# S.I. & C.I. (23)

1. A man saves Rs 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
1. Rs 662
2. Rs 662.01
3. Rs 662.02
4. Rs 662.03
5. None of these

Explanation :-

Money to be lent (For 1st year)= Rs. 200
Therefore,  Interest (for 1st year) = 5% of 200 = Rs.10
Money to be lent (for 2nd year) = 200 + 210 = Rs. 410
Therefore,  Interest (for 2nd year) = 5% of 410 = Rs. 20.5
Money to be lent (for 3rd year) = 410 + 200 + 20.5 = Rs. 630.5
Therefore , Interest (for 3rd year) = 5% of 630.5 = Rs. 31.525
Therefore, Total Amount = 630.5 + 31.525 =Rs. 662.025

2. Find the compound interest on Rs.16,000 at 20% per annum for 9 months, compounded quarterly
1. Rs 2520
2. Rs 2521
3. Rs 2522
4. Rs 2523
5. None of these

Explanation :-

P = Rs. 16000,  T = 9 months = 3 quarters;
Rate = 20% p.a. = (20/4) per quarter = 5% per quarter.
Amount = Rs. [16000 x (1 + (5/100)) ^3] = Rs. 18522.

3. At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years
1. 3%
2. 4%
3. 5%
4. 6%
5. None of these

Explanation :-

Let the rate of interest be R%
P = 1200,    T = 2 years
Amount = 1348.32
1200 (1+R/100) ^ 2 = 1348.32
(1+R/100) ^2 = 1348.32/1200
(1+R/100)^2 = 134832/120000
(1+R/100)^2 = 2809/2500
(1+R/100) = 53/50
R/100 = (53/50) – 1 = 3/50
R = 6%

4. Simple interest on a certain sum of money for 3 years at 8% per annum is half the compound interest on Rs. 4000 for 2 years at 10% per annum. The sum placed on simple interest is
1. Rs 1650
2. Rs 1750
3. Rs 1850
4. Rs 1950
5. None of these

Explanation :-

C.I.=[4000×(1+10/100)^2 ] − 4000 = [4000∗(11/10)∗(11/10)] − 4000 =Rs. 840
So  S.I. = 840/= Rs. 420
So Sum = (S.I.100)/(RT) = (420100)/(38) Rs.1750

5. What will be the difference between simple and compound interest @ 10% per annum on the sum of Rs 1000 after 4 years
1. Rs 62.10
2. Rs 63.10
3. Rs 64.10
4. Rs 65.10
5. None of these