple interest and compound on Rs. 900 for one year at 10% per annum reckoned half-yearly is:
1. Rs. 3
2. Rs. 2.25
3. Rs. 4.5
4. Rs. 4

Explanation :-

Simple Interest = (PRT/100) = (900×10×1)/100 = Rs. 90
P(1+(R/200)^2T 900(1+[10/200)^(2×1)]
=> 900(1+5/100)^2 = 900(105/100)^2
=> (900×105×105) / (100×100) = Rs. 992.25
Compound Interest = 992.25 – 900 = 92.25
Difference between SI and CI = 92.25 – 90 = Rs.2.25

4. What will be the compound interest on a sum of Rs. 40,000 after 3 years at the rate of 11 p.c.p.a.?
1. Rs. 14705.24
2. Rs. 14602.25
3. Rs. 14822.26
4. Rs. 14322.10

Explanation :-

Amount after 3 years = (1+R/100)^T=40000 (1+11/100) ^3
Amount = 40000(111/100)^= (40000×111×111×111)/(100×100×100) 54705.24
Compound Interest = 54705.24 – 40000 = Rs. 14705.24

5. At what rate of compound interest per annum will a sum of Rs. 1400 become Rs. 1573.04 in 2 years?
1. 4%
2. 5%
3. 6%
4. 8%